Equilibrium State Research Articles

Dynamic Active Sites In Situ Formed in Metal Nanoparticle Reshaping under Reaction Conditions.

Understanding the nonequilibrium transformation of nanocatalysts under reaction conditions is important because metastable atomic structures may be created during the process, which offers unique activities in reactions. Although reshaping of metal nanoparticles (NPs) under reaction conditions has been widely recognized, the dynamic reshaping process has been less studied at the atomic scale. Here, we develop an atomistic kinetic Monte Carlo model to simulate the complete reshaping process of Pt nanoparticles in a CO environment and reveal the in situ formation of atomic clusters on the NP surface, a new type of active site beyond conventional understanding, boosting the reactivities in the CO oxidation reaction. Interestingly, highly active peninsula and inactive island clusters both form on the (111) facets and interchange in varying states of dynamic equilibrium, which influences the catalytic activities significantly. This study provides new fundamental knowledge of nanocatalysis and new guidance for the rational design of nanocatalysts.

Ultrahigh tunneling magnetoresistance ratios in the sandwich-structured full MXene Cr2NO2/Ti2CO2/Cr2NO2 van der Waals heterojunction

In this study, the structure, magnetism, energy-band, and spin-dependent electron transport properties of the Cr2NO2/Ti2CO2/Cr2NO2 magnetic tunnel junction (MTJ) were investigated using a combination of density functional theory and non-equilibrium Green’s function methods. The calculation band structures indicate that Cr2NO2 MXene is an “ideal” half-metal with a magnetic moment of 5.00 μB. Ti2CO2 MXene is an indirect band-gap semiconductor, and the Cr2NO2/Ti2CO2-stacked heterojunction reserve 100 % spin polarization because of the weak Van der Waals interface interaction. For the equilibrium state of the most stable Cr2NO2/Ti2CO2/Cr2NO2 MTJ, the total transmission coefficient for parallel configuration is about eleven orders of magnitude larger than that for anti-parallel configuration. An ultrahigh tunneling magnetoresistance (TMR) ratio of 1.92×1013% can be detected. For the non-equilibrium state, our calculation results show that the Cr2NO2/Ti2CO2/Cr2NO2 MTJ has a good transport performance when bias voltage ranges from 0 V to 0.1 V. The minimum TMR ratio of 7.51×1012% is detected at the bias voltage of 0.09 V, which can be considered as an excellent TMR ratio. Therefore, the Cr2NO2/Ti2CO2/Cr2NO2 MTJ is an excellent candidate for spintronic device application.

Sediment DNA Records the Critical Transition of Bacterial Communities in the Arid Lake

It is necessary to predict the critical transition of lake ecosystems due to their abrupt, non-linear effects on social-economic systems. Given the promising application of paleolimnological archives to tracking the historical changes of lake ecosystems, it is speculated that they can also record the lake’s critical transition. We studied Lake Dali-Nor in the arid region of Inner Mongolia because of the profound shrinking the lake experienced between the 1300 s and the 1600 s. We reconstructed the succession of bacterial communities from a 140-cm-long sediment core at 4-cm intervals and detected the critical transition. Our results showed that the historical trajectory of bacterial communities from the 1200 s to the 2010s was divided into two alternative states: state1 from 1200 to 1300 s and state2 from 1400 to 2010s. Furthermore, in the late 1300 s, the appearance of a tipping point and critical slowing down implied the existence of a critical transition. By using a multi-decadal time series from the sedimentary core, with general Lotka-Volterra model simulations, local stability analysis found that bacterial communities were the most unstable as they approached the critical transition, suggesting that the collapse of stability triggers the community shift from an equilibrium state to another state. Furthermore, the most unstable community harbored the strongest antagonistic and mutualistic interactions, which may imply the detrimental role of interaction strength on community stability. Collectively, our study showed that sediment DNA can be used to detect the critical transition of lake ecosystems.

