Stability Of State Research Articles

Metal(triphenylphosphine)-atovaquone Complexes: Synthesis, Antimalarial Activity, and Suppression of Heme Detoxification.

To ascertain the bioinorganic chemistry of metals conjugated with quinones, the complexes [Ag(ATV)(PPh3)2] (1), [Au(ATV)(PPh3)]·2H2O (2), and [Cu(ATV)(PPh3)2] (3) were synthesized by the coordination of the antimalarial naphthoquinone atovaquone (ATV) to the starting materials [Ag(PPh3)2]NO3, [Au(PPh3)Cl], and [Cu(PPh3)2NO3], respectively. These complexes were characterized by analytical and spectroscopical techniques. X-ray diffraction of single crystals precisely confirmed the coordination mode of ATV to the metals, which was monodentate or bidentate, depending on the metal center. Both coordination modes showed high stability in the solid state and in solution. All three complexes showed negative log D values at pH 5, but at pH 7.4, while complex 2 continued to have a negative log D value, complexes 1 and 3 displayed positive values, indicating a more hydrophilic character. ATV and complexes 1-3 could bind to ferriprotoporphyrin IX (FePPIX); however, only complexes 1-3 could inhibit β-hematin crystal formation. Phenotype-based activity revealed that all three metal complexes are able to inhibit the growth of P. falciparum with potency and selectivity comparable to those of ATV, while the starting materials lack this activity. The outcomes of this chemical design may provide significant insights into structure-activity relationships for the development of new antimalarial agents.

High-Speed Atomic Force Microscopy Reveals Fluctuations and Dimer Splitting of the N-Terminal Domain of GluA2 Ionotropic Glutamate Receptor-Auxiliary Subunit Complex.

α-Amino-3-hydroxy-5-methyl-4-isoxazole propionic acid glutamate receptors (AMPARs) enable rapid excitatory synaptic transmission by localizing to the postsynaptic density of glutamatergic spines. AMPARs possess large extracellular N-terminal domains (NTDs), which are crucial for AMPAR clustering at synaptic sites. However, the dynamics of NTDs and the molecular mechanism governing their synaptic clustering remain elusive. Here, we employed high-speed atomic force microscopy (HS-AFM) to directly visualize the conformational dynamics of NTDs in the GluA2 subunit complexed with TARP γ2 in lipid environments. HS-AFM videos of GluA2-γ2 in the resting and activated/open states revealed fluctuations in NTD dimers. Conversely, in the desensitized/closed state, the two NTD dimers adopted a separated conformation with less fluctuation. Notably, we observed individual NTD dimers transitioning into monomers, with extended monomeric states in the activated/open state. Molecular dynamics simulations provided further support, confirming the energetic stability of the monomeric NTD states within lipids. This NTD-dimer splitting resulted in subunit exchange between the receptors and increased the number of interaction sites with synaptic protein neuronal pentraxin 1 (NP1). Moreover, our HS-AFM studies revealed that NP1 forms a ring-shaped octamer through N-terminal disulfide bonds and binds to the tip of the NTD. These findings suggest a molecular mechanism in which NP1, upon forming an octamer, is secreted into the synaptic region and binds to the tip of the GluA2 NTD, thereby bridging and clustering multiple AMPARs. Thus, our findings illuminate the critical role of NTD dynamics in the synaptic clustering of AMPARs and contribute valuable insights into the fundamental processes of synaptic transmission.

Intermediate-based virtual screening of c-Kit kinase inhibitors as potential anti-tumor agents via ab inito folding, molecular dynamics simulation, and molecular docking

