Two-dimensional Phase Research Articles

Simulation Study of The Jerk System Based on Multisim

Make an equivalent transformation of the equations of state for a class of Jerk systems, its chaotic dynamics behavior was analyzed. According to the equation of state, the schematic diagram of the chaotic circuit of the Jerk system was designed, and the Jerk circuit was simulated and experimented with Multisim software, and the corresponding two-dimensional phase diagram and time domain waveform diagram appeared, which explained the feasibility of simulating the chaotic circuit with Multisim, and was an effective experimental tool for studying and exploring the chaotic circuit.

Phase field model of microstructure formation during cooling slope slurry generation of novel Al-15Mg2Si-4.5Si composite

The present study discusses the development of a two-dimensional phase field model of semi solid microstructure evolution of the novel Al-15Mg2Si-4.5Si composite during cooling slope rheoprocessing. The superheated melt of the said composite undergoes partial solidification during its shear flow over the slope free surface, prior to get collected within the isothermal slurry holding furnace. Seed undercooling based nucleation model is adopted in the present PF model to simulate slurry microstructure of the composite. Experimentally determined cooling rate values are considered to simulate slurry microstructure for different process conditions. Micrographs of melt samples collected during experimentation establishes the developed PF model as an accurate microstructure prediction tool for the composite slurry. Apart from morphological features such as size and degree of sphericity values of the evolving primary Mg2Si and α-Al grains, the model predictions includes melt temperature as well as solid content at any given instant of slurry processing.

Fault Diagnostics and Faulty Pattern Analysis of High-Speed Roller Bearings Using Deep Convolutional Neural Network

Abstract In this article, vibration-based fault diagnostics and response classification have been done for defective high-speed cylindrical bearing operating under unbalance rotor conditions. An experimental study has been performed to capture the vibration signature of faulty bearings in the time domain and for different speeds of the unbalanced rotor. Two-dimensional phase trajectories are generated by estimating the time delay and embedding dimension corresponding to vibration signatures. Qualitative analysis involves the implementation of a deep convolutional neural network (DCNN) utilizing the phase portraits as input to classify the nonlinear vibration responses. Comparison with the state-of-art classifiers such as artificial neural network (ANN), deep neural network (DNN), and k-nearest neighbor (KNN) is presented based on classification accuracy values. Thus, the values obtained are 61%, 67%, 72%, and 99% for ANN, DNN, KNN, and DCNN, respectively. Hence, the proposed intelligent classification model accurately identifies the dynamic behavior of bearing under unbalanced rotor conditions.

Chaotic pattern, bifurcation, sensitivity and traveling wave solution of the coupled Kundu–Mukherjee–Naskar equation

In this paper, the coupled Kundu–Mukherjee–Naskar equation is considered, which is usually used to describe the oceanic rogue waves, hole waves and Bragg grating fibers. Firstly, the traveling wave transformation is applied to convert the coupled Kundu–Mukherjee–Naskar equation into two-dimensional planar dynamic system. Secondly, bifurcation and two-dimensional phase portrait of the coupled Kundu–Mukherjee–Naskar equation are discussed by using the plane dynamics system. What is more, after adding periodic perturbation term, two-dimensional phase portrait, three-dimensional phase portrait, Poincaré section and sensitivity of its perturbed system are plotted by the Maple software. Finally, the optical soliton solutions of the coupled Kundu–Mukherjee–Naskar equation are obtained by using planar dynamical system method.

Dynamical behavior of analytical soliton solutions, bifurcation analysis, and quasi-periodic solution to the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) system

Nonlinear evolution equations (NLEEs) are extensively used to establish the elementary propositions of natural circumstances. In this work, we study the Konopelchenko–Dubrovsky (KD) equation which depicts non-linear waves in mathematical physics with weak dispersion. The considered model is investigated using the combination of generalized exponential rational function (GERF) method and dynamical system method. The GERF method is utilized to generate closed-form invariant solutions to the (2+1)-dimensional KD model in terms of trigonometric, hyperbolic, and exponential forms with the assistance of symbolic computations. Moreover, 3D, 2D combined line graph and their contour graphics are displayed to depict the behavior of obtained solitary wave solutions. The model is observed to have multiple soliton profiles, kink-wave profiles, and periodic oscillating nonlinear waves. These generated solutions have never been published in the literature. All the newly generated soliton solutions are checked by putting them back into the associated system with the soft computation via Wolfram Mathematica. Moreover, the system is converted into a planer dynamical system using a certain transformation and the analysis of bifurcation is examined. Furthermore, the quasi-periodic solution is investigated numerically for the perturbed system by inserting definite periodic forces into the considered model. With regard to the parameter of the perturbed model, two-dimensional and three-dimensional phase portraits are plotted.