Methodological bases for balanced development of the food supply of the population

A retrospective analysis of the economic theories of marginal utility, general economic equilibrium, spatial economics, production factors, and organization theory was carried out from the position of forming the methodological basis for the emergence of the theory of balanced development of food supply for the population. The substantive aspects of the critical concepts of the identified theories are detailed in their influence on the formation and formation of the methodology for food supply to the population, including maintaining a balanced and equilibrium state in the conditions of continuous influence of external factors on food systems. For each identified theory, provisions have been established that determine the relationship with the methodology of the area under study. It has been established that the emergence of the theory and methods of balanced development of food supply for the population is a natural stage in the evolution of economic science in the context of increasing the role and importance of man in the modern economy. The methodological grounds identified are the need to achieve and maintain a balanced human diet, ensure coordination and maintain a balance of social and economic interests of consumers and food producers, ensure a balanced state of food production and consumption, maintain a balance of resource capabilities and future food needs of people, prevent the emergence of imbalances in the food sector. The work results can be used to develop new conceptual frameworks for developing the domestic agro-industrial complex and allow us to form a more holistic and detailed understanding of the specifics and features of achieving balanced agri-food sector development.

Limited effect of the confluence angle and tributary gradient on Alpine confluence morphodynamics under intense sediment loads

Abstract. Confluences are dynamic morphological nodes that are found in all river networks. In mountain regions, they are influenced by hydraulic and sedimentary processes that occur in steep channels during extreme events in small watersheds. Sediment transport in the tributary channel and aggradation in the confluence can be massive, potentially causing overbank flooding and sedimentation into adjacent settlement areas. Previous works dealing with confluences have mainly focused on lowland regions, and those that have focused on mountain areas have used sediment concentrations and channel gradients that are largely under-representative of mountain river conditions. The presented work contributes to filling this research gap with 45 experiments that use a large-scale physical model. Geometric model parameters, the applied grain size distribution, and the considered discharges represent the conditions at 135 confluences in South Tyrol (Italy) and Tyrol (Austria). The experimental program allowed for a comprehensive analysis of the effects of (i) the confluence angle, (ii) the tributary gradient, (iii) the channel discharges, and (iv) the tributary sediment concentration. In contrast to most research dealing with confluences, results indicate that, in the presence of an intense tributary sediment supply and a small tributary-to-main-channel discharge ratio (0.1), the confluence angle does not have a decisive effect on confluence morphology. Adjustments to the tributary channel gradient yielded the same results. A reoccurring range of depositional geomorphic units was observed in which a deposition cone transitioned to a bank-attached bar. The confluence morphology and tributary channel gradient rapidly adjusted, tending towards an equilibrium state to accommodate both water discharges and the sediment load from the tributary. Statistical analyses demonstrated that the confluence morphology was controlled by the combined channel discharge and the depositional or erosional extent was controlled by the sediment concentration. Applying conclusions drawn from lowland confluence dynamics could misrepresent depositional and erosional patterns and the related flood hazard at mountain river confluences.

Competitive adsorption mechanisms of multicomponent gases in kaolinite under electric fields: A molecular perspective

The investigation of the competitive adsorption mechanisms of gas mixtures within the inorganic nanopores of shale influenced by an electric field holds paramount importance for improving shale gas recovery and enhancing CO2 storage efficiency. This study employs molecular dynamics (MD) simulations to investigate the competitive adsorption mechanisms of gas mixtures on kaolinite surfaces. Subsequently, the engineering parameters governing electric field-enhanced CO2 sequestration and enhanced gas recovery (CS-EGR) are explored and optimized. In the absence of an electric field, the analysis reveals that water molecules exhibit the highest adsorption capacity in a ternary H2O–CO2–CH4 mixture, resulting in the formation of a water film of a specific thickness. CO2 displays a superior adsorption capability over CH4. As the CO2 volume injected into the reservoir increases, CH4 undergoes desorption due to the dominant adsorption effect of CO2. However, the efficiency of CO2 displacing CH4 diminishes significantly. The introduction of an electric field alters the equilibrium state of the gas mixture, leading to a further increase in CO2 adsorption and enhancing its selectivity relative to that of CH4 by 33%. These findings lay the foundation for the practical implementation of electric field-enhanced CS-EGR in shale reservoirs.

Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping

Recently, Li–Fu–Wang (Li et al., 2022) established the optimal temporal decay rates of solutions near the equilibrium state to the 3D compressible magnetohydrodynamic system with nonlinear damping αuβ−1u for β⩾3. In this paper, we further extend Li–Fu–Wang’s result to the case β>1 by finer energy estimates.

Concerning for the solvent-polarity-dependent conformational equilibrium and ESIPT mechanism in Pz3HC system: A novel insight

In this report, we propose a new insight into the interaction between the solvent-polarity-dependent conformational equilibrium and excited state intramolecular proton transfer (ESIPT) behavior of Pz3HC system in four different polar solvents (polarity order: ACN > THF > TOL > CYC). Using quantum chemistry method, we first announce a coexistence mechanism between Pz3HC-1 and Pz3HC-3 in the ground state in four solvents based on the Boltzmann distribution. In particular, Pz3HC-1 is the principal configuration in non-polar solvent, but Pz3HC-3 is the principal configuration in polar solvent. In addition, the simulated fluorescence spectra interprets the negative solvatochromism effect of Pz3HC-1 and Pz3HC-3 in four solvents. The evidence from intramolecular hydrogen bonding (IHB) parameters and electronic perspective collectively confirms the light-induced IHB enhancement and intramolecular charge transfer (ICT) properties in Pz3HC-1 and Pz3HC-3, which raises the likelihood of the ESIPT process. Combining the calculation of potential energy curve (PEC) and intrinsic reaction coordinate (IRC), we demonstrate that the ESIPT ease of Pz3HC-1 in different polar solvents obeys the order of CYC > TOL > THF > ACN, while the order of ESIPT ease in Pz3HC-3 is opposite. Notably, the ESIPT process of Pz3HC-3 in CYC solvent is accompanied by the twisted intramolecular charge transfer (TICT) process. In addition, we also reveal that the enol* and keto* fluorescence peaks of Pz3HC-3 in CYC solvent are quenched by ISC and TICT process, respectively. Our work not only provides a satisfactory explanation of the novel dynamics mechanism for Pz3HC system, but also brings light to the design and application of new sensing molecules in the future.

Casein-quaternary chitosan complexes induced the soft assembly of egg white peptide and curcumin for ulcerative colitis alleviation

Soft assembly of peptide and curcumin (Cur) molecules enables functional integration by finding dynamic equilibrium states through non-covalent interactions. Herein, we developed two soft assembly systems, curcumin-egg white peptides (Cur-EWP) aggregations (AGs) and Cur-EWP-casein-quaternary chitosan (Cur-EWP-CA-QC) nanoparticles (NPs) to comparatively investigate their therapeutic effects on ulcerative colitis in mice and elucidate their underlying mechanism. Results revealed that Cur-EWP AGs, despite gastrointestinal tract instability, exhibited a propensity for swift accumulation within the colorectal region, enriching mucus-associated and short-chain fatty acid (SCAF)-producing bacteria, restoring the intestinal barrier damage. Whereas, Cur-EWP-CA-QC NPs, benefiting from their remarkable stability and exceptional mucosal adsorption properties, not only enhanced permeability of Cur and EWP in the small intestine to activate the immune response and boost tight junction protein expression but also, in their unabsorbed state, regulated the intestinal flora, exerting potent anti-inflammatory activity. Soft assembly of peptides and hydrophobic nutraceuticals could synergize biological activities to modulate chronic diseases.

Streamlining Protein Fractional Synthesis Rates Using SP3 Beads and Stable Isotope Mass Spectrometry: A Case Study on the Plant Ribosome.