Uncontrolled activation of c-Kit is closely related to the pathogenesis and progression of leukemia, gastrointestinal cancer, and other malignant diseases. Although there are several inhibitors available, due to the limitation of selectivity and the unfavorable side effects, designing and discovering highly selective inhibitors targeting c-Kit kinase, especially the gain of function mutation (for example c-Kit D816V), is still necessary. To identify novel c-Kit inhibitors, a metastable state-based virtual screening approach, which was successfully implemented in other kinase inhibitors, was employed in the current study. The results from our current study demonstrated the residues adjacent to the DFG motif within the activation loop could fold into short α-helices aside from the random coil, which was commonly found in the crystal structure. By expanding the conformation pool of the activation loop via PyRosetta-based ab initio folding protocol, we constructed a series of structural models of the c-Kit kinase intermediate between the inactive and active states. After evaluation of the thermal stability of the metastable state with molecular dynamics simulation, one structural model showed higher stability of α-helix, and the activation loop was retained. Considering the wild-type and D816V mutated KIT kinase shared similar metastable states during the kinase activation process, we developed a hypothesis that the identified intermediate might hold the potential to identify inhibitors targeting D816V mutations from the compound database. As expected, the intermediate structure showed higher selectivity to KIT D816V selective inhibitors, such as bezuclastinib, avapritinib, BLU-263, and elenestinib, than imatinib or masitinib. The virtual screening of the available KIT kinase inhibitor database further identified vorolanib, semaxanib, henatinib, and pexmetinib may possess potential inhibitory effects against wild type, as well as the mutated c-Kit kinase. The results from our current study not only proposed a novel structural model that could be used for the identification of selective c-Kit D816V inhibitors but also identified several potential inhibitors from available kinase inhibitors, which might shed new light on the design of new therapeutic approaches for c-Kit mutation-driven malignant diseases.

A sliding mode based foot-end trajectory consensus control method with variable topology for legged motion of heavy-duty robot

Rational foot-end trajectory planning and control are of great significance for stable-legged walking of heavy-duty multi-legged robots. To achieve a fast, active, and compliant response of the leg actuator to disturbances for improvement of the stability and flexibility of the heavy-duty legged robot system during continuous walking on rough roads, a legged consensus control method (LCC) is proposed. Firstly, the LCC includes a foot-end trajectory planner model for designing the trajectory during the swing phase to ensure that the robot’s feet are always in a safe workspace during legged motion with continuously variable direction. Secondly, LCC constructs a consensus control method for encoding foot-end position and velocity consensus error based on variable topology networks. Six legs are treated as six intelligent agents and divided into two fully connected networks: the swing phase and stance phase, to achieve smooth and consistent motion that satisfies the geometric constraints of the robot. The foot-end agent can switch between swing and stance groups according to the state of the contact with the environment accompanied by the amendment topology, to enhance the robustness of the robot system through fast compliance control of the foot-end kinematics state. Then, the sliding mode control method based on consensus velocity and position error is deduced in LCC. The sliding mode surface is designed to make the three control variables realize stable movement with a consistent state of foot-end in three X,Y,Z-axis respectively, thereby enhancing the stability of foot-end state and fuselage posture. Finally, simulation and experiments have verified that the proposed LCC can assist legged-robot perform relatively steady legged motion with continuously variable direction on various rugged roads. The body attitude Root Mean Square Error (RMSE) is quickly reduced by 81.0% compared with independent PI control. The LCC algorithm code is publicly available at https://github.com/bjmyX/LCC_code.

Accuracy analysis and improvement methods for revolving parts in counter-rotating electrochemical machining with continuous radial feeding

Counter-rotating electrochemical machining (CRECM) stands out as an efficient and cost-effective method for machining aero-engine casings. To maintain stability in the CRECM process equilibrium state, continuous feeding of the cathode tool is essential. However, this continuous feeding approach with single direction of rotation may result in poor roundness and reduced machining accuracy. This paper aims to analyze the sources and rules of roundness error and asymmetry in CRECM. Based on simulation results, a method involving periodic reverse rotation of electrodes with continuous feeding is proposed for CRECM. This approach aims to mitigate the cumulative machining error, thereby significantly improving machining accuracy. Experimental results validate the efficacy of the proposed method at a rotation speed of 0.2 rpm. The roundness error is markedly reduced from 0.19 mm to 0.04 mm, resulting in a more symmetric convex structure. Additionally, the sidewall taper angle is reduced from 14.5 degrees to 6.4 degrees. This underscores the effectiveness of the proposed method in enhancing machining accuracy.

