One-step Transition Research Articles

Ising-Like Model Hasn't Yet Said Its Last Word: Exact and Mean-Field Investigations of 2, 3 and 4-Body Interactions in 1D Ising Chain of Binuclear Spin-Crossover Solids.

We investigate the static properties of a new class of 1D Ising-like Hamiltonian for binuclear spin-crossover materials accounting for two-, three-, and four-body short-range interactions between binuclear units of spins and . The following 2-, 3-, and 4-body , , and terms are considered, in addition to intra-binuclear interactions, such as effective ligand-field energy and exchange-like coupling. An exact treatment is carried out within the frame of the transfer matrix method, leading to a 4×4 matrix from which, we obtained the thermal evolution of the thermodynamic quantities. Several situations of model parameter values were tested, among which that of competing intra- and inter-molecular interactions, leading to the occurrence of (i) one-step spin transition, (ii) two-, three-, and four-step transitions, obtained with a reasonable number of parameters. To reproduce first-order phase transitions, we accounted for inter-chains interactions, treated in the mean-field approach. Hysteretic multi-step transitions, recalling experimental observations, are then achieved. Overall, the present model not only suggests new landscapes of interaction configurations between SCO molecules but also opens new avenues to tackle the complex behaviors often observed in the properties of SCO materials.

Microstructural evolution and phase transformation behavior of Ni-Ti alloys prepared by accumulative roll bonding-deformation diffusion process

Ni-Ti shape memory alloys were prepared by accumulative roll bonding-deformation diffusion (ARB-DD) process. Effects of deformation heat treatment on the microstructural evolution and phase transition behavior of ARB-DD Ni-Ti alloy were investigated by thermodynamic calculations, and the intrinsic mechanism was revealed. The results show that strong shear is induced by intensified plastic flow of the metal at the interface, resulting the interfaces engage with each other. The simultaneous opening and cross-tangling of multi-directional dislocations leads to the dislocation cells and Taylor lattice interact near the interface, and the compounds are preferentially formed. The ARB-DD treatment resulted in a one-step phase transition for the Ni-Ti alloy. After deformation heat treatment, R-phases appear and the phase transition is transformed into two-step. During heating and cooling the phase transitions are B19’→R→B2 and B2→R→B19’, respectively. The thermal hysteretic temperature increases and reaches 57.0 °C. The microstructure transforms from dislocations to nano-twin. A lattice distortion zone with a width of about 10 nm exists at the interface between precipitates and the matrix. It reduces the energy barrier required for phase transformation, leading to stabilization of the B2 phase and de-stabilization of the B19’ phase. Eventually, a wider temperature interval for the phase transformation is obtained. This process is an effective way to prepare Ni-Ti alloys with favorable shape memory effect.

Effect of interchange spacing on drivers' visual characteristics in interchange merging areas

To explore the effect of interchange spacing on drivers' visual characteristics in the merging areas of interchange, a high-density group of five interchanges on the expressway of Chongqing, China, was selected as the test site. An naturalistic driving test was conducted with 47 participants, and the Tobii Glasses II portable eye tracker was used to collect gaze data during driving. The drivers' fixation field was divided into six areas by applying a K-means dynamic clustering algorithm combined with the actual scenario. Markov chains were used to calculate the drivers' gaze transition probability matrices under different driving conditions, and the analysis of gaze transition behaviors was directed at common spacing interchanges, small spacing interchanges, and composite interchanges. Under the ramp-mainline condition, drivers’ fixations were primarily concentrated on the near ahead and the left side areas, with higher rates of repeated fixations on the left rearview mirror and left-side line areas. The average value of fixation duration, saccade distance, and saccade speed of small spacing interchange is higher than common spacing interchange. Additionally, under the mainline condition, the probability of one-step transition and repeated fixation rates significantly increased for the right-side lane areas, and the average values of fixation index and saccade index of small spacing interchange are lower than those of common spacing interchange. The results show that the highest probabilities of repeated fixation by drivers occurred in the near ahead and far ahead areas in the interchange merging areas. Insufficient spacing resulted in more frequent occurrences of zero values in one-step transition probability matrices. The research conclusions provide theoretical support for the optimal design and safe operation of the merging area of high-density interchange group of urban expressway.

