Non-zero State Research Articles

Stable Multi-Level Monotonic Eroders

Eroders are monotonic cellular automata with a linearly ordered state set that eventually wipe out any finite island of nonzero states. One-dimensional eroders were studied by Gal’perin in the 1970s, who presented a simple combinatorial characterization of the class. The multi-dimensional case has been studied by Toom and others, but no such characterization has been found. We prove a similar characterization for those one-dimensional monotonic cellular automata that are eroders even in the presence of random noise.

Minimum-time and minimum-triggering impulsive stabilization for multi-agent systems over finite fields

This paper investigates the problem of stabilization for multi-agent systems over finite fields via two types of impulsive control, that is, time-triggered impulsive control (TTIC) and state-triggered impulsive control (STIC). Inspired by the fact that finite-field networks (FFNs) cannot achieve stability at a nonzero state over the finite fields F p , p > 2 , two kinds impulse-controlled FFNs (ICFFNs) are introduced subject to time-triggering sequence and state-triggering set, respectively. In order to save time and control cost, the minimum-time control and minimum-triggering control of FFNs are both investigated. The time-optimal and triggering-optimal TTIC and STIC are successively designed. It reveals that designing such optimal TTIC for stabilizing ICFFNs can be transformed into finding the shortest path in the pretreated transition graph, and designing such optimal STIC for the global stabilization of ICFFNs is converted into finding the minimum spanning in-tree. Two examples are given to illustrate the control design procedures. Finally, we discuss the applications of the proposed control design methods on the synchronization problem and the switched FFNs including deterministic switched FFNs, probabilistic FFNs and Markovian jumping FFNs.

Field-induced quantum breakdown of superconductivity in magnesium diboride

The quantum breakdown of superconductivity (QBS) is the reverse, comprehensive approach to the appearance of superconductivity. A quantum phase transition from superconducting to insulating states tuned by using nonthermal parameters is of fundamental importance to understanding the superconducting (SC) phase but also to practical applications of SC materials. However, the mechanism of the transition to a nonzero resistive state deep in the SC state is still under debate. Here, we report a systematic study of MgB2 bilayers with different thickness ratios for undamaged and damaged layers fabricated by low-energy iron-ion irradiation. The field-induced QBS is discovered at a critical field of 3.2 Tesla (=Hc), where the quantum percolation model best explains the scaling of the magnetoresistance near Hc. As the thickness of the undamaged layer is increased, strikingly, superconductivity is recovered from the insulating state associated with the QBS, showing that destruction of quantum phase coherence among Cooper electron pairs is the origin of the QBS.

The Augment Algorithm and its Role in Cognitive Diagnosis

Both the augment algorithm and the reduction algorithm can be used to obtain non-zero knowledge states vector in testing. In particular, the augment algorithm based on the reachability matrix can imply the structure of the Q-matrix and its non-zero columns, thus proving the set of Q-matrix columns forms an algebraic structure (Lattice). Applying the augment algorithm based on the reachability matrix and the test Q-matrix, respectively, we can obtain the theoretical construct validity of the test Q-matrix (i.e., the degree of the test Q-matrix fitting the cognitive model) and use the results to evaluate test quality. We can also use the algorithm when constructing and evaluating cognitive models, as well as when developing cognitive diagnostic models. Moreover, the augment algorithm and its reverse algorithm (reduction algorithm) are suitable for analyzing and evaluating retrofitting data.

3D X-ray Microscopy as a Tool for in Depth Analysis of the Interfacial Interaction between a Single Carbon Fiber and an Epoxy Matrix after Mechanical Loading

The benefit of fiber-reinforced composites originates from the interaction between the fiber reinforcement and the matrix. This interplay controls many of its mechanical properties and is of utmost importance to enable its unique performance as a lightweight material. However, measuring the fiber−matrix interphase strength with micromechanical tests, like the Broutman test, is challenging, due to the many, often unknown boundary conditions. Therefore, this study uses state-of-the-art, high-resolution X-ray computed microtomography (XRM) as a tool to investigate post mortem the failure mechanisms of single carbon fibers within an epoxy matrix. This was conducted at the example of single carbon fiber Broutman test specimens. The capabilities of today’s XRM analysis were shown in comparison to classically obtained light microscopy. A simple finite element model was used to enhance the understanding of the observed fracture patterns. In total, this research reveals the possibilities and limitations of XRM to visualize and assess compression-induced single fiber fracture patterns. Furthermore, comparing two different matrix systems with each other illustrates that the failure mechanisms originate from differences in the fiber−matrix interphases. The carbon fiber seems to fail due to brittleness under compression stress. Observation of the fiber slippage and deformed small fracture pieces between the fragments suggests a nonzero stress state at the fragment ends after fiber failure. Even more, these results demonstrate the usefulness of XRM as an additional tool for the characterization of the fiber−matrix interphase.