Chiral liquid crystal dimers with smectic phases for stabilization of anticlinic state in surface-stabilised geometry

The growing demand for enhanced optical quality and faster electro-optical response in liquid crystal (LC) photonic devices has expanded the search for advanced materials capable of improving the properties of LCs beyond conventional ones. Among these compounds are LC dimers with ferroelectric and antiferroelectric properties which can be incorporated into LC mixtures to enhance performance. However, existing dimers often feature high melting temperatures, enthalpies, and other physicochemical characteristics that render them unsuitable as dopants in antiferroelectric liquid crystal (AFLC) mixtures targeted to modern photonic devices. Here, we show the design and physicochemical properties of novel dimers which are characterized by low melting points, high tilt angles and spontaneous polarizations, temperature-stable helical structures, and reasonably broad temperature ranges of ferroelectric or antiferroelectric phases. These features have facilitated the effective use of one dimer as a dopant in AFLCs. This eliminates the primary drawback of the electro-optical effect based on the surface-stabilised geometry of AFLCs by strongly promoting the anticlinic state in this effect. Importantly, for the first time, the above can be achieved without affecting any other physicochemical or optical properties of AFLCs. Thus, the obtained results represent a pivotal link between the longstanding concept of developing AFLCs that meet the stringent requirements for electro-optical effects based on surface-stabilised geometry and the realization of novel photonic devices demonstrating all the benefits of this effect.

First-principles study on electronic and mechanical properties of Ru2XAl (X = Mn, Zr, Ti, Hf) alloys

The magnetic properties of Heusler alloys have been a hot research topic. However, the current understanding of the properties of Ru-based Heusler alloys is still very limited. The magnetic, electronic, and mechanical properties of four Ru-based Heusler alloys, Ru2XAl (X = Mn, Zr, Ti, and Hf) were calculated by the first-principles. This article studied the basic mechanical parameters of four types of Heusler alloys, such as bulk elastic modulus, Cauchy pressure, Pugh’s ratio, shear modulus, Kleinman parameter, Young’s modulus, Poisson’s ratio, and elastic constant. The calculated results of the elastic constant prove that all four alloys are mechanically stable. Ru2MnAl alloy exhibits brittleness, while the other three alloys exhibit excellent ductility based on Poisson’s ratio and Pugh’s ratio. The Kleinman parameter of the four alloys are all greater than 0.5, indicating that they have stronger stability in the tensile state. In addition, the spin magnetic moment of Ru2MnAl alloy is 2.113 μB, which is consistent with the SP rule and other theoretical calculations.

Analyzing Bifurcations and Optimal Control Strategies in SIRS Epidemic Models: Insights from Theory and COVID-19 Data

This study investigates the dynamic behavior of an SIRS epidemic model in discrete time, focusing primarily on mathematical analysis. We identify two equilibrium points, disease-free and endemic, with our main focus on the stability of the endemic state. Using data from the US Department of Health and optimizing the SIRS model, we estimate model parameters and analyze two types of bifurcations: Flip and Transcritical. Bifurcation diagrams and curves are presented, employing the Carcasses method. for the Flip bifurcation and an implicit function approach for the Transcritical bifurcation. Finally, we apply constrained optimal control to the infection and recruitment rates in the discrete SIRS model. Pontryagin’s maximum principle is employed to determine the optimal controls. Utilizing COVID-19 data from the USA, we showcase the effectiveness of the proposed control strategy in mitigating the pandemic’s spread.

Tailored Sticky Solutions: 3D-Printed Miconazole Buccal Films for Pediatric Oral Candidiasis.

