Vector Order Research Articles

Axialgravisolitons at infinite corner

Abstract Gravitational solitons (gravisolitons) are particular exact solutions of Einstein field equation in vacuum build on a given background solution. Their interpretation is not yet fully clear but they contain many of the physically relevant solutions low N-solitons solutions. 
However, a systematic study and characterization of gravisolitons solution for every N is lacking and their relevance in a theory of quantum gravity is not fully understood. This work aims to investigate and characterize some properties of N-axialsoliton solutions such as their asymptotically behaviour and asymptotic symmetries given minimal assumptions on the background metric. We develop an explicit systematic asymptotically expansion for the N-axialsoliton solution and we compute the leading order of the asymptotic killing vectors. Moreover, in the perspective to better understand the role of gravisolitons in quantum gravity we make a link, and a one of the first explicit test, to the corner symmetry proposal deriving which subalgebra of the universal corner symmetry algebra is generated by the asymptotic Killing vectors of N-axialsoliton solution. In the spirit of the corner proposal, the axialgravisoliton corner symmetry algebra (agcsa) can be useful for the quantization of the non-asymptotically flat sector of gravity while, in the spirit of IR triangle, new soft theorems and memory effects could emerge.

An Active Distribution Grid Exceedance Testing and Risk-Planning Simulation Based on Carbon Capture and Multisource Data from the Power Internet of Things

In order to achieve peak carbon and carbon neutrality targets, a high number of distributed power sources have been connected to distribution networks. How to realize the planning of a distribution network containing integrated energy under the condition of carbon capture and complete the exceedance test of the distribution network under the condition of accessing a large number of distributed generators has become an urgent problem. To solve the above problem while promoting sustainable development, this work proposes an active distribution network risk-planning model based on multisource data from carbon capture and the Power Internet of Things. The model calculates the semi-invariants of each order of the node state vectors and branch circuit current vectors and then utilizes Gram–Charlier-level expansion to obtain the exceeding probability density function and the probability distribution functions of the node voltages and line powers in the distribution network. Combined with multisource data, an active distribution network with an integrated energy system designed for carbon capture was modeled. According to the risk scenario of the distribution network, the nonconvex constraints in the model were simplified by second-order cone relaxation, and the optimal planning scheme of the distribution network was solved by combining the Gurobi solver with the risk index as the first-level objective and the economic benefit as the second-level objective. The simulation results of a coupled network consisting of a 39-node distribution network and an 11-node transportation network verified the effectiveness of the proposed model.

Computing Multivalued Mathematical Morphology on Multiband Images Using Algorithms for Multicriteria Analysis

Mathematical morphology (MM) is a powerful tool for spatial multispectral and hyperspectral image analyses. However, MM was originally developed for single-band images in which each pixel is represented by a numerical value. The most commonly used method for extending MM to multiband images is to process each band independently without considering its correlations with other bands. This can lead to the creation of artificial false spectral signatures and result in object misidentification. Therefore, extending MM to multiband images requires the use of an adequate vector ordering strategy to fully exploit its potential. This work proposes new vector ordering algorithms for the computation of multivalued MM. A multicriteria analysis (MCA) system is used as a tool for establishing an ordering of vectors. Two MCA approaches, namely, an "analytic hierarchy process" and a "preference ranking organization method for enrichment evaluation," are developed to define ordering relations between vectors. To ensure the validity of the proposed vector ordering algorithms, the computed multivalued morphological profiles are compared using the proposed vector ordering approaches and conventional schemes. The results of applying the proposed vector ordering algorithms for computing morphological profiles show that good classification accuracies were achieved for urban structures in ROSIS hyperspectral images.

Effects of temperature on the dynamic and static properties of a non-heisenberg anisotropic ferromagnet

In the mean-field approximation, the influence of both temperature and the value of the single-ion anisotropy constant of the “easy axis” type on the phase states and excitation spectra of a non-Heisenberg ferromagnet with S = 1 is studied. The temperature dependences of the vector and tensor order parameters in both the ferromagnetic and nematic phases have been determined. The dependence of excitation spectra on temperature and the value of the anisotropy constant is studied. It is shown that at a temperature different from zero, an additional (non-relaxation) branch of excitations arises in both the ferromagnetic and nematic phases. The temperature dependence of the phase diagram is studied.

