Concise Criterion Research Articles

Auxiliary Rather Than Dominant. The Role of Direct Dy-S Coordination in Single-Molecule Magnet Unveiled via ab initio Study.

The role of Dy-S coordination in a single-molecule magnet (SMM) is investigated via an ab initio study in a group of mononuclear structures. The SMM performance of this group is well interpreted via a concise criterion consisting of long quantum tunneling of magnetization (QTM) time τQTM and high effective barrier for magnetic reversal Ueff. The best SMMs in the selected group, i.e., 1Dy (CCDC refcode: PUKFAF) and 2Dy (CCDC refcode: NIKSEJ), are just those holding the longest τQTM and the highest Ueff simultaneously. Further analysis based on the crystal field model and ab initio magneto-structural exploration indicates that the influence of Dy-S coordination on the SMM performance of 1Dy is weaker than that of axial Dy-O coordination. Thus, Dy-S coordination is more likely to play an auxiliary role rather than a dominant one. However, if placed at the suitable equatorial position, Dy-S coordination could provide important support for good SMM performance. Consequently, starting from 1Dy, we built two new structures where Dy-S coordination only exists at the equatorial position and two axial positions are occupied by strong Dy-O/Dy-F coordination. Compared to 1Dy and 2Dy, these new ones are predicted to have significantly longer τQTM and higher Ueff, as well as a nearly doubled blocking temperature TB. Thus, they are probable candidates of SMM having clearly improved performance.

Ab initio prediction of key parameters and magneto-structural correlation of tetracoordinated lanthanide single-ion magnets.

Single-molecule magnets (SMMs) have great potential in becoming revolutionary materials for micro-electronic devices. As one type of SMM and holding the performance record, lanthanide single-ion magnets (Ln-SIMs) stand at the forefront of the family. Lowering the coordination number (CN) is an important strategy to improve the performance of Ln-SIMs. Here, we report a theoretical study on a typical group of low-CN Ln-SIMs, i.e., tetracoordinated structures. Our results are consistent with those of experiments and they identify the same three best Ln-SIMs via a concise criterion, i.e., the co-existence of long τQTM and high Ueff. Compared to the record-holding dysprosocenium systems, the best SIMs here possess τQTM values that are shorter by several orders of magnitude and Ueff values that are lower by ∼1000 Kelvin (K). These are important reasons for the fact that the tetracoordinated Ln-SIMs are clearly inferior to dysprosocenium. A simple but intuitive crystal-field analysis leads to several routes to improve the performance of a given Ln-SIM, including compression of the axial bond length, widening the axial bond angle, elongation of the equatorial bond length and usage of weaker equatorial donor ligands. Although these routes are not brand-new, the most efficient option and the degree of improvement resulting from it are not known in advance. Consequently, a theoretical magneto-structural study, covering various routes, is carried out for the best Ln-SIM here and the most efficient route is shown to be widening the axial ∠O-Dy-O angle. The most optimistic case, having a ∠O-Dy-O of 180°, could have a τQTM (up to 103 s) and Ueff (∼2400 K) close to those of the record-holders. Subsequently, a blocking temperature (TB) of 64 K is predicted to be possible for it. A more practical case, with ∠O-Dy-O being 160°, could have a τQTM of up to 400 s, Ueff of around 2200 K and the possibility of a TB of 57 K. Although having an inherent precision limit, these predictions provide a guide to performance improvement, starting from an existing system.

Stabilization of Memristor-Based Chua’s Circuits via Dynamic Event-Triggered Mechanism

This brief is concerned with the event-triggered stabilization for a memristor-based Chua’s circuits. A dynamic-periodic event-triggered approach is proposed, whose distinguishing feature is the introduction of two periodic triggering thresholds. One of the thresholds is an exponential decay function, and the other is an internal dynamic variable. Both thresholds contribute to the reduction of events. By Lyapunov theory, a concise criterion is developed for the stabilization of memristor-based Chua’s circuits. Simulation results are offered to support the theoretical results.