In this research, 3D-printed antifungal buccal films (BFs) were manufactured as a potential alternative to commercially available antifungal oral gels addressing key considerations such as ease of manufacturing, convenience of administration, enhanced drug efficacy and suitability of paediatric patients. The fabrication process involved the use of a semi-solid extrusion method to create BFs from zein-Poly-Vinyl-Pyrrolidone (zein-PVP) polymer blend, which served as a carrier for drug (miconazole) and taste enhancers. After manufacturing, it was determined that the disintegration time for all films was less than 10min. However, these films are designed to adhere to buccal tissue, ensuring sustained drug release. Approximately 80% of the miconazole was released gradually over 2h from the zein/PVP matrix of the 3D printed films. Moreover, a detailed physicochemical characterization including spectroscopic and thermal methods was conducted to assess solid state and thermal stability of film constituents. Mucoadhesive properties and mechanical evaluation were also studied, while permeability studies revealed the extent to which film-loaded miconazole permeates through buccal tissue compared to commercially available oral gel formulation. Histological evaluation of the treated tissues was followed. Furthermore, in vitro antifungal activity was assessed for the developed films and the commercial oral gel. Finally, films underwent a two-month drug stability test to ascertain the suitability of the BFs for clinical application. The results demonstrate that 3D-printed films are a promising alternative for local administration of miconazole in the oral cavity.

Impact of environmental stochastic fluctuations on the evolutionary stability of imitation dynamics.

To show the impact of environmental noise on imitation dynamics, the stochastic stability and stochastic evolutionary stability of a discrete-time imitation dynamics with random payoffs are studied in this paper. Based on the stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model, we extend the concept of stochastic evolutionary stability to the stochastic imitation dynamics, which is defined as a strategy such that, if all the members of the population adopt it, then the probability for any mutant strategy to invade the population successfully under the influence of natural selection is arbitrarily low. Our main results show clearly that the stochastic evolutionary stability of the system depends only on the properties of the mean matrix of the random payoff matrix and is independent of the randomness of the random payoff matrix. Moreover, as two examples, we show also that under the framework of stochastic imitation dynamics, the noise intensity affects the evolution of cooperative behavior in a stochastic prisoner's dilemma game and the system's nonlinear dynamic behavior.

Uncovering quantum characteristics of incipient evolutions at the photosynthetic oxygen evolving complex

Water oxidation of photosynthesis at the oxygen evolving complex (OEC) is driven by the polarization field induced by the photoelectric hole. By highlighting the role of the polarization field in reshaping the spin and orbit potentials, we reveal in this work the characteristics and underlying mechanism in the relatively simpler OEC evolutions within the states S0–S2 prior to the water oxidation. The characteristic shifts of the density of states (DOS) of the electron donor Mn atom are observed in the vicinity of the Fermi surface to occur with the spin flips of Mn atoms and the change in the Mn oxidation states during the electron transfer. Notably, the spin flips of Mn atoms point to the resulting spin configuration of the next states. It is found that the electron transfer tends to stabilize the catalyst OEC itself, whereas the proton transfer pushes the evolution forward by preparing a new electron donor, demonstrating the proton-coupled electron transfer. Meanwhile, it shows that the Mn–O bonds around the candidate Mn atom of the electron donor undergo characteristic changes in the bond lengths during the electron transfer. These concomitant phenomena uncovered in first-principle calculations characterize the essential equilibrium of the OEC between the state evolution and stability that forms the groundwork of the dynamic OEC cycles. In particular, the characteristic undulation of the DOS around the Fermi level occurring at the proton-coupled electron transfer can be used to reveal crucial processes in a wide range of realistic systems.

Enhancing freeze-thaw stability of frozen dough with deacetylated konjac glucomannan: The role of degree of deacetylation

The effect of different degrees of deacetylation (DDs) of deacetylated konjac glucomannan (DKGM) on the gluten structure, water state, and yeast activity of frozen dough was evaluated. The moderate DKGM group maintained a more continuous gluten network after three freeze-thaw cycles, as evidenced by an 8.67% increase in disulfide bond content and a 15.01% increase in α-helix content compared to the KGM group. DKGM effectively impeded bound water migration, with the moderate DKGM group retaining 8.28% more bound water than the KGM group after three freeze-thaw cycles. The stabilization of gluten structure and water state in frozen dough by DKGM resulted in higher yeast activity in the low and moderate deacetylation groups (DD = 31.31% and 50.24%). Additionally, DKGM enhanced the quality of frozen steamed bread. The results indicate that DKGM with a moderate DD (50.24%) effectively alleviates the quality deterioration of frozen dough. These findings suggest that DKGM has great potential as a novel cryoprotectant for frozen dough, with DD being a crucial factor in its cryoprotective effect.