Solid–liquid transition in a skyrmion matter

We report Monte-Carlo studies of the orientational order and melting of a 2D skyrmion lattice containing more than one million spins. Two models have been investigated, a microscopic model of lattice spins with Dzyaloshinskii–Moryia interaction that possesses skyrmions, and the model in which skyrmions are treated as point particles with repulsive interaction derived from a spin model. They produce similar results. The skyrmion lattice exhibits a sharp one-step transition between solid and liquid phases on temperature and the magnetic field. This solid–liquid transition is characterized by the kink in the magnetization. The field-temperature phase diagram is computed. We show that the application of the field gradient to a 2D system of skyrmions produces a solid–liquid interface that must be possible to observe in experiments.

A Markov method for a mechanical system reliability assessment using discrete degradation data

Abstract A homogenous continuous-time Markov model (HCTMM) has the advantage of high accuracy and is usually used in reliability analysis. However, the transition intensities (rates) between any two states cannot be accurately obtained due to the discrete data obtained from a mechanical system and little expert knowledge. This paper proposes a method in which the transition intensity matrix of an HCTMM can be obtained indirectly using the actual discrete degradation data of a mechanical system. Firstly, the one-step transition probability matrix can be calculated by a hidden Markov model using the discrete degradation data. Secondly, the unit-time transition intensity matrix can be calculated from the one-step transition probability matrix. At last, an HCTMM is established to assess the reliability of a mechanical system based on the unit-time transition intensity matrix. Moreover, considering the maintenance activities cannot restore a mechanical system as a fire-new one, the random transition of a mechanical system after maintenance is expressed by a quasi-renewal process in this paper. Finally, three cases are studied to validate the proposed method.

Neural calibration of hidden inhomogeneous Markov chains: information decompression in life insurance

Markov chains play a key role in a vast number of areas, including life insurance mathematics. Standard actuarial quantities as the premium value can be interpreted as compressed, lossy information about the underlying Markov process. We introduce a method to reconstruct the underlying Markov chain given collective information of a portfolio of contracts. Our neural architecture characterizes the process in a highly explainable way by explicitly providing one-step transition probabilities. Further, we provide an intrinsic, economic model validation to inspect the quality of the information decompression. Lastly, our methodology is successfully tested for a realistic data set of German term life insurance contracts.

Preparation and application of waste cigarette butts-derived mulch film with excellent mechanical properties and optical transparency

Abstract The small waste cigarette butts every year worldwide added up is a significant threat to the environment. The main component of cigarette butts is cellulose acetate, which is an excellent film-forming material. Here, a one-step phase transition method was employed to successfully convert waste cigarette butts into a transparent film. This film (160×18×0.5 mm) derived from waste cigarette butts (CB) has high mechanical strength (fracture stress 23.5 MPa, Young’s modulus 13.1 MPa), good thermal stability, and excellent optical transmittance (91.8%), and low haze (40.3%). Its properties rival those of traditional low-density polyethylene (PE) film. Meanwhile, the CB film displayed fascinating bending-ability and folding resistance. The cigarette butt-derived film with low cost and excellent properties exhibits a promising application as agricultural mulch and provides recycle solution for waste cigarette butts.

Optimizing anaerobic digestion: Benefits of mild temperature transition from thermophilic to mesophilic conditions

Anaerobic digestion (AD) plays a significant role in renewable energy recovery. Upgrading AD from thermophilic (50–57 °C) to mesophilic (30–38 °C) conditions to enhance process stability and reduce energy input remains challenging due to the high sensitivity of thermophilic microbiomes to temperature fluctuations. Here we compare the effects of two decreasing-temperature modes from 55 to 35 °C on cell viability, microbial dynamics, and interspecies interactions. A sharp transition (ST) is a one-step transition by 20 °C d−1, while a mild transition (MT) is a stepwise transition by 1 °C d−1. We find a greater decrease in methane production with ST (88.8%) compared to MT (38.9%) during the transition period. ST mode overproduced reactive oxygen species by 1.6-fold, increased membrane permeability by 2.2-fold, and downregulated microbial energy metabolism by 25.1%, leading to increased apoptosis of anaerobes by 1.9-fold and release of intracellular substances by 2.9-fold, further constraining methanogenesis. The higher (1.6 vs. 1.1 copies per gyrA) metabolic activity of acetate-dependent methanogenesis implied more efficient methane production in a steady mesophilic, MT-mediated system. Metagenomic binning and network analyses indicated that ST induced dysbiosis in keystone species and greatly enhanced microbial functional redundancy, causing loss of microbial syntrophic interactions and redundant metabolic pathways. In contrast, the greater microbial interconnections (average degrees 44.9 vs. 22.1) in MT at a steady mesophilic state suggested that MT could better maintain necessary system functionality and stability through microbial syntrophy or specialized pathways. Adopting MT to transform thermophilic digesters into mesophilic digesters is feasible and could potentially enhance the further optimization and broader application of practical anaerobic engineering.