Inhomogeneous charge distribution of simple substances

Using density function theory calculation method, we investigated the charge distribution in nano- or low-dimension materials and some high pressure three-dimensional solids in many simple substances. It is found that if an atom in simple substances has different atomic environment from the other(s) nearby, they always have spontaneous charge inhomogeneity within local area. Charge inhomogeneity introduced by inequivalent atomic positions is a general phenomenon in simple substances, especially in their nano-materials. Such self-ionization significantly changes elemental matter’s physical and chemical properties. These results can advance the understanding on condensed matters, especially the internal structures and physical or chemical properties of elemental nano-materials, and could be a starting point for experimental investigation of self-ionization in them. The charge inhomogeneity of simple substances means their nonzero oxidation state or nonzero valence.

Multipole polarizabilities for hydrogen-like atoms in Hulthén potential with and without spherical confinement

The multipole polarizabilities for hydrogen-like atoms with Hulthen potential are calculated with the sum-over-states formalism where the system bound and pseudocontinuum states are produced by employing the generalized pseudospectral method. Energies for nonzero angular momentum states, transition oscillator strengths, and dipole polarizabilities for the ground state of H atom with HP are calculated with high accuracy and compared with previous calculations. Quadrupole, octupole, and hexadecapole polarizabilities for both the ground and excited states are reported for the first time. The combined effect of Hulthen potential and impenetrable sphere on the polarizabilities is investigated, and the relation of such system with the confined H atom and particle in a box is discussed. Further comparison among Hulthen, screened Coulomb, and exponential cosine screened Coulomb potentials reveals that although the ground state energies follow the comparison theorem very well, their first-order energy corrections show complicated variations.

Observation of Distinct Spatial Distributions of the Zero and Nonzero Energy Vortex Modes in (Li_{0.84}Fe_{0.16})OHFeSe.

The energy and spatial distributions of vortex bound state in superconductors carry important information about superconducting pairing and the electronic structure. Although discrete vortex states, and sometimes a zero energy mode, had been observed in several iron-based superconductors, their spatial properties are rarely explored. In this study, we used low-temperature scanning tunneling microscopy to measure the vortex state of (Li,Fe)OHFeSe with high spatial resolution. We found that the nonzero energy states display clear spatial oscillations with a period corresponding to bulk Fermi wavelength; while in contrast, the zero energy mode does not show such oscillation, which suggests its distinct electronic origin. Furthermore, the oscillations of positive and negative energy states near E_{F} are found to be clearly out of phase. Based on a two-band model calculation, we show that our observation is more consistent with an s_{++} wave pairing in the bulk of (Li, Fe)OHFeSe, and superconducting topological states on the surface.

Local and nonlocal solitons in a coupled real system of Landau–Lifshitz equations

We consider the gauge equivalence of all NLS-type reductions with a coupled system of Landau–Lifshitz equations. In the local case it is shown to reduce to the continuum limit of the classical isotropic Heisenberg ferromagnet equation. All nonlocal reductions, however, are shown to be equivalent to a two-sublattice antiferromagnetic system. Nonlocal solitons are shown to represent excitations from nonzero ground state magnetization and antiferromagnetic vectors, indicative of a ferrimagnetic system. An alternate geometric interpretation is given by means of a coupled Hasimoto transformation, establishing the connection between the nonlocal reductions of the AKNS system and the motion of a curve in ℂ3. Through Darboux transformations, the one-soliton solutions of the coupled LL equations are obtained.

Synthesis, structure and magnetic properties of an oxamate-based 1D coordination polymer built on pentametallic links

The solvothermal reaction of the hexadentate 2-(oxamato)benzoic acid ligand (oaba) with copper(II) and cobalt(II) ions has yielded the [Cu4Co3(oaba)4(OH)2(DMF)6]·2(DMF)·1H2O (1) 1D coordination polymer. The single-crystal X-ray diffraction study reveals the formation of a neutral chain built from pentametallic complexes where each multi-polydentate ligand bridges four metal centres. The atypical morphology observed here for an oxamate-based 1D polymer arises from the use of a ligand bearing extra coordination sites. Magnetometry indicates strong dominating antiferromagnetic interactions within the polymer resulting in a non-zero ferrimagnetic state at low temperature.