Dynamics of chains of a large number of fully coupled oscillators, as well as oscillators with one-way and two-way delay couplings

This articles considers chains consisting of identical nonlinear equations of second order with couplings in linear elements. It is assumed that there is a large delay in the coupling elements. Moreover, we assume that the chain possesses a large number of elements. Therefore, instead of the original system with many elements, we can study a second order nonlinear integro-differential equation with periodic boundary conditions. The main study is focused on the local dynamics of chains with one-sided, two-sided couplings, as well as fully coupled chains. Also, we study the stability of equilibrium states and identify the critical cases. The condition of a sufficiently large delay helps to determine the parameters for the implementation of critical cases explicitly. Our methodology is based on the infinite-dimensional normalisation method proposed by the author, namely the method of quasinormal forms. We construct quasinormal forms for the chains under consideration that determine the asymptotics of the leading terms of the asymptotic expansions of the solutions to the original system.

Ab initio analysis of structural, electronic, magnetic, thermodynamic, and elastic properties of Half Heusler alloys ZMnAs (Z = Be, Mg) for spintronics applications

In this study, the structural, electronic, magnetic, thermodynamic, and elastic attributes of ZMnAs (Z = Be, Mg) have been investigated. These Half-Heusler alloys exhibit stability in the ferromagnetic state (FM), as demonstrated by optimization-related energy release. The half-metallicity (HM) of these compounds is examined through the band structures and density of states (DOS). In addition, the crystal field and exchange energies are reported to confirm the control of electron spin. Additionally, the double exchange process and exchange constants were premeditated. In this case, ferromagnetism (FM) is caused by the quantum exchange of electrons, as evidenced by the negative pd exchange energy and the exchange constants, rather than being a result of clustering effects. The quasi-harmonic Debye model, included within the Gibbs code, was utilized to calculate the thermodynamic properties. These two compounds are mechanically stable and show ductile nature confirmed by the value of Poisson's ratio (v), Pugh's ratio (B/G), and Cauchy pressure (CP), which demonstrates the ability to withstand substantial plastic deformation before fracturing. Based on our calculations, the half-metallic (HM) nature, thermodynamic, ferromagnetic, ductile, and high inherent magnetic moment have been evaluated. These alloys are crucial in the advancement of spintronics and renewable energy systems.

Influence of HfO2 oxide layer on crystallization properties of In3SbTe2 phase change material

Phase Change Memory (PCM) represents a potential paradigm in the realm of non-volatile memory technologies, and several phase change materials are studied for utilization in PCM devices. This work employs a less explored In3SbTe2 (IST) phase change material (active layer) integrated with an oxide (HfO2) layer and investigates the influence of the oxide layer on the active layer. The oxide layer remains amorphous when annealed at 400 °C, and it doesn’t alter the crystallization temperature (290 °C) of the active layer in IST with HfO2 thin-film. However, after crystallization, the grain size of the active layer is reduced to ∼8.23 nm in IST with HfO2 thin-film, compared to only IST thin-film. XPS core-level spectra (In 3d, Sb 3d, Te 3d) of IST active layer reveal the peak shifting towards higher binding energy at 300 °C and 400 °C annealed films, implying bond energy increase with crystallization and film stability improves. The Hf or O atoms of the oxide layer don’t diffuse into the active layer with annealing, suggesting no interference with the phase switching property of IST. A higher optical bandgap of 1.154 eV in as-deposited IST with HfO2 thin-film compared to the only IST thin-film illustrates better stability of the amorphous state in the film with the oxide layer. In addition, the fabricated PCM device using the IST with the oxide layer demonstrates phase switching at a lower threshold voltage of (2.1 ± 0.1) V, compared to the IST-based device. The findings indicate that the enhanced structural and electrical switching characteristics of IST phase change layer coupled with an oxide layer make it beneficial for data storage PCM applications.