An urban-scale method for building roofs available wind resource evaluation based on aerodynamic parameters of urban sublayer surfaces

• A convenient urban-scale wind resource assessment method was proposed. • A moving grid was proposed to calculate the aerodynamic parameters. • The potential of low-rise buildings in urban areas using wind energy was revealed. • A criterion to assess the wind energy above urban building roofs was developed. For the limited areas of building rooftops, installing wind turbines can increase energy production, as compared to paving over the photovoltaic panels, and can serve as a viable means for complementary power generation. However, a concise criterion for estimating the availability of wind energy in the built environment is lacking. In this work, the aerodynamic parameters method was integrated with a moving grid of a semicircle with a radius of 500 m to develop an urban-scale wind energy evaluation model. The wind energy utilisation potential of buildings’ rooftops in a given city (in this case, Hangzhou) was estimated. The results show that a certain portion of low-rise buildings has considerable available wind resources. By statistical analysis of the millions of calculated results, two criteria for rooftop's wind resources assessment have been developed. Compared with the buildings in a previously planned region having small spacing and low average height characteristics, the buildings of the newly planned region were spacious, resulting in its suitability for wind energy utilisation proportion being 10.2% higher. Besides, the proportion of residential buildings that are suitable for wind use is higher than that of public buildings and industrial buildings, for the average height difference.

The coexistence of long τQTM and high Ueff as a concise criterion for a good single-molecule magnet: a theoretical case study of square antiprism dysprosium single-ion magnets.

A systematic theoretical study is performed on a group of 16 square antiprism dysprosium single-ion magnets. Based on ab initio calculations, the quantum tunneling of magnetization (QTM) time, i.e., τQTM, and effective barrier of magnetic reversal, Ueff, are theoretically predicted. The theoretical τQTM is able to identify the ones with the longest QTM time with small numerical deviations. Similar results occur with respect to Ueff too. The systems possessing the best single-molecule magnet (SMM) properties here are just the ones having both the longest τQTM and the highest Ueff, from either experiment or theory. Thus, our results suggest the coexistence of long τQTM and high Ueff to be a criterion for high-performance SMMs. Although having its own limits, this criterion is easy to be applied in a large number of systems since both τQTM and Ueff could be predicted by theory with satisfactory efficiency and reliability. Therefore, this concise criterion could provide screened candidates for high-performance SMMs quickly and, hence, ease the burden of further exploration aiming for a higher degree of precision. This screening is important since the further exploration could easily demand tens or even hundreds of ab initio calculations for a single SMM. A semi-quantitative crystal field (CF) analysis is performed and shown here to be capable of indicating the general trends in a more chemically intuitive way. This analysis could help to identify the most important coordinating atoms for both diagonal and non-diagonal CF components. Thus, it could give some direct clues for improving the SMM properties: reducing the distance of the axial atom to the central ion, rotating the axial atom closer to the easy axis or increasing the amount of its negative charge. Correspondingly, opposite operations on the equatorial atom could give the same result.

Basic theorem and global exponential stability of differential–algebraic neural networks with delay

A differential–algebraic neural network (DANN) with delay (DDANN) is proposed. Firstly, the global existence and uniqueness theorems are established for a DDANN, respectively. Next, a new differential–algebraic inequality is established. Then, a theorem on global exponential stability of DDANN is shown by using this inequality. As an application of DDANN, a very concise criterion on global exponential stability for a neutral-type neural network is given by using DDANNs. Finally, two examples are given to illustrate the theoretical results.

Analysis of the ROA of an anaerobic digestion process via data-driven Koopman operator

Abstract Nonlinear biochemical systems such as the anaerobic digestion process experience the problem of the multi-stability phenomena, and thus, the dynamic spectrum of the system has several undesired equilibrium states. As a result, the selection of initial conditions and operating parameters to avoid such states is of importance. In this work, we present a data-driven approach, which relies on the generation of several system trajectories of the anaerobic digestion system and the construction of a data-driven Koopman operator to give a concise criterion for the classification of arbitrary initial conditions in the state space. Unlike other approximation methods, the criterion does not rely on difficult geometrical analysis of the identified boundaries to produce the classification.

Study of a multi-ring cavity based single-frequency fiber laser and associated thermal effects

• A concise criterion for length selection is proposed for multi-ring fiber cavities. • Influence of thermal tampering on modal selection is analyzed and verified. • Stable single-frequency Yb-doped fiber lasers of multi-ring cavities are achieved. In this paper we present a detailed study of compound ring resonator based fiber lasers for single-frequency (SF) generation and associated thermal effects. A concise criterion to select a single longitudinal mode (SLM) by the multi-ring cavity (MRC) scheme is proposed and confirmed with experiments on fiber lasers with zero, one, and two sub-ring cavities. The results demonstrate the necessity of using at least two sub-rings of tight length differential to ensure stable SF laser emission by the MRC scheme. Subsequent studies of temperature variation upon the two sub-rings reveal that the robustness of SF emission status can be further secured by a controlled thermal tampering process. Stable SF emission, centered at 1064.2 nm with a 3-dB linewidth of <10 kHz, are thus achieved by Yb-doped all-fiber lasers with the MRC scheme.