Three-Step Ferroelastic Transitions from Hexagonal to Triclinic Phases in a Hybrid Perovskite: (1-Fluoromethyl-1-methylpyrrolidine)[CdCl3

Hybrid ferroelastic crystals have emerged as a hot research topic in recent years owing to their prospective applications in piezoelectric sensors, mechanical switches, and optoelectronic devices. Nevertheless, most of the documented materials exhibit one-step or two-step ferroelastic phase transition(s), and those with multistep ferroelastic transitions are extremely scarce. We present a new hexagonal molecular perovskite based on a fluoro-substituted flexible cyclic ammonium cation, (1-fluoromethyl-1-methylpyrrolidine)[CdCl3] (1), undergoing unusual three-step ferroelastic phase transitions from hexagonal paraelastic phase to orthorhombic, monoclinic, and triclinic ferroelastic phases at 388, 376, and 311 K, respectively, with Aizu notation of 6/mmmFmmm, mmmF2/m, and 2/mF-1, featuring spontaneous strain of 0.002, 0.023, and 0.110, respectively. Furthermore, variable-temperature single-crystal diffraction reveals that the phase-transition mechanism in 1 principally originates from intriguing dynamic change of organic cations and synchronous displacement of inorganic chains. This scarce instance of multistep hybrid ferroelastic provides important clues for finding advanced ferroelastic materials.

Molecular Twist-Induced Single-Crystal Isomerization and Valence Tautomeric Transitions in a Cobalt-Dioxolene Complex.

A mononuclear valence tautomeric (VT) complex, [Co(pycz)2(Sq)(Cat)] (1-trans), where pycz = 9-(pyridin-4-yl)-9H-carbazole, Sq⋅- = 3,5-di-tert-butyl-semiquinonato, and Cat2- = 3,5-di-tert-butyl-catecholato, is synthesized in the trans configuration, which undergoes one-step valence tautomeric transition above room temperature. Remarkably, 1-trans can transform into its isomeric structure, [Co(pycz)2(Sq)(Sq)] (1-cis), at temperature above 350 K in a single-crystal-to-single-crystal way by in situ molecular twist, and the resulting 1-cis exhibits a pronounced two-step VT transition during magnetic measurements that is rare for mononuclear VT complexes. Such drastic solid-state structural transformation is reported in VT compounds for the first time, which is actuated by a crystal surface's melting-recrystallization induced phase transition process. DFT calculations offer an underlying mechanism suggesting a concerted bond rotation during the structural transformation. The results demonstrate an unconventional approach that realizes structural transformation of VT complexes and the control of VT performance.

Verification of Parametric Properties of Linear Discrete-time Stochastic Systems

We study the problem of verifying parametric properties of linear discrete-time stochastic systems (linear DTSSs) over bounded and unbounded time horizons. A linear DTSS captures random processes, where the one-step transition relation between the current random vector X and the next-step random vector X’ is linear and is given by X’ = AX + W, where A is an n x n matrix and W is a random noise vector. We assume that the initial and noise random vectors are multivariate normal, each of which is expressed as a pair of two parameters, namely, mean and covariance. We are interested in verifying whether the system always satisfies a given parametric property specified as a subset of the parameters’ space over bounded or unbounded time horizons. For bounded time steps, we reduce the problem to the satisfiability of a semidefinite programming problem. For the unbounded time steps, we propose a novel abstraction procedure to reduce the verification problem to that of a finite graph, wherein, the nodes of the graph correspond to the regions of a partition of the random vector space, in contrast to existing works that partition the state-space. More precisely, we partition the parameter space of normal random vectors, namely, the space of means and covariance matrices, and apply semi-definite programming to compute the edges. We show that our abstraction procedure is sound. Our experiments with varying number of vehicle dynamics and different dimensions of random models show that our methods are reasonably scalable.

Cluster Synchronization of Finite-Field Networks.

This technical paper investigates the cluster synchronization of finite-field networks (FFNs) based on the algebraic state space representation. By resorting to the semi-tensor product of matrices, the cluster synchronization of an FFN can be completely converted into the set stability of state trajectory. Then, a necessary and sufficient condition for the cluster synchronization of FFNs is obtained based on the invariant subset and one-step transition matrix. In particular, the obtained results are applicable to check the leader-follower synchronization and group consensus of FFNs. Finally, a numerical example is given to illustrate the feasibility of the obtained results.