Developing Catalysts for the Hydrolysis of Glycosidic Bonds in Oligosaccharides Using a Spectrophotometric Screening Assay.

In a proof-of-concept study, a method for the empirical design of polyacrylate gel catalysts with the ability to cleave 1→4 α-glycosidic bonds in di- and trisaccharides was elaborated. The study included the synthesis of a 300-gel member library based on two different cross-linkers and 10 acrylate monomers, identification of monomodal gels by dynamic light scattering, and a 96-well plate spectrophotometric screening assay to monitor the hydrolysis of chromophore-free maltose into glucose units. The composition of the matrix of the most efficient catalysts in the library was found to enable CH-π, hydrophobic, and H-bond accepting interactions during the hydrolysis as typically seen in glycosylases. The same gel catalysts allowed the hydrolysis of the trisaccharide maltotriose with a catalytic proficiency of 2 × 106 indicating transition state stabilization during the hydrolysis of 5 × 10-7. The results place the developed gels among the most efficient catalysts developed for the hydrolysis of natural saccharides. The elaborated strategy may lead to catalysts that can transform polysaccharides into valuable synthons in the near future.

Nitrogen: A promising doping strategy for high-performance ovonic threshold switching selectors

The Ovonic Threshold Switching (OTS) selector serves as an essential component in the development of three-dimensional high-density memory integration technology. Nevertheless, the state-of-the-art high-performance OTS materials usually contain toxic elements such as arsenic (As), posing significant risks to both environmental and human health. Nitrogen (N), which belongs to the same group as arsenic (As), has emerged as a highly promising alternative for As doping. However, the underlying mechanisms that govern N-based OTS materials have not yet been extensively investigated. In this study, we delve into the effects of N doping on the structural, bonding, and electronic properties of amorphous GeSe (a-GeNSe) by ab initio molecular dynamics simulations to bridge the knowledge gap. Our findings indicate that upon N doping in a-GeSe, the formation of robust Ge-N bonds, along with N-centered tetrahedral and triangular structures, resulting in the sluggish atomic movement that enhances the thermal stability and endurance of a-GeNSe. The OTS characteristics are significantly influenced by the material’s electronic band structure, and thus the relatively slow performance drift can be attributed to the stabilization of mid-gap states, a result of N doping which effectively slows down the aging process of chalcogenide glass. Moreover, the increased mobility gap in a-GeNSe raises the threshold voltage (Vth), making it more compatible with commercially available phase-change memory materials. Our findings reveal the extensive impact of the N element on a typical OTS material and offer valuable perspectives for alternative doping strategies that could potentially supplant As practices.

Magnetic Field Driven Dynamic Reorganization of Electrocatalytic Interface for Sustainable Enhancement in Oxygen Evolution

Hydrogen with high calorific content (150 MJ/kg) and environment-friendly combustion product (H2O) becomes the alternative fossil fuel. Catalytic electrolysis of water is one of the attractive routes for generating H2. Energy-efficient and cost-effective electrolytic production of H2 has predominantly focused on lowering the overpotential for water splitting process by developing newer non-Pt group-based catalysts.This work demonstrates a new direction towards sustainable oxygen evolution reaction (OER) by exploiting the fundamental interplay of electromagnetic forces. Introducing an external magnetic field (Hext = 100 mT) perpendicular to the heterogeneous electrocatalytic interface produces an unprecedented increase in rate of electrocatalytic OER in phosphate buffer with pH=7. Such electromagnetic catalysis is achieved with metal phosphides (NiCoP and NiCoFeP) with different morphology, leading 2.5 fold increase in the OER current density and concomitant lowering of overpotential by 10% (Hext = 100 mT). Thereby, 50% lowering of charge transfer resistance (Rct) is achieved. This is substantiated by the lowering of the Tafel slope (by 5%) in the presence of Hext. Thus, we report two important observations influenced by the magnetic field: (a) direct effect of magnetic field on the catalyst surface to reduce the charge-transfer resistance, (b) spin-dependant OER process to get influenced under magnetic field and (c) indirect effect of magnetic field to sustain the magneto-electrocatalytic enhancement even after removing the magnetic field. The time-scale of magnetic relaxation is million times higher than conventional spin-lattice relaxation events in para/ferromagnetic systems. Such long-term stability of magnetized states is predominantly proposed to be originating from the NiCoP and NiCoFeP interface. So, we attribute the long-lived states to be additionally contributed from the volumetric expansion and active site expansion of the catalyst upon magnetization. Catalyst interface is arising due to the dendritic structure of catalyst. Such synergism of magnetization, is expected to increase the applicability of magneto-electrocatalysis as a more sustainable electrocatalytic approach towards a hydrogen-driven economy. Figure 1