Induced superconductivity in the two-dimensional topological insulator phase of cadmium arsenide

Hybrid structures between conventional, s-wave superconductors, and two-dimensional topological insulators (2D TIs) are a promising route to topological superconductivity. Here, we investigate planar Josephson junctions fabricated from hybrid structures that use thin films of cadmium arsenide (Cd3As2) as the 2D TI material. Measurements of superconducting interference patterns in a perpendicular magnetic field are used to extract information about the spatial distribution of the supercurrent. We show that the interference patterns are distinctly different in junctions with and without mesa-isolation. In mesa-defined junctions, the bulk of the 2D TI appears to be almost completely shunted by supercurrent flowing along the edges, whereas the supercurrent is much more uniform across the junction when the Cd3As2 film extends beyond the device. We discuss the possible origins of the observed behaviors.

Universal early warning signals of phase transitions in climate systems.

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modelling techniques is quite difficult. This has led to the development of an alternative suite of methods that seek to identify signatures of critical phenomena in data, which are expected to occur in advance of many classes of dynamical bifurcation. Crucially, the manifestations of these critical phenomena are generic across a variety of systems, meaning that data-intensive deep learning methods can be trained on (abundant) synthetic data and plausibly prove effective when transferred to (more limited) empirical datasets. This paper provides a proof of concept for this approach as applied to lattice phase transitions: a deep neural network trained exclusively on two-dimensional Ising model phase transitions is tested on a number of real and simulated climate systems with considerable success. Its accuracy frequently surpasses that of conventional statistical indicators, with performance shown to be consistently improved by the inclusion of spatial indicators. Tools such as this may offer valuable insight into climate tipping events, as remote sensing measurements provide increasingly abundant data on complex geospatially resolved Earth systems.

Atomic-thick metastable phase RhMo nanosheets for hydrogen oxidation catalysis

Metastable phase two-dimensional catalysts provide great flexibility for modifying their chemical, physical, and electronic properties. However, the synthesis of ultrathin metastable phase two-dimensional metallic nanomaterials is highly challenging, mainly due to the anisotropic nature of metallic materials and their thermodynamically unstable ground-state. Here, we report free-standing RhMo nanosheets with atomic thickness and a unique core/shell (metastable phase/stable phase) structure. The polymorphic interface between the core region and shell region stabilizes and activates metastable phase catalysts; the RhMo Nanosheets/C shows excellent hydrogen oxidation activity and stability. Specifically, the mass activities of RhMo Nanosheets/C is 6.96 A mgRh−1; this is 21.09 times higher than that of commercial Pt/C (0.33 A mgPt−1). Density functional theory calculations suggest that the interface aids in the dissociation of H2 and the H species can then spillover to weak H binding sites for desorption, providing excellent hydrogen oxidation activity for RhMo nanosheets. This work advances the highly controlled synthesis of two-dimensional metastable phase noble metals and provides great directions for the design of high-performance catalysts for fuel cells and beyond.

Modeling the Transition between Localized and Extended Deposition in Flow Networks through Packings of Glass Beads

We use a theoretical model to explore how fluid dynamics, in particular, the pressure gradient and wall shear stress in a channel, affect the deposition of particles flowing in a microfluidic network. Experiments on transport of colloidal particles in pressure-driven systems of packed beads have shown that at lower pressure drop, particles deposit locally at the inlet, while at higher pressure drop, they deposit uniformly along the direction of flow. We develop a mathematical model and use agent-based simulations to capture these essential qualitative features observed in experiments. We explore the deposition profile over a two-dimensional phase diagram defined in terms of the pressure and shear stress threshold, and show that two distinct phases exist. We explain this apparent phase transition by drawing an analogy to simple one-dimensional mass-aggregation models in which the phase transition is calculated analytically.