Linear and nonlinear optical absorption of 2D monolayer NbOCl2

The in-layer crystal structure of a two-dimensional material is stable, but the interaction force between the atomic layers is much weaker. Niobium oxide dichloride (NbOCl2) not only has high second-order nonlinear coefficients unique to common monolayer two-dimensional materials but also weak electronic coupling between layers. These characteristics make NbOCl2 very suitable as a quantum light source in quantum optical systems. This article mainly studies the linear and nonlinear optical absorption of two-dimensional monolayer NbOCl2. The characterization means include a surface distance projection map and three views, total density of states, photoelectron spectrum, charge density difference, transition dipole moment density, one-photon absorption spectrum, and two-photon absorption spectrum. There is a size effect on the total density of states, photoelectronic energy spectrum, and one-photon absorption spectrum, that is, as the size increases, the total density of states is red-shift, the photoelectronic energy spectrum is blue-shift, and the absorption spectrum has a significant red-shift. The charge density difference indicates that there is charge transfer around the Nb atom of NbOCl2. The transition dipole moment density changes periodically. The study of the two-photon absorption spectrum shows that it is dominated by a one-step transition. In summary, our work provides an in-depth understanding of its optical properties and is of great significance for the miniaturization of quantum light sources.

Feedback Stabilization of Boolean Control Networks With Missing Data.

Data loss is often random and unavoidable in realistic networks due to transmission failure or node faults. When it comes to Boolean control networks (BCNs), the model actually becomes a delayed system with unbounded time delays. It is difficult to find a suitable way to model it and transform it into a familiar form, so there have been no available results so far. In this article, the stabilization of BCNs is studied with Bernoulli-distributed missing data. First, an augmented probabilistic BCN (PBCN) is constructed to estimate the appearance of data loss items in the model form. Based on this model, some necessary and sufficient conditions are proposed based on the construction of reachable matrices and one-step state transition probability matrices. Moreover, algorithms are proposed to complete the state feedback stabilizability analysis. In addition, a constructive method is developed to design all feasible state feedback controllers. Finally, illustrative examples are given to show the effectiveness of the proposed results.

A new path integration method for the stochastic system under Poisson white noise excitation based on a probability mapping

In this paper, a new path integration method is proposed for stochastic dynamical systems excited by Poisson white noise. An efficient one-step transition probability density function (TPDF) matrix is constructed based on a decoupling probability mapping. The new method can handle the case of multiple impulses occurring in a one-step transition time interval and considers the randomness of the impulse instant, which compensates for a drawback of previous path integration methods. The probability mapping realizes the decoupling of randomness and the one-step TPDF matrix, which can be extended to general stochastic systems satisfying the Markov property. The stochastic responses of two dynamical systems excited by Poisson white noises for different mean arrival rates are obtained by using the new path integration method, and MC simulations prove that the new method is very effective, and it maintains good accuracy even for large mean arrival rates.

Hysteretic Spin Crossover with High Transition Temperatures in Two Cobalt(II) Complexes.

Cooperative spin crossover transitions with thermal hysteresis loops are rarely observed in cobalt(II) complexes. Herein, two new mononuclear cobalt(II) complexes with hysteretic spin crossover at relatively high temperatures (from 320 to 400 K), namely, [Co(terpy-CH2OH)2]·X2 (terpy-CH2OH = 4'-(hydroxymethyl)-2,2';6',2″-terpyridine, X = SCN-(1) and SeCN- (2)), have been synthesized and characterized structurally and magnetically. Both compounds are mononuclear CoII complexes with two chelating terpy-CH2OH ligands. Magnetic measurements revealed the existence of the hysteretic SCO transitions for both complexes. For compound 1, a one-step transition with T1/2↑= 334.5 K was observed upon heating, while a two-step transition is observed upon cooling with T1/2↓(1) = 329.3 K and T1/2↓(2) = 324.1 K (at a temperature sweep rate of 5 K/min). As for compound 2, a hysteresis loop with a width of 5 K (T1/2↓ = 391.6 K and T1/2↑ = 396.6 K, at a sweep rate of 5 K/min) can be observed. Thanks to the absence of the crystallized lattice solvents, their single crystals are stable enough at high temperatures for the structure determination at both spin states, which reveals that the hysteretic SCO transitions in both complexes originate from the crystallographic phase transitions involving a thermally induced order-disorder transition of the dangling -CH2OH groups in the ligand. This work shows that the modification of the terpy ligand has an important effect on the magnetic properties of the resulting cobalt(II) complexes.

Synthesis and Magnetic Studies of Two Neutral, Bis-Ligand Fe(II) Complexes Containing Carbazole-Bis(tetrazole) Ligands.