Magnetic phase transitions in two-dimensional two-valley semiconductors with in-plane magnetic field

A two-dimensional electron gas (2DEG) in two-valley semiconductors has two discrete degrees of freedom given by the spin and valley quantum numbers. We analyze the zero-temperature magnetic instabilities of two-valley semiconductors with SOI, in-plane magnetic field, and electron-electron interaction. The interplay of an applied in-plane magnetic field and the SOI results in non-collinear spin quantization in different valleys. Together with the exchange intervalley interaction this results in a rich phase diagram containing four non-trivial magnetic phases. The negative non-analytic cubic correction to the free energy, which is always present in an interacting 2DEG, is responsible for first order phase transitions. Here, we show that non-zero ground state values of the order parameters can cut this cubic non-analyticity and drive certain magnetic phase transitions second order. We also find two tri-critical points at zero temperature which together with the line of second order phase transitions constitute the quantum critical sector of the phase diagram. The phase transitions can be tuned externally by electrostatic gates or by the in-plane magnetic field.

Half-Dirac semimetals and the quantum anomalous Hall effect in Kagome Cd2N3 lattices.

Half-Dirac semimetals (HDSs), which possess 100% spin-polarizations for Dirac materials, are highly desirable for exploring various topological phases of matter as low-dimensionality opens unprecedented opportunities for manipulating the quantum state of low-cost electronic nanodevices. The search for high-temperature HDSs is still a current hotspot and yet challenging experimentally. Herein based on first-principles calculations, we propose the realization of Half Dirac semimetals (HDS) in two-dimensional (2D) Kagome transition-metal nitride Cd2N3, which is robust against strain engineering. Monte Carlo simulations reveal that Cd2N3 possesses a Curie temperature reaching up to TC = 225 K, which is much higher than that of the reported monolayers CrI3 (TC = 45 K) and Cr2Ge2Te6 (TC = 20 K). The band crossings in Cd2N3 are gapped out by the spin–orbit coupling, which brings about the quantum anomalous Hall (QAH) effect with a sizeable band gap of Eg = 4.9 meV, characterized by the nonzero Chern number (C = 1) and chiral edge states. A tight-binding model is further used to clarify the origin of HDSs and nontrivial electronic properties. The results suggest monolayer transition-metal nitrides as a promising platform to explore fascinating physical phenomena associated with novel 2D emergent HDSs and QAH insulators toward realistic spintronics devices, thus stimulating experimental interest.

Glassy magnetic state and negative temperature coefficient of resistivity in Mn3+δIn

The complex metallic alloy ${\mathrm{Mn}}_{3}\mathrm{In}$ has recently attracted attention for being a probable candidate for the fully compensated half-metallic ferrimagnet. The compound is associated with a rather unusual negative coefficient of resistivity approximately above the ferrimagnetic, ${T}_{C}=80\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. Our investigation indicates that that the ground state of the alloy is spin-glass like, which possibly coexists with the ferrimagnetic state. The carrier density obtained from the Hall-effect measurement shows a jump below ${T}_{C}$; afterward, it gradually increases with lowering temperature and shows a saturating tendency at the lowest temperature. The electronic structure calculations indicate that, at the Fermi energy, dominant contributions come from minority-spin channels with larger bandwidth. In contrast, very weak but nonzero states arise from the majority-spin channel, and half metallicity can be ruled out. The calculations also found that the antiferromagnetic alignment of Mn spins with nonzero resultant magnetic moment confirms the ferrimagnetic nature consistent with the experimental results. The high-temperature phase with negative temperature coefficient of resistivity can be related to the localization of charge carriers through electron-phonon interactions.

Covalent Surface Alteration of MXenes and Its Effect on Superconductivity

Surface functional groups such as F, O, and OH attached to MXenes have a profound impact on the electronic properties. Generally, MXenes are synthesized by the aqueous acidic etching of the MAX phase, and these functional groups are inherently incorporated during the synthesis. Recently, covalent surface modification of MXene has been demonstrated at low temperature using molten inorganic salts.

Fractional-Order Iterative Learning Control with Initial State Learning for a Class of Multiagent Systems

To solve the consensus problem of fractional-order multiagent systems with nonzero initial states, both open- and closed-loop PDα-type fractional-order iterative learning control are presented. Considering the nonzero states, an initial state learning mechanism is designed. The finite time convergences of the proposed methods are discussed in detail and strictly proved by using Lebesgue-p norm theory and fractional-order calculus. The convergence conditions of the proposed algorithms are presented. Finally, some simulations are applied to verify the effectiveness of the proposed methods.

Features of the Algorithmic Implementation of Difference Analogues of the Logistic Equation with Delay

The logistic equation with delay or Hutchinson’s equation is one of the fundamental equations of population dynamics and is widely used in problems of mathematical ecology. We consider a family of mappings built for this equation based on central separated differences. Such difference schemes are usually used in the numerical simulation of this problem. The presented mappings themselves can serve as models of population dynamics; therefore, their study is of considerable interest. We compare the properties of the trajectories of these mappings and the original equation with delay. It is shown that the behavior of the solutions of the mappings constructed on the basis of the central separated differences does not preserve, even with a sufficiently small value of the time step, the basic dynamic properties of the logistic equation with delay. In particular, this map does not have a stable invariant curve bifurcating under the oscillatory loss of stability of a nonzero equilibrium state. This curve corresponds in such mappings to the stable limit cycle of the original continuous equation. Thus, it is shown that such a difference scheme cannot be used for numerical modeling of the logistic equation with delay.