Ribosomes are an archetypal ribonucleoprotein assembly. Due to ribosomal evolution and function, r-proteins share specific physicochemical similarities, making the riboproteome particularly suited for tailored proteome profiling methods. Moreover, the structural proteome of ribonucleoprotein assemblies reflects context-dependent functional features. Thus, characterizing the state of riboproteomes provides insights to uncover the context-dependent functionality of r-protein rearrangements, as they relate to what has been termed the ribosomal code, a concept that parallels that of the histone code, in which chromatin rearrangements influence gene expression. Compared to high-resolution ribosomal structures, omics methods lag when it comes to offering customized solutions to close the knowledge gap between structure and function that currently exists in riboproteomes. Purifying the riboproteome and subsequent shot-gun proteomics typically involves protein denaturation and digestion with proteases. The results are relative abundances of r-proteins at the ribosome population level. We have previously shown that, to gain insight into the stoichiometry of individual proteins, it is necessary to measure by proteomics bound r-proteins and normalize their intensities by the sum of r-protein abundances per ribosomal complex, i.e., 40S or 60S subunits. These calculations ensure that individual r-protein stoichiometries represent the fraction of each family/paralog relative to the complex, effectively revealing which r-proteins become substoichiometric in specific physiological scenarios. Here, we present an optimized method to profile the riboproteome of any organism as well as the synthesis rates of r-proteins determined by stable isotope-assisted mass spectrometry. Our method purifies the r-proteins in a reversibly denatured state, which offers the possibility for combined top-down and bottom-up proteomics. Our method offers a milder native denaturation of the r-proteome via a chaotropic GuHCl solution as compared with previous studies that use irreversible denaturation under highly acidic conditions to dissociate rRNA and r-proteins. As such, our method is better suited to conserve post-translational modifications (PTMs). Subsequently, our method carefully considers the amino acid composition of r-proteins to select an appropriate protease for digestion. We avoid non-specific protease cleavage by increasing the pH of our standardized r-proteome dilutions that enter the digestion pipeline and by using a digestion buffer that ensures an optimal pH for a reliable protease digestion process. Finally, we provide the R package ProtSynthesis to study the fractional synthesis rates of r-proteins. The package uses physiological parameters as input to determine peptide or protein fractional synthesis rates. Once the physiological parameters are measured, our equations allow a fair comparison between treatments that alter the biological equilibrium state of the system under study. Our equations correct peptide enrichment using enrichments in soluble amino acids, growth rates, and total protein accumulation. As a means of validation, our pipeline fails to find "false" enrichments in non-labeled samples while also filtering out proteins with multiple unique peptides that have different enrichment values, which are rare in our datasets. These two aspects reflect the accuracy of our tool. Our method offers the possibility of elucidating individual r-protein family/paralog abundances, PTM status, fractional synthesis rates, and dynamic assembly into ribosomal complexes if top-down and bottom-up proteomic approaches are used concomitantly, taking one step further into mapping the native and dynamic status of the r-proteome onto high-resolution ribosome structures. In addition, our method can be used to study the proteomes of all macromolecular assemblies that can be purified, although purification is the limiting step, and the efficacy and accuracy of the proteases may be limited depending on the digestion requirements. Key features • Efficient purification of the ribosomal proteome: streamlined procedure for the specific purification of the ribosomal proteome or complex Ome. • Accurate calculation of fractional synthesis rates: robust method for calculating fractional protein synthesis rates in macromolecular complexes under different physiological steady states. • Holistic ribosome methodology focused on plants: comprehensive approach that provides insights into the ribosomes and translational control of plants, demonstrated using cold acclimation [1]. • Tailored strategies for stable isotope labeling in plants: methodology focusing on materials and labeling considerations specific to free and proteinogenic amino acid analysis [2].