Previously reported carbazole-bis(tetrazole) (CzTR) ligands (where R = iPr and CH2-2,4,6-C6H2Me3) were used to synthesize air-stable, six-coordinate, octahedral bis-ligand Fe(II) complexes (CzTR)2Fe. The synthesis and characterization of these complexes using 1H nuclear magnetic resonance (NMR), X-ray crystallography, Mössbauer spectroscopy, and density functional theory (DFT) calculations are reported. Analysis of the magnetic properties revealed that the isopropyl derivative displays thermally induced spin crossover (SCO) over a temperature range of 150-350 K. This transition appears as an abrupt two-step transition in the solid state but simplifies to a smooth one-step transition in solution. The two-step transition in the solid state has been postulated to be due to lattice and solvation effects. In contrast, the slightly bulkier substituted CH2-2,4,6-C6H2Me3 (CH2Mes) Fe complex displays dramatically different magnetic behavior with no SCO and magnetic data suggesting low-spin Fe(II) with a possible TIP contribution. DFT calculations support the postulate that the change in magnetic behavior is primarily due to the nature of the ligand substituents.

Resolving the Perovskite Degradation Mechanism by Machine Learning Potential: The Case of CsPbI3

The perovskite prototype is one of the most promising solar cell materials. However, perovskite suffers from a phase transition leading to thermodynamic instability, which tightly influences the solar cell operation performance. Thus, modulating transition dynamics would extend its lifetime, which needs an in-depth understanding of the potential energy surface (PES) and the phase transition kinetics at the atomic level. In this work, taking CsPbI3 as an example of a perovskite prototype, we map out the PES and resolve the three lowest energy barrier paths of γ-CsPbI3 degradation by using a stochastic surface walking method integrated with high-dimensional neural-network potential. Path I is γ-CsPbI3 to hexagonal δ′-CsPbI3, a five-step transition with (110)Pv to (001)hex with the energy barrier 0.25 eV/f.u.; Path II is γ-CsPbI3 to cmcm-CsPbI3, a two-step transition with an over all energy barrier 0.22 eV/f.u. and (001)Pv//(110)cmcm + [010]Pv//[001]cmcm; Path III is γ-CsPbI3 to δ-CsPbI3, a one-step transition without forming an inherent interface, with the highest energy barrier 0.34 eV/f.u. Interestingly, We find that with the substitution of the A-site and/or B-site by other atoms, such as Bi and Te, the γ-CsPbI3 to δ-CsPbI3 transition could be extensively hindered. In this work, by resolving the potential energy surface, we not only reveal the degradation mechanism at the atomic level but also find a way to design perovskites with high and long-term stability.

Manipulating Electron-Transfer Events in [Fe4 Co4 ] Cubes via a Mixed-Ligand Approach: The Impact of Elastic Frustration.

The engineering of intermolecular interaction is challenging but critical for magnetically switchable molecules. Here, we prepared two cyanide-bridged [Fe4 Co4 ] cube complexes via the alkynyl- and alcohol-functionalized trispyrazoyl capping ligands. The alkynyl-functionalized complex 1 exhibited a thermally-induced incomplete metal-to-metal electron transfer (MMET) behaviour at around 220 K, while the mixed alkynyl/alcohol-functionalized cube of 2 showed a complete and abrupt MMET behaviour at 232 K. Remarkably, both compounds showed a long-lived photo-induced metastable state up to 200 K. The crystallographic study demonstrated that the incomplete transition of 1 was likely due to the possible elastic frustration originating from the competition between the anion-propagated elastic interactions and inter-cluster alkynyl-alkynyl & CH-alkynyl interactions, whereas the latter are eliminated in 2 as a result of the partial substitution by the alcohol-functionalized ligand. Additionally, the introduction of chemically distinguishable cobalt centers within the cube unit of 2 did not lead to a two-step but a one-step transition, possibly because of the strong ferroelastic intramolecular interaction through the cyanide bridges.

The bilateral birth–death chain generated by the associated Jacobi polynomials

AbstractWe give a probabilistic interpretation of the associated Jacobi polynomials, which can be constructed from the three‐term recurrence relation for the classical Jacobi polynomials by shifting the integer index n by a real number t. Under certain restrictions, this will give rise to a doubly infinite tridiagonal stochastic matrix, which can be interpreted as the one‐step transition probability matrix of a discrete‐time bilateral birth–death chain with state space on . We also study the unique UL and LU stochastic factorizations of the transition probability matrix, as well as the discrete Darboux transformations and corresponding spectral matrices. Finally, we use all these results to provide an urn model on the integers for the associated Jacobi polynomials.