Chaotic pattern, phase portrait, sensitivity and optical soliton solutions of coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion in birefringent fibers

In this paper, coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion is introduced, which is usually used to simulate the propagation model of pulses’ temporal evolution in birefringent fibers. Firstly, the traveling wave transformation is applied to convert the conformable time–space fractional Fokas-Lenells model into two-dimensional planar dynamic system. Secondly, the qualitative analysis of the coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion is discussed by using the plane dynamics system. Moreover, two-dimensional phase portraits, three-dimensional phase portraits, Poincaré sections and sensitivity analysis of its perturbed system are drawn by using the Maple mathematical software. Finally, the optical soliton solutions of the coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion are obtained by using planar dynamical system method.

Spatiotemporal Mapping of Hole Nucleation and Growth during Block Copolymer Terracing with High-Speed Atomic Force Microscopy.

As a platform for investigating two-dimensional phase separation, we track the structural evolution of block copolymer thin films during thermal annealing with environmentally controlled atomic force microscopy (AFM). Upon thermal annealing, block copolymer films with incommensurate thickness separate into a terraced morphology decorated with holes. With in situ imaging at 200 °C, we follow the continuous progression of terrace formation in a single region of a cylinder-forming poly(styrene-block-methyl methacrylate) thin film, beginning with the disordered morphology on an unpatterned silicon substrate and continuing through nucleation and coarsening stages. Topographic AFM imaging with nanoscale resolution simultaneously captures ensemble hole growth statistics while locally tracking polymer diffusion through measurements of the film thickness. At early times, we observe homogeneous hole nucleation and isotropic growth, with kinetics following the predictions of classical nucleation theory. At later times, however, we find anomalous hole growth which arises due to the combination of Ostwald ripening and coalescence mechanisms. In each case, our real-space observations highlight the importance of hole interactions for determining coarsening kinetics, mediated either through the interconnected phase for Ostwald ripening or through binary collision events for coalescence.

Emergent Edge Modes in Shifted Quasi-One-Dimensional Charge Density Waves.

We propose and study a two-dimensional phase of shifted charge density waves (CDW), which is constructed from an array of weakly coupled 1D CDW wires whose phases shift from one wire to the next. We show that the fully gapped bulk CDW has topological properties, characterized by a nonzero Chern number, that imply edge modes within the bulk gap. Remarkably, these edge modes exhibit spectral pseudoflow as a function of position along the edge, and are thus dual to the chiral edge modes of Chern insulators with their spectral flow in momentum space. Furthermore, we show that the CDW edge modes are stable against interwire coupling. Our predictions can be tested experimentally in quasi-1D CDW compounds such as Ta_{2}Se_{8}I.

Two-dimensional phase unwrapping based on Fourier transforms and the Yukawa potential spectrum.

The two-dimensional phase unwrapping problem (PHUP) has been solved with discrete Fourier transforms (FTs) and many other techniques traditionally. Nevertheless, a formal way of solving the continuous Poisson equation for the PHUP, with the use of continuous FT and based on distribution theory, has not been reported yet, to our knowledge. The well-known specific solution of this equation is given in general by a convolution of a continuous Laplacian estimate with a particular Green function, whose FT does not exist mathematically. However, an alternative Green function called the Yukawa potential, with a guaranteed Fourier spectrum, can be considered for solving an approximated Poisson equation, inducing a standard procedure of a FT-based unwrapping algorithm. Thus, the general steps for this approach are described in this work by considering some reconstructions with synthetic and real data.