Positivity and Stability of Delayed Timescale-Type Differential-Difference Equations

In this article, positivity and global exponential stability for a class of timescale-type differential-difference equations with bounded time-varying delay are considered. At first, a sufficient and necessary condition for the positivity of matrix-valued timescale-type exponential function is obtained. Based on this, an explicit criterion for the positivity of coupled timescale-type differential-difference equations with delays bounded above is acquired by timescale-type induction method. Besides, a sufficient and necessary condition of its positivity is obtained when the delay is both bounded above and below by two positive reals. Then, a concise criterion that guarantees the global exponential stability of the considered system is derived based upon analytical techniques of time scales and positivity constraint. On top of that, the theoretical results are applied to investigate the positivity and stability for a class of timescale-type neutral linear systems with bounded time-varying delays. Two numerical examples are given to illustrate the validity of the results.

Constructions of Involutions Over Finite Fields

An involution over finite fields is a permutation polynomial whose inverse is itself. Owing to this property, involutions over finite fields have been widely used in applications, such as cryptography and coding theory. Following the idea by Wang to characterize the involutory behavior of the generalized cyclotomic mappings, this paper gives a more concise criterion for $x^{r}h(x^{s})\in {\mathbb F} _{q}[x]$ being involutions over the finite field ${\mathbb F}_{q}$ , where $r\geq 1$ and $s\,|\, (q-1)$ . By using this criterion, we propose a general method to construct involutions of the form $x^{r}h(x^{s})$ over ${\mathbb F}_{q}$ from given involutions over some subgroups of ${\mathbb F}_{q}^{*}$ by solving congruent and linear equations over finite fields. Then, many classes of explicit involutions of the form $x^{r}h(x^{s})$ over ${\mathbb F}_{q}$ are obtained.

Uniform stability of homogeneous time-varying systems

ABSTRACT A sufficient condition for uniform asymptotic stability of nonlinear time-varying systems is proposed within the Narendra-Annaswamy (NA) framework. Based on homogeneity, a class of strict Lyapunov functions is established, in which time-varying terms are included. By using the new Lyapunov functions, concise criterion is provided. Unlike the classical NA approach, divergent time sequence in the criterion is not needed. The utility of our result is illustrated through the study of applications and numerical examples.

Controllability of Boolean Control Networks With Multiple Time Delays

In this paper, the controllability of Boolean control networks (BCNs) with multiple time delays is investigated. The concept of controllability matrices for BCNs with multiple time-varying delays is proposed, and an iterative algorithm is proposed to calculate all controllability matrices. Based on this, a concise criterion for controllability is proposed, which states that a BCN with delays is controllable if and only if all elements of its controllability matrix are nonzero. The proposed method is applied to BCNs with periodic and constant delays, respectively. Sufficient and necessary conditions for controllability are presented. Finally, two examples are given to illustrate the main results.

Distribution Optimal Power Flow With Real-Time Price Elasticity

This letter investigates a new class of optimal power flow problem for distribution systems, where elastic loads respond to real-time nodal prices by adjusting their demands. A fixed-point iteration algorithm is suggested to identify an equilibrium. A concise criterion is devised to judge convergence.

Invalid Microstate Densities for Model Systems Lead to Apparent Violation of Thermodynamic Law

It is often incorrectly assumed that the number of microstates Ω ( E , V , N , . . . ) available to an isolated system can have arbitrary dependence on the extensive variables E , V , N , ... However, this is not the case for systems which can, in principle, reach thermodynamic equilibrium since restrictions arise from the underlying equilibrium statistical mechanic axioms of independence and a priori equal probability of microstates. Here we derive a concise criterion specifying the condition on Ω which must be met in order for a system to be able, in principle, to reach thermodynamic equilibrium. Natural quantum systems obey this criterion and therefore can, in principle, reach thermodynamic equilibrium. However, models which do not respect this criterion will present inconsistencies when treated under equilibrium thermodynamic formalism. This has relevance to a number of recent models in which negative heat capacity and other violations of fundamental thermodynamic law have been reported.

Criterion for determining crossover phenomenon in volume-translated equation of states

Volume translation is widely adopted in cubic equation of state (CEOS) to achieve more accurate density predictions for pure compounds and mixtures. Previous research reveals that a temperature-dependent volume-translated EOS could result in crossing of pressure-volume isotherms for a pure compound, which leads to an anomalous behavior that the predicted molar volume for a pure component can possibly be lower at a higher temperature at an isobaric condition. Such crossover phenomenon fails to consistently predict the thermodynamic properties of a pure compound, e.g., giving a negative isobaric thermal expansivity. In this study, we develop a concise criterion to judge whether a volume-translated EOS will result in crossover issues, and if so, the extent of the temperature and pressure range over which the crossover phenomenon occurs. The recently proposed volume translations are evaluated on the basis of the developed criterion. For the various types of temperature-dependent volume translations, we obtain the specific temperature/pressure conditions over which there is certainly no crossover phenomenon.