Holographic timelike superconductor

We explore the state of matter characterized by the charged timelike vector order parameter. We employ holographic duality in order to construct such a state and study its thermoelectric transport, fermionic spectral function and the character of the Meissner effect. We uncover the unusual features of this “timelike superconductor”: the absence of the gap in the fermionic spectrum and co-existence of Drude peak and supercurrent in the AC transport, which are reminiscent to those of time-reversal-odd and gapless superconductors, correspondingly. We show that this state is dynamically stable and thermodynamically at least metastable. Along the way we develop the holographic model of the charged vector field, which acquires mass due to a variant of the Stueckelberg mechanism with the adjoint Higgs field.

Reordering method of test set based on vector eigenvalues using critical area estimation

With the continuous shrinkage of integrated circuit feature sizes, circuit design has become increasingly complex, leading to issues such as rising test complexity and inefficiency. A dynamic adjustment method of test vectors for effective transistor critical area coverage based on the internal structure of the circuit is proposed. The test quality of the test vector is measured in terms of the transistor feature size relative to the size of the circuit unit. First, this method comprehensively considers the problem of circuit complexity. The test eigenvalue of each test vector is comprehensively calculated based on the overall test results. Then, the test vectors are sorted from the highest to the lowest test quality. Furthermore, during the testing process, the order of the test vectors is dynamically adjusted according to the eigenvalues of the test vectors. This method can significantly reduce the test time for failed integrated circuits. Experiments using ISCAS 89 and ITC 99 circuits show that the test process after reordering reduces the test time by 37.98% and 36.15%, respectively. Therefore, the test efficiency of the chip is improved and the test cost is optimized.

Development of the solution search method using the population algorithm of global search optimization

The research objects are decision making support systems. subject research is a decision making process in management tasks using bio-inspired algorithms. A method of finding solutions using the population algorithm of global search optimization is proposed. Joint use of invasive weed algorithm is proposed, genetic algorithm and evolving artificial neural networks are improved. The method has the following sequence of actions: ‒ an input of initial data; ‒ processing of initial data taking into account the degree of uncertainty; ‒ formation of the optimization vector; ‒ creation of descendant vectors; ‒ ordering of vectors in descending order; ‒ reducing the dimensionality of the feature space; ‒ teaching knowledge bases. The peculiarity of the proposed method lies in the placement of agents-weeds, taking into account the uncertainty of the initial data, improved procedures for reducing the space of signs about the analysis object state. Training of synaptic weights of an artificial neural network, type and parameters of the membership function and the architecture of individual elements, and the architecture of an artificial neural network as a whole is carried out. The proposed method was simulated in the MathСad 14 software environment. The task to be solved during the simulation was to determine the route of the ships in the operational zones of the Black and Azov seas in the conditions of hybrid actions of the enemy. The use of the method makes it possible to increase the efficiency of data processing at the level of 21–27 % due to the use of additional improved procedures. The proposed method should be used to solve the problems of evaluating complex and dynamic processes in the interests of solving national security problems

Spatially segmented SVD clutter filtering in cardiac blood flow imaging with diverging waves

Ultrafast ultrasound imaging enables the visualization of rapidly changing blood flow dynamics in the chambers of the heart. Singular value decomposition (SVD) filters outperform conventional high pass clutter rejection filters for ultrafast blood flow imaging of small and shallow fields of view (e.g., functional imaging of brain activity). However, implementing SVD filters can be challenging in cardiac imaging due to the complex spatially and temporally varying tissue characteristics. To address this challenge, we describe a method that involves excluding the proximal portion of the image (near the chest wall) and divides the reduced field of view into overlapped segments, within which tissue signals are expected to be spatially and temporally coherent. SVD filtering with automatic selection of cut-off singular vector orders to remove tissue and noise signals is implemented for each segment. Auto-thresholding is based on the coherence of spatial singular vectors, delineating tissue, blood, and noise subspaces within a spatial similarity matrix calculated for each segment. Filtered blood flow signals from the segments are reconstructed and then combined and Doppler processing is used to form a set of blood flow images. Preliminary experimental results suggest that the spatially segmented approach improves the separation of the tissue and blood subsets in the spatial similarity matrix so that automatic thresholding is significantly improved, and tissue clutter can then be rejected more effectively in cardiac ultrafast imaging, compared to using the full field of view. In the case studied, spatially segmented SVD improved the rate of correct automatic selection of thresholds from 78% to 98.7% for the investigated cases and improved the post-filter power of blood signals by an average of more than 10 dB during a cardiac cycle.