Effect of void geometry and magnetic anisotropy in controlling the vortex in sub-micron annular Permalloy disc

Ferromagnetic rings, particularly asymmetric Permalloy (Py) rings are recognized as promising configurations for spintronic devices, offering additional degrees of freedom for manipulating magnetic states, especially in vortex configurations. Through micromagnetic simulations, our study explores the impact on magnetization states and spin configuration concerning ring symmetry, aligning with the interest in controlling vortex states for information storage. We initially obtained zero-field spin configurations by varying ring thickness (t), observing a 360° domain wall in rings with t < 12 nm and bi-vortex wall in rings with t ∼36 nm during magnetization reversal. Notably, an extended stability of the global-vortex state was observed in rings with t > 36 nm, indicating the dominance of global-vortex nucleation in thick asymmetric rings during domain wall movement. We investigate the hysteresis loops and spin configurations by varying the in-plane and out-of-plane anisotropy values. Our findings reveal the presence of multiple vortex cores with different polarities and sense of rotations in the ring for the in-plane anisotropy ∼30 to ∼40 kJ m−3. Additionally, a global-vortex with two vortex cores was formed due to demagnetization energy. We analysed the energy profile of stable magnetization states for various t and anisotropy values. Interestingly, the shape of the hysteresis loop changes significantly for the disc containing different shapes of void. Circular and square-shaped geometries suggest that the bi-vortex state is a stable configuration during magnetization reversal in both cases. The study also indicates the stability of the vortex with a square-shaped void geometry up to a sufficiently large field. For the case of triangular-shaped voids, the global-vortex state was favored with even the small fields. The estimated spin canting angles are found to be correlated with the presence of vortex spin configurations. Overall, these results are important for the development of magnetization vortex-based spintronics devices.

Stability of equilibrium states for a stochastic difference equation of exponential form

It is well know that many process and problems in different fields of sciences and engineering can be modelled by linear and nonlinear difference equations. Particularly, in case of systems biology, ecology, biochemistry, genetics and physiology dynamics, many population models are governed by exponential difference equations, and lot of papers were published in this matter. The goal of this work is to study a nonlinear second order difference equation of exponential form: Xn+1 = bXn + cXne−σXn−1, n ≥ 0 where the parameters b, c have arbitrary values, σ &gt; 0 and the initial values, X0, X−1 are arbitrary positive numbers. Our equation has an equilibrium points and is exposed to additive stochastic perturbations that are assumed a sequence of independent random variables with zero mean, unit variance and these perturbations are proportional to the deviation of the system state Xn from equilibrium points, and the result is stochastic difference equation. We cannot find the solutions of nonlinear stochastic difference equations of exponential form in all cases. So, one can study the behavior of solutions by asymptotic stability of equilibrium points. Additionally, with the general method of Lyapunov functional constructions for stochastic difference equations with discrete time, we provide the necessary and sufficient conditions for the asymptotic mean square stability of the two equilibrium points (zero and positive) within the linear approximation of the stochastic difference equation. These conditions also serve as sufficient conditions for the stability in probability of the equilibrium points of the initial nonlinear equation. Finally, to demonstrate the validity of the obtained results, some numerical examples and simulations of equations solutions are made and numerous graphical illustrations of stability trajectories of solutions are plotted.