Development of an On-Line Two-dimensional Normal Phase Liquid Chromatography System for Analysis of Weakly Polar Samples

In this study, a novel on-line two-dimensional (2D) normal phase × normal phase liquid chromatography (NPLC × NPLC) was developed for the separation of weakly polar samples. The 2D NPLC was integrated by a unique designed solvent evaporation (SE) interface, including a 6-port 2-position valve and a 10-port 2-position valve in conjunction with two silica gel-packed enrichment columns. The enrichment columns played a pivotal role in evaporating normal phase (NP) solvent from the first dimensional NPLC under vacuum and elevated temperature condition. The working parameters of the interface were evaluated comprehensively. To demonstrate the resolving powerful 2D system, we analyzed three natural-sourced weakly polar compounds from the extracts of toad venom, dammar resin, and propolis. To this end, we studied the effects of mobile phase combinations, the second dimensional column length for separation of the extracts from toad venom, and propolis, respectively. In general, we have found that excellent separation can be obtained with diversity of NP solvent combinations and longer NPLC column (150 mm long). Moreover, compared with the generally used 2D reversed-phase liquid chromatography (RPLC × RPLC), the NPLC × NPLC method exhibited better separation orthogonality. In conclusion, the new NPLC × NPLC separation method provides potential advantages for analysis of weakly polar samples.

Biomechanical Behaviors and Degradation Properties of Multilayered Polymer Scaffolds: The Phase Space Method for Bile Duct Design and Bioengineering.

This article reports the electrospinning technique for the manufacturing of multilayered scaffolds for bile duct tissue engineering based on an inner layer of polycaprolactone (PCL) and an outer layer either of a copolymer of D,L-lactide and glycolide (PLGA) or a copolymer of L-lactide and ε-caprolactone (PLCL). A study of the degradation properties of separate polymers showed that flat PCL samples exhibited the highest resistance to hydrolysis in comparison with PLGA and PLCL. Irrespective of the liquid-phase nature, no significant mass loss of PCL samples was found in 140 days of incubation. The PLCL- and PLGA-based flat samples were more prone to hydrolysis within the same period of time, which was confirmed by the increased loss of mass and a significant reduction of weight-average molecular mass. The study of the mechanical properties of developed multi-layered tubular scaffolds revealed that their strength in the longitudinal and transverse directions was comparable with the values measured for a decellularized bile duct. The strength of three-layered scaffolds declined significantly because of the active degradation of the outer layer made of PLGA. The strength of scaffolds with the PLCL outer layer deteriorated much less with time, both in the axial (p-value = 0.0016) and radial (p-value = 0.0022) directions. A novel method for assessment of the physiological relevance of synthetic scaffolds was developed and named the phase space approach for assessment of physiological relevance. Two-dimensional phase space (elongation modulus and tensile strength) was used for the assessment and visualization of the physiological relevance of scaffolds for bile duct bioengineering. In conclusion, the design of scaffolds for the creation of physiologically relevant tissue-engineered bile ducts should be based not only on biodegradation properties but also on the biomechanical time-related behavior of various compositions of polymers and copolymers.

A Parallel InSAR Phase Unwrapping Method Based on Separated Continuous Regions

Phase unwrapping is an imperative step in interferometry processing that has a significant influence on the quality of subsequent products. Many existing phase unwrapping algorithms have been designed to solve for the unwrapped phase under the assumption that noisy areas with discontinuities are small or that reliable continuity can be recovered there. They attempt to restore the unwrapped phase by using continuity and data quality measures, such as residues. However, when the observing field is divided into separate zones of continuous phase due to a large range of noise, such as those caused by rivers or mountains, it is difficult to use traditional phase unwrapping techniques to recover global continuity in these noisy areas. To address this challenge, we present a two-dimensional parallel phase unwrapping method that is designed to handle cases where the continuity of the phase is separated by closed noisy loops. Based on continuity distances, this method aims to identify continuous regions that are free of hidden phase discontinuities and restore phase continuity between the separated regions. A heterogeneous residual diffusion scheme is used to restore the unwrapped phase outside continuous regions. The parallel algorithm for extracting continuous regions, restoring continuity between the regions, and diffusing residuals was implemented on a GPU device to increase the processing efficiency. We applied our method to typical TanDEM-X data covering rivers, islands, and mountains and demonstrated that it is a promising solution for large-scale, heavily noisy phase unwrapping problems.