A novel competitive exact approach to solve assembly line balancing problems based on lexicographic order of vectors

The assembly line balancing problem (ALBP) is an eminent NP-hard topic that is discussed in mass production systems with low diversity. Primarily, two types of ALBPs are discussed in the literature as type I, which aims to find the minimum number of workstations for a given cycle time, and type II, which assigns some tasks to a given number of workstations such that the maximum workstation load is minimized. To solve ALBPs, various exact, heuristic, and metaheuristic methods have been proposed. However, these methods lose their efficiency when handling large-size problems. Therefore, researchers have focused on proposing heuristic and metaheuristic algorithms to solve large-size problems, especially when they deal with real-life case problems in the industry. This study aims to present a novel and competitive exact method for solving ALBP type II based on the lexicographic order of vectors for feasible solutions. To evaluate the performance of the developed method, a group of highly used standard test problems in the literature is utilized, and the results are compared and discussed in detail. The computational results in this study specify that the developed solution approach performs efficiently and yields the best global solution of all the ALB test problems, which proves the proposed method's potential and its competitive advantage.

Holographic entanglement entropy probe on spontaneous symmetry breaking with vector order

We study holographic entanglement entropy in 5-dimensional charged black brane geometry obtained from Einstein-SU(2)Yang-Mills theory defined in asymptotically AdS space. This gravity system undergoes second order phase transition near its critical point, where a spatial component of the Yang-Mills fields appears, which is normalizable mode of the solution. This is known as phase transition between isotropic and anisotropic phases, where in anisotropic phase, SO(3)-isometry(spatial rotation) in bulk geometry is broken down to SO(2) by emergence of the spatial component of Yang-Mills fields, which corresponds to a vector order in dual field theory. We get analytic solutions of holographic entanglement entropies by utilizing the solution of bulk spacetime geometry given in arXiv:1109.4592, where we consider subsystems defined on AdS boundary of which shapes are wide and thin slabs and a cylinder. It turns out that the entanglement entropies near the critical point shows scaling behavior such that for both of the slabs and cylinder, {Delta}_{varepsilon }Ssim {left(1-frac{T}{T_c}right)}^{beta } and the critical exponent β = 1, where ∆εS ≡ Siso− Saniso, and Siso denotes the entanglement entropy in isotropic phase whereas Saniso denotes that in anisotropic phase. We suggest a quantity O12≡ S1− S2 as a new order parameter near the critical point, where S1 is entanglement entropy when the slab is perpendicular to the direction of the vector order whereas S2 is that when the slab is parallel to the vector order. O12 = 0 in isotropic phase but in anisotropic phase, the order parameter becomes non-zero showing the same scaling behavior. Finally, we show that even near the critical point, the first law of entanglement entropy is held. Especially, we find that the entanglement temperature for the cylinder is {mathcal{T}}_{cy}=frac{c_{textrm{ent}}}{a} , where cent = 0.163004 ± 0.000001 and a is the radius of the cylinder.

Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation

AbstractFor convenience, this study mainly focuses on the reduced order of coefficient vectors for the classical finite spectral element Crank–Nicolson (CFSECN) solutions about the two‐dimensional (2D) nonstationary Stokes problem, resulting that the reduced order model can possess the same basis functions together with same precision as the CFSECN one. To this end, the CFSECN format of the 2D nonstationary Stokes problem about vorticity function and stream function and, the existence and stability as well as error estimations for the CFSECN solutions are first proposed. Afterwards, a reduced order extrapolation finite spectral element Crank–Nicolson (ROEFSECN) model is created by means of proper orthogonal decomposition method, and the existence together with stability as well as errors of the ROEFSECN solutions is analyzed by the matrix tool, resulting that the theory analysis turns into very simple. Finally, two numerical examples are provided to confirm the correctness for the theory consequences. Therefore, the study is absolutely distinguished from the existed ones.

Влияние большой одноионной анизотропии на динамические и статические свойства негейзенберговского ферримагнетика

The influence of a large single-ion anisotropy of the “easy plane” type on the phase states and spectra of elementary excitations of a ferrimagnet with sublattices S=1 and σ=1/2 and non-Heisenberg exchange interaction for a sublattice with S=1 is studied. It is shown that for different ratios of the material parameters of the system, only one phase state is possible, characterized by both vector and tensor order parameters (quadrupole-ferrimagnetic). The condition for sublattice spin compensation is determined, as well as the behavior of the spectra of elementary excitations near the spin compensation line. In the vicinity of the spin compensation line, the magnon spectra are "antiferromagnetically similar".