Research Progress on Inhibition of Osteoclast Differentiation by Traditional Chinese Medicine

Background: Bone tissue undergoes continuous remodeling to maintain a steady state of bone equilibrium. During this process, osteoblasts actively stimulate bone formation, while osteoclasts continuously engage in bone resorption. The dynamic equilibrium between bone formation and bone resorption is crucial for maintaining bone structure. In a healthy human skeletal structure, the two components are constantly in a state of benign dynamic equilibrium. However, due to factors such as aging, trauma, bone diseases, and other influences, the activity of osteoblasts decreases while the activity of osteoclasts increases. This disrupts the dynamic equilibrium, leading to a decrease in bone metabolism. As a result, bone resorption gradually surpasses bone production, making it challenging to maintain a normal amount of bone mass. The effectiveness of traditional Chinese medicine in treating bone-related disorders is extraordinary, and its molecular biological mechanism has become a widely discussed subject. Objectives: This study aims to unravel the classical signaling pathways and potential targets involved in the effects of traditional Chinese medicine on osteoclast differentiation, and to provide evidence for its clinical efficacy. Methodology: The main keywords chosen for this study were “Traditional Chinese Medicine (TCM)”, “osteoclast differentiation”, “natural plant”, and “medicinal plant”. To gather relevant literature, we utilized multiple online search engines, including PubMed, Web of Science, and CNKI, as well as other publication resources. Results: The results indicated that Traditional Chinese Medicine (TCM) can modulate signaling pathways, including NF-κB, MAPKs, STATs, and Wnt/β-catenin pathways., to influence osteoclast differentiation. This modulation involves maintaining the balance of inflammatory interactions, inhibiting oxidative stress. Conclusion: The impact of traditional Chinese medicine on osteoclast differentiation is reflected on multiple levels and through various pathways. Future research is envisioned to delve deeper from the perspective of precision-targeted therapy, aiming to provide insights for identifying the core targets of traditional Chinese medicine in treating orthopedic diseases.

Stochastic distinguishability of Markovian trajectories.

The ability to distinguish between stochastic systems based on their trajectories is crucial in thermodynamics, chemistry, and biophysics. The Kullback-Leibler (KL) divergence, DKLAB(0,τ), quantifies the distinguishability between the two ensembles of length-τ trajectories from Markov processes A and B. However, evaluating DKLAB(0,τ) from histograms of trajectories faces sufficient sampling difficulties, and no theory explicitly reveals what dynamical features contribute to the distinguishability. This work provides a general formula that decomposes DKLAB(0,τ) in space and time for any Markov processes, arbitrarily far from equilibrium or steady state. It circumvents the sampling difficulty of evaluating DKLAB(0,τ). Furthermore, it explicitly connects trajectory KL divergence with individual transition events and their waiting time statistics. The results provide insights into understanding distinguishability between Markov processes, leading to new theoretical frameworks for designing biological sensors and optimizing signal transduction.

Thermodynamic information geometry of criticality, fluctuation anomaly and hyperscaling breakdown in the spin-3/2 chain

Equilibrium state space geometry is worked out for the exactly solved one-dimensional spin-3/2 lattice with a Blume–Emery–Griffiths (BEG) Hamiltonian as well as a more general one with a non-zero field coupled to the octopole moments. The phase behaviour of the spin-3/2 chain is revisited and novel observations of anomaly in the hyperscaling relation and in the decay of fluctuations are reported for the first time. Using the method of constrained fluctuations developed earlier in Sahay (2017); Sanwari and Sahay (2022) three appropriate state space sectional curvatures and a 3d curvature are shown to separately encode dipolar, quadrupolar and octopolar correlations both near and away from pseudo-criticality. In all observations of hyperscaling breakdown the 3d scalar curvature is found to encode the correlation length while the relevant sectional curvature equals the inverse of singular free energy. For parameter values where the order parameter fluctuation anomalously decays despite a divergence in its correlation length the relevant scalar curvature undergoes a sign change to positive values, signalling a possible change in the nature of the underlying statistical interactions.