Extended analytical solutions of the Bohr Hamiltonian with the sextic oscillator: Pt-Os isotopes

The sextic oscillator adapted to the Bohr Hamiltonian has been used to describe even Pt and Os isotopes from A = 188 to 198 and A = 186 to 192, respectively. The purpose of this study was to investigate the possible transition from the γ-unstable to the spherical vibrator shape phases. In this setup the potential appearing in the Bohr Hamiltonian is independent from the γ shape variable, and the physical observables (energy eigenvalues, B(E2)) can be obtained in closed analytical form within the quasi-exactly solvable formalism for the model space containing 30 of the lowest-lying levels. Experimental energy levels have been associated with the theoretical ones. The available electric quadrupole transition data (B(E2), decay preferences) have been taken into account in matching the experimental and theoretical levels. Special attention has been paid to transitions from the first two excited 0+ levels to the and levels, as these indicate the change of shape phases with spherical and deformed potential minimum. The three parameters of the Hamiltonian have been determined by a weighted least square fit procedure. Trends in the location of states belonging to the ground-state, the K π = 2+ and two excited K π = 0+ bands have been analysed. The trajectory determined by the fitted parameters in the two-dimensional phase space has also been plotted, and it has been found that all the nuclei are characterized by a deformed potential minimum, except for the heaviest Pt isotope (198Pt), for which the transition to the spherical shape phase is realised. Although the spectroscopic information on the next isotopes of the chains (200Pt and 194Os) is far less complete, there are indications that these nuclei are also close to or fall within the domain of spherical potential minimum.

Quantification of the Diversity in Gene Structures Using the Principles of Polarization Mapping.

Results of computational analysis and visualization of differences in gene structures using polarization coding are presented. A two-dimensional phase screen, where each element of which corresponds to a specific basic nucleotide (adenine, cytosine, guanine, or thymine), displays the analyzed nucleotide sequence. Readout of the screen with a coherent beam characterized by a given polarization state forms a diffracted light field with a local polarization structure that is unique for the analyzed nucleotide sequence. This unique structure is described by spatial distributions of local values of the Stokes vector components. Analysis of these distributions allows the comparison of nucleotide sequences for different strains of pathogenic microorganisms and frequency analysis of the sequences. The possibilities of this polarization-based technique are illustrated by the model data obtained from a comparative analysis of the spike protein gene sequences for three different model variants (Wuhan, Delta, and Omicron) of the SARS-CoV-2 virus. Various modifications of polarization encoding and analysis of gene structures and a possibility for instrumental implementation of the proposed method are discussed.

Molten salt electrosynthesis of Cr2GeC nanoparticles as anode materials for lithium-ion batteries.

The two-dimensional MAX phases with compositional diversity are promising functional materials for electrochemical energy storage. Herein, we report the facile preparation of the Cr2GeC MAX phase from oxides/C precursors by the molten salt electrolysis method at a moderate temperature of 700°C. The electrosynthesis mechanism has been systematically investigated, and the results show that the synthesis of the Cr2GeC MAX phase involves electro-separation and in situ alloying processes. The as-prepared Cr2GeC MAX phase with a typical layered structure shows the uniform morphology of nanoparticles. As a proof of concept, Cr2GeC nanoparticles are investigated as anode materials for lithium-ion batteries, which deliver a good capacity of 177.4mAhg-1 at 0.2 C and excellent cycling performance. The lithium-storage mechanism of the Cr2GeC MAX phase has been discussed based on density functional theory (DFT) calculations. This study may provide important support and complement to the tailored electrosynthesis of MAX phases toward high-performance energy storage applications.

Ground-state bistability of cold atoms in a cavity

We experimentally demonstrate an optical bistability between two hyperfine ground states of trapped, cold atoms, using a single mode of an optical resonator in the collective strong coupling regime. Whereas in the familiar case, the bistable region is created through atomic saturation, we report an effect between states of high quantum purity, which is essential for future information storage. The source of nonlinearity is a cavity-assisted pumping between ground states of the atoms and the stability depends on the intensity of two driving lasers. We interpret the phenomenon in terms of the recent paradigm of first-order, driven-dissipative phase transitions, where the transmitted and driving fields are understood as the order and control parameters, respectively. A semiclassical mean-field theory is invoked to describe the nontrivial two-dimensional phase diagram arising from the competition of the two drive. The saturation-induced bistability is recovered for infinite drive in one of the controls. The order of the transition is confirmed experimentally by hysteresis in the order parameter when either of the two control parameters is swept repeatedly across the bistability region.