Effect of large single-ion anisotropy on the dynamic and static properties of a non-heisenberg ferrimagnet

The influence of a large single-ion anisotropy of the "easy plane" type on the phase states and spectra of elementary excitations of a ferrimagnet with sublattices S = 1 and sigma=1/2 and non-Heisenberg exchange interaction for a sublattice with S = 1 is studied. It is shown that for different ratios of the material parameters of the system, only one phase state is possible, characterized by both vector and tensor order parameters (quadrupole-ferrimagnetic). The condition for sublattice spin compensation is determined, as well as the behavior of the spectra of elementary excitations near the spin compensation line. In the vicinity of the spin compensation line, the magnon spectra are "antiferromagnetically similar". Keywords: large single-ion anisotropy, biquadratic exchange interaction, ferrimagnet.

Phase-field method explored ferroelectric vortex topology structure and morphotropic phase boundaries

The perovskite crystal structure determines the appearance of ferroelectricity and the polarization direction of ferroelectric ceramics. When the polarization direction has a certain order, different domain structures will combine to form a multiparticle system with a specific morphology, i.e. the topological structure existing in ferroelectrics. In this study, the domain structures of potassium sodium niobate (<inline-formula><tex-math id="M2">\begin{document}$ {\rm{K}}_{0.5}{\rm{N}\rm{a}}_{0.5}\rm{N}\rm{b}{\rm{O}}_{3} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221898_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221898_M2.png"/></alternatives></inline-formula>) thin films under different hysteresis electric fields and thickness are simulated and observed by the phase field method. According to the different switching paths of the domain structure under the electric field, the domain is divided into fast and slow switching process. Based on this, a method is proposed to first determine the domain switching state of the desired experiment and then conduct directional observation. Through the analysis of the domain structures combined with the polarization vector, a clear multi-domain combined with vortex-antivortex pair topological structure is observed for the first time in <inline-formula><tex-math id="M3">\begin{document}$ {\rm{K}}_{0.5}{\rm{N}\rm{a}}_{0.5}\rm{N}\rm{b}{\rm{O}}_{3} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221898_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221898_M3.png"/></alternatives></inline-formula> film. The vortex structure is further analyzed for its switching process, and it is observed that this vortex topological microstructure can make the domain more likely to switch, so that more small-scale polarization vectors can be ordered, forming the desired multiparticle system topology. The mechanism of improving the dielectric properties of ferroelectric material by this polarization vector ordering is similar to that of the microscopic phase boundary formed by the specific polarization directions on both sides of the quasi morphotropic phase boundary.

Adaptive BIST for Concurrent On-Line Testing on Combinational Circuits

Safety-critical systems embedding concurrent on-line testing techniques are vulnerable to design issues causing the degradation of totally self-checking (TSC) property, which is proved to be fatal for further operations (e.g., space electronics, medical devices). In addition to the exploration of the degradation of TSC property over time, a concurrent on-line testing architecture is offered that adjusts the input activity, addressing the absence of input values or the low frequency of their appearance (e.g., during sleep mode). During concurrent on-line testing, the inputs of the circuit under test (CUT) are, at the same time, its test vectors. This architecture tolerates possible degradation of the terms that contribute to the calculation of the totally self-checking goal (TSCG(t)). An adaptive built-in self-test (BIST) unit is proposed that dynamically applies test vector subsets when permitted, based on the frequency of appearance of the input values. The clustering of the inputs is based on the k-means algorithm and, in combination with the ordering of the test vectors to minimize the subsets, results in partitioning the test procedure in a significantly shorter time. The comparison to other solutions used for concurrent on-line testing showed that the proposed adaptive BIST has significant advantages. It can cope with rare occurrences, or even no occurrence, of input values by enabling the BIST mechanism appropriately. The results showed that it may increase the TSCG(t) up to almost 90% when applied during a low-power mode and present better concurrent test latency (CTL) when assumptions regarding the availability of all input values and the probability of occurrence are not realistic.