First-principles investigations of hydrogen trapping in Y2O3 and the Y2O3|bcc Fe interface

Based on first-principles calculations, the binding energy of hydrogen atom to Y2O3 and Y2O3|bcc Fe interface (relative to bcc Fe side) with cube-on-cube orientation is at least 0.45 eV, if hydrogen substitutional is considered, or at least 0.26 eV if only hydrogen interstitial is considered. The calculated binding energies do not have a unique fixed value, because they are dependent on the interface structure, the Fermi level of Y2O3 near the interface and the chemical potential of Y/O. Hydrogen substitutional is more stable than hydrogen interstitial near the interface for Fermi level around calculated Schottky barrier height (SBH) at equilibrium. The Y2O3 particle interior can be an effective trapping site for hydrogen. Hydrogen interstitial, hydrogen substitutional and Y/O vacancy have a much lower energy near the interface than within the Y2O3 particle, presumably due to image charge interaction related to their non-zero charge state. For neutral impurities or defects, the energy near interface and that far away from the interface are similar (⩽0.1 eV difference) for a perfect coherent interface. The Y2O3|bcc Fe interface should provide effective trapping sites for hydrogen atoms in oxide dispersion strengthened (ODS) steels.

Number of nonzero states in prefractal sets generated by cellular automata

We count the number of nonzero states in the spatio-temporal or spatial patterns of cellular automata. By observing self-similar structures, we determine the number of nonzero states in the pattern. For Rule 90 and Rule 150 of one-dimensional elementary cellular automata, we provide an overview of previous studies on the number of nonzero states in spatio-temporal patterns until the finite time step 2n − 1. In this study, we calculate the numbers in spatial patterns for each time step t∈Z≥0 that allow us to compute future activities more efficiently than that by simulating the entire spatio-temporal pattern. We obtain results regarding the numbers for Rule 90, Rule 150, a generalization of Rule 90 to a two-dimensional case, and a modified Ulam’s model, which is a two-dimensional crystal growth model. In addition, we examine the relationship between spatio-temporal patterns generated by cellular automata and a singular function. Representing the number of nonzero states by specific numeric values, we show that they are described by a difference form of the singular function.

FPGA-based Experimental Validations of Electrical Activities in Two Adjacent FitzHugh–Nagumo Neurons Coupled by Memristive Electromagnetic Induction

ABSTRACT With the consideration of electromagnetic induction generated by the difference of membrane potentials between two adjacent neurons, a five-dimensional (5-D) memristor-coupled FitzHugh–Nagumo (FHN) bi-neuron model derived from connecting two FHN neurons with the memristive electromagnetic induction is presented. Then, with the 5-D memristor-coupled FHN bi-neuron model, the equilibrium states and their stabilities are explored by theoretical and numerical analyses. It is indicated that the proposed model has two non-zero equilibrium states with the same stability of unstable saddle-focus or unstable saddle point associating to the considered model parameters. The parameter-associated electrical activities of periodic, quasi-periodic, and chaotic behaviors are disclosed by bifurcation plots, dynamical maps, phase plane plots and further confirmed by 0–1 tests. Besides, the phenomena of initial-associated bi-stability with the coexistence of chaotic and periodic behaviors, as well as the riddled attraction basin, are revealed by local attraction basins and phase plane plots. Furthermore, based on field programmable gate array (FPGA), a digitally implemented electronic circuit is made, from which the electrical activities are experimentally captured to verify the numerical ones.

Serendipity for Topological Insulator as Multifunctional Electrocatalyst

The design for multifunctional two-dimensional (2D) materials is considered as one of the main strategies to expand its application. Here, we propose that the already-synthesized organometallic lattice (Ni3(CNH)12) concurrently hosts topological and catalytic properties. Using first-principles calculations combined with tight-binding (TB) model, we demonstrate that the 2D Ni3(CNH)12 intrinsically possesses multiple Dirac cones along with flat bands passing through the Dirac bands. Taking the spin–orbital coupling (SOC) into account, all the degenerate points open gaps, spawning abundant topologically nontrivial insulating phases characterized by a nonzero Z2 topological invariant and edge states. Furthermore, because of its special geometry and electronic states, the 2D lattice can serve as a bifunctional electrocatalytic activity for overall water splitting with low overpotentials. Our current results offer a viable approach for the discovery of 2D organometallic materials with multifunctional application in spintronics devices and catalysts from the emerging field of topological materials.