Modeling the Transmission Dynamics of Tuberculosis in Humans

Tuberculosis (TB) is a major threat to human health particularly in most of developing countries. In this article, we formulate and analyze a deterministic model for the transmission dynamics of pulmonary and extra-pulmonary tuberculosis. The next generation method is employed to find the basic reproduction number R0 which helps to determine whether TB clears or persists in the human population. Global stability of model equilibria is done through Lyapunov functions whereas the normalized forward sensitivity index method is adopted to determine parameters that drive tuberculosis. Analysis shows that both TB free and endemic equilibria exist. The TB free equilibrium is globally asymptotically stable whenever the basic reproduction number R0 < 1 whereas the endemic equilibrium is globally asymptotically stable whenever R0 > 1. Sensitivity analysis shows that the TB infection rate, the fraction of individuals who progress to pulmonary tuberculosis and its induced death drive TB. Numerical results indicate that when there are no interventions, susceptible humans decline significantly with time until when they are attracted to the steady state whereas latently infected, pulmonary and extra-pulmonary TB individuals increase until when they settle at the equilibrium states supporting the analytical results for existence of the endemic equilibrium. In light of these findings, we recommend treating humans infected with pulmonary TB who are carriers of the disease.

Measuring friction from simulations of folded graphene sheets.

We ran molecular dynamics simulations of folded graphene sheets and present a procedure to measure the sliding friction in these systems based on the rate of decay of a damped harmonic oscillator. This procedure allowed us to study the effect that the size, geometry, and the temperature of the graphene sheet had on the ability to propagate the initial fold and the rate at which it settles to a final "fully folded" equilibrium state. We offer simple rationalizations for the relationships between the initial geometries of our simulations and the friction values that emerge.

Study on the Influence of Runner and Overflow Area Design on Flow-Fiber Coupling in a Multi-Cavity System.

Fiber-reinforced composites (FRPs) are characterized by their lightweight nature and superior mechanical characteristics, rendering them extensively utilized across various sectors such as aerospace and automotive industries. Nevertheless, the precise mechanisms governing the interaction between the fibers present in FRPs and the polymer melt during industrial processing, particularly the manipulation of the flow-fiber coupling effect, remain incompletely elucidated. Hence, this study introduces a geometrically symmetrical 1 × 4 multi-cavity mold system, where each cavity conforms to the ASTM D638 Type V standard specimen. The research utilizes theoretical simulation analysis and experimental validation to investigate the influence of runner and overflow design on the flow-fiber coupling effect. The findings indicate that the polymer melt, directed by a geometrically symmetrical runner, results in consistent fiber orientation within each mold cavity. Furthermore, in the context of simulation analysis, the inclusion of the flow-fiber coupling effect within the system results in elevated sprue pressure levels and an expanded core layer region in comparison to systems lacking this coupling effect. This observation aligns well with the existing literature on the subject. Moreover, analysis of fiber orientation in different flow field areas reveals that the addition of an overflow area alters the flow field, leading to a significant delay in the flow-fiber coupling effect. To demonstrate the impact of overflow area design on the flow-fiber effect, the integration of fiber orientation distribution analysis highlights a transformation in fiber arrangement from the flow direction to cross-flow and thickness directions near the end-of-fill region in the injected part. Additionally, examination of the geometric dimensions of the injected part reveals asymmetrical geometric shrinkage between upstream and downstream areas in the end-of-fill region, consistent with microscopic fiber orientation changes influenced by the delayed flow-fiber coupling effect guided by the overflow area. In brief, the introduction of the overflow area extends the duration in which the polymer melt exerts control in the flow direction, consequently prolonging the period in which the fiber orientation governs in the flow direction (A11). This leads to the impact of fiber orientation on the flow of the polymer melt, with the flow reciprocally affecting the fibers. Subsequently, the interaction between these two elements persists until a state of equilibrium is achieved, known as the flow-fiber coupling effect, which is delayed.