On hyperbolicity of 13-moment system

We point out that the thermodynamic equilibrium is not an interior point of the hyperbolicity region of Grad's 13-moment system. With a compact expansion of the phase density, which is more compact than Grad's expansion, we derive a modified 13-moment system. The new 13-moment system admits the thermodynamic equilibrium as an interior point of its hyperbolicity region. We deduce a concise criterion to ensure the hyperbolicity, and thus the hyperbolicity region can be quantitatively depicted.

Face Recognition Using Local Variation

In this paper, a novel approach, namely local variation projection (LVP), is presented for face recognition. LVP defines an adjacency graph to model the variation among nearby face images, which includes the within-class variation and between-class variation, also called margin. In order to better detect the discriminant structure, we assign a small weight to the variation among nearby face images from the same class. Based on this content, a concise feature extraction criterion is built for dimensionality reduction. Experiments indicate the effectiveness of our proposed approach.

THE ENTROPY OF NON-ERGODIC COMPLEX SYSTEMS — A DERIVATION FROM FIRST PRINCIPLES

In information theory the 4 Shannon-Khinchin1,2 (SK) axioms determine Boltzmann Gibbs entropy, S ~ -∑i pi log pi, as the unique entropy. Physics is different from information in the sense that physical systems can be non-ergodic or non-Markovian. To characterize such strongly interacting, statistical systems – complex systems in particular – within a thermodynamical framework it might be necessary to introduce generalized entropies. A series of such entropies have been proposed in the past decades. Until now the understanding of their fundamental origin and their deeper relations to complex systems remains unclear. To clarify the situation we note that non-ergodicity explicitly violates the fourth SK axiom. We show that by relaxing this axiom the entropy generalizes to, S ~∑i Γ(d + 1, 1 - c log pi), where Γ is the incomplete Gamma function, and c and d are scaling exponents. All recently proposed entropies compatible with the first 3 SK axioms appear to be special cases. We prove that each statistical system is uniquely characterized by the pair of the two scaling exponents (c, d), which defines equivalence classes for all systems. The corresponding distribution functions are special forms of Lambert-W exponentials containing, as special cases, Boltzmann, stretched exponential and Tsallis distributions (power-laws) – all widely abundant in nature. This derivation is the first ab initio justification for generalized entropies. We next show how the phasespace volume of a system is related to its generalized entropy, and provide a concise criterion when it is not of Boltzmann-Gibbs type but assumes a generalized form. We show that generalized entropies only become relevant when the dynamically (statistically) relevant fraction of degrees of freedom in a system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen. Systems governed by generalized entropies are therefore systems whose phasespace volume effectively collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for accelerating random walks, and a spin system on a constant-conectancy network. We argue that generalized entropies should be relevant for self-organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.

Automatic extracellular spike detection with piecewise optimal morphological filter

Neuronal spike detection is a technical challenge because of large amounts of background noise and contributions of many neurons to recorded signals. In this paper, we propose an automatic spike detection algorithm in which piecewise optimal morphological filters are designed to separate action potentials (spikes) from background noise. The structure elements of morphological filters are constructed with Gaussian function and a concise criterion is introduced to piecewise optimized structure elements. An adaptive amplitude threshold is utilized to detect spike events when the spikes are extracted by the morphological filter, which increases the detection accuracy. We evaluate our algorithm with both synthesized neural recordings and real neural data, and compare it with two established spike detection methods.

Effects of lateral heat and carrier diffusion on thermal runaway of cw DH semiconductor lasers

Effects of lateral heat and carrier diffusion on the maximum output intensity, above which thermal runaway takes place, are determined for cw semiconductor lasers. The effects are depicted by an aspect ratio of cavity length to stripe width and a dimensionless quantity representing the efficiency of heat transfer. A concise criterion for no thermal runaway is given. The results show that the output intensity can be increased by an order of magnitude by reducing the stripe width sufficiently but that only about a twofold increase in the output power can be realized. However, a laser with a smaller stripe width can be operated at a higher temperature for the same output power. An optimization with respect to the aspect ratio and the dimensionless quantity should result in a three-to-fourfold increase even in the output power. >