Momentum dependent gap in holographic superconductors revisited

We reconsider the angular dependence in gap structure of holographic superconductors, which has not been treated carefully so far. For the vector field model, we show that the normalizable ground state is in the p-wave state because s-wave state is not normalizable. On the other hand, in the scalar order model, the ground state is in the s-wave. The angle dependent gap function is explicitly constructed in these models. We also suggest the modified ansatz of the vector order which enables to discuss the order px ± ipy gap. We have also analytically investigated the critical temperature and the behavior of the gap near there. Interestingly, for the fixed conformal dimension of the Cooper pair operator, the critical temperature in vector model is higher than that of the scalar model.

Vector formalism for active nematic liquid crystals in two dimensions.

Specific features of two-dimensional nematodynamics give rise to shortfalls of the tensor representation of the nematic order parameter commonly used in computations, especially in theory of active matter. The alternative representation in terms of the vector order parameter follows with small adjustments the classical director-based theory, but is applicable to 2D problems where both nematic alignment and deviation from the isotropic state are variable. Stability analysis of nematic alignment and flow is used as a testing ground. A director-based analysis demonstrates a shortfall of the standard theory, which does not ensure relaxation to equilibrium in a passive system. It also demonstrates the inadequacy of the director-based description, which misses a stabilizing effect of perturbations of the modulus ensuring stability of a passive system on scales far exceeding the healing length.

Generation and Computational Characterization of a Complex Staphylococcus aureus Lipid Bilayer.

Studies indicate a crucial cell membrane role in the antibiotic resistance of Staphylococcus aureus. To simulate its membrane structure and dynamics, a complex molecular-scale computational representation of the S. aureus lipid bilayer was developed. Phospholipid types and their amounts were optimized by reverse Monte Carlo to represent characterization data from the literature, leading to 19 different phospholipid types that combine three headgroups [phosphatidylglycerol, lysyl-phosphatidylglycerol (LPG), and cardiolipin] and 10 tails, including iso- and anteiso-branched saturated chains. The averaged lipid bilayer thickness was 36.7 Å, and area per headgroup was 67.8 Å2. Phosphorus and nitrogen density profiles showed that LPG headgroups tended to be bent and oriented more parallel to the bilayer plane. The water density profile showed that small amounts reached the membrane center. Carbon density profiles indicated hydrophobic interactions for all lipids in the middle of the bilayer. Bond vector order parameters along each tail demonstrated different C-H ordering even within distinct lipids of the same type; however, all tails followed similar trends in average order parameter. These complex simulations further revealed bilayer insights beyond those attainable with monodisperse, unbranched lipids. Longer tails often extended into the opposite leaflet. Carbon at and beyond a branch showed significantly decreased ordering compared to carbon in unbranched tails; this feature arose in every branched lipid. Diverse tail lengths distributed these disordered methyl groups throughout the middle third of the bilayer. Distributions in mobility and ordering reveal diverse properties that cannot be obtained with monodisperse lipids.

Nonlocal Problem with Impulsive Action for Parabolic Equations of the Vector Order

Nonlocal Problem with Impulsive Action for Parabolic Equations of the Vector Order

Anatomy of a Discovery: The Twist–Bend Nematic Phase

New fluid states of matter, now known as liquid crystals, were discovered at the end of the 19th century and still provide strong themes in scientific research. The applications of liquid crystals continue to attract attention, and the most successful so far has been to the technology of flat panel displays; this has diversified in recent years and LCDs no longer dominate the industry. Despite this, there is plenty more to be uncovered in the science of liquid crystals, and as well as new applications, novel types of liquid crystal phases continue to be discovered. The simplest liquid crystal phase is the nematic together with its handed or chiral equivalent, named the cholesteric phase. In the latter, the aligned molecules of the nematic twist about an axis perpendicular to their alignment axis, but in the 1970s a heliconical phase with a tilt angle of less than 90° was predicted. The discovery of this phase nearly 40 years later is described in this paper. Robert Meyer proposed that coupling between a vector order parameter in a nematic and a splay or bend elastic distortion could result in spontaneously splayed or bent structures. Later, Ivan Dozov suggested that new nematic phases with splay–bend or twist–bend structures could be stabilised if the appropriate elastic constants became negative. Theoretical speculation on new nematic phases and the experimental identification of nematic–nematic phase transitions are reviewed in the paper, and the serendipitous discovery in 2010 of the nematic twist–bend phase in 1″,7″-bis(4-cyanobiphenyl-4′-yl)heptane (CB7CB) is described.