A mixed trigger volumetric growth law for cylindrical deformation in stressed configurations

Soft tissue growth is crucial across various physiological applications, with mathematical modelling playing a pivotal role in understanding the underlying processes. The volumetric growth theory serves as a commonly used mathematical framework in this context. Our previous research on volumetric growth theory primarily concentrated on defining the incremental growth tensor in loaded and stressed configurations, revealing that this approach closely aligns with experimental observations of residual hoop stress distribution. However, given the assumptions employed, the approach has limitations in accurately predicting the growth timeline. In this work, we address these issues by incorporating the effect of initial residual strain and introducing a new mixed trigger growth evolution law. In this growth law, we do not use growth saturation as an upper limit, as this assumption cannot represent many physiological conditions. Instead, we propose that growth in soft tissues leads to a new equilibrium state. To illustrate this idea, we introduce a growth incompatibility function, denoted as [Formula: see text]. We establish the analytical relationship between [Formula: see text] and the opening angle in a simplified cylindrical geometry resembling the structure of the heart or arteries. We put forth a revised growth law that is both stress and incompatibility driven/Our results show that by using this mixed trigger growth law, tissues will not grow indefinitely. Instead, a stress-driven homeostasis incompatibility state will be reached. In addition, by accounting for the initial opening angle in the model, we can accurately trace the growth history of the heart, aligning with experimental data obtained from measuring the opening angle in young pigs from birth to maturity.

Autogenic shrinkage and channel destabilization of an overexpanded downstream alluvial system under steady rise of relative sea level: An experimental study

The dynamics of downstream alluvial systems undergoing relative sea level (RSL) rise exhibit significant variations depending on spatial size. According to autostratigraphy theory, such systems cannot sustain deltaic sedimentation under a steady RSL rise (rate Rslr), and are prone to non-deltaic transgression once their plain area A exceeds the critical limit Acrt. During this transgression, A decreases asymptotically toward Acrt, while the overall alluvial aggradation rate Ragg_overall increases toward Rslr. In this study, we investigated the behavior and morphodynamics of an overexpanded system through physical modeling, with a focus on the inherent area scale of the depositional system. In the early stages of non-deltaic transgression (A >> Acrt, Ragg_overall << Rslr), the alluvial channels experience minimal aggradation rate Ragg_channel (< Rslr), leading to stabilization and inundation. As the transgression progresses, the channels aggrade more rapidly, increasing the likelihood of lateral migration and avulsion. Eventually, a state of morphodynamic equilibrium is reached, characterized by A ∼ Acrt, Ragg_overall ∼ Rslr, and Ragg_channel ∼ constant > Rslr despite sustained non-deltaic transgression. During this equilibrium stage, the channels undergo rapid aggradation, resulting in complete destabilization with continuous lateral migration and frequent avulsion, forming system-wide subaqueous steps. The implications of overexpansion and autogenic shrinkage in response to RSL rise extend to stratigraphic convergence during RSL cycles and provide insights into Holocene non-deltaic transgression. Moreover, when combined with decelerating RSL rise, this process could have facilitated marine delta development. However, projected accelerated RSL may lead many modern marine deltas to transition into non-deltaic transgressive systems. Additionally, natural alluvial channels may exhibit varying behavior depending on the spatial size of the non-deltaic transgressive system. Furthermore, the autogenic shrinkage model may offer an explanation for the stepped surfaces observed on alluvial fans and deltas on Mars.

Stability analysis of uncertain simple pendulum equation *

The law of motion of a simple pendulum system is described by an uncertain simple pendulum equation which is a second-order uncertain differential equation driven by Liu process (LP). The stability of a simple pendulum system refers to whether the system tends to the equilibrium state under small perturbation. In order to discuss the sensitivity of the uncertain simple pendulum equation to the perturbation in the initial state, we give the concept of many kinds of stability of the uncertain simple pendulum equation, including almost deterministic stability, distributional stability and exponential stability. And, the sufficient conditions of almost deterministic stability, distributional stability and exponential stability of the uncertain simple pendulum equation are proved respectively.

Finite and fixed‐time stabilization of discrete‐time systems using passivity‐based control

AbstractIn this paper, we propose a new passivity‐based controller design technique for discrete‐time fully actuated systems. The controller establishes finite‐time and fixed‐time convergence of dynamical system trajectories to an equilibrium state. A new form of a dissipation function, selected a priori, is introduced to design a feedback control rule to achieve such convergence properties. An energy shaping and damping injection methodology is extended to achieve non‐asymptotic stabilization. A numerical example to validate the proposed methods is provided.