Search Results (86)

Direct methods provide a model-free approach to solving the crystallographic phase problem and deliver unbiased atomic structures. However, conventional iterative projection algorithms such as Hybrid Input–Output (HIO) face two critical challenges: discontinuous density modification at the protein-solvent boundary and inaccurate molecular envelope reconstruction that fails to account for trapped solvent, particularly in crystals with solvent content approaching the lower limits of direct phasing applicability. We introduced four continuous iterative projection algorithms, including our improved continuous version, which implements smooth density modification at protein-solvent interfaces. To address envelope inaccuracy, we developed a two-step refined reconstruction scheme using sequential large-radius and small-radius Gaussian filters to identify trapped solvent molecules within surface cavities and internal channels. This scheme enhances the performance of both continuous and classical algorithms, including HIO, the difference map, and our improved versions. Benchmarking on 28 protein structures (solvent contents 55–78%, resolutions 1.46–3.2 Å, reported R-factor less than 0.22) showed that the refined envelope scheme increased average success rates of continuous algorithms by 45.7% and classical algorithms by 60.5%. The performance of continuous algorithms and improved classical algorithms proved comparable to the well-established HIO algorithm, forming a top-tier group that exceeded other classical algorithms. Integrating a genetic algorithm co-evolution strategy further enhanced average success rates by approximately 2.5-fold and accelerated convergence through population-wide information sharing. Although the success rate correlates with solvent content, our strategy improved success probability at any given solvent level, extending the practical boundaries of direct methods. The high success rate enabled averaging of multiple independent solutions, which reduced mean phase error by approximately 6.83° and yielded atomic models with backbone root-mean-square deviation (RMSD) typically below 0.5 Å relative to structures reported in the Protein Data Bank (PDB). This work introduces novel algorithms, a refined envelope reconstruction methodology, and an effective optimization strategy with genetic algorithm evolution. The complete framework enhances the capability and reliability of direct methods for phasing protein crystals with limited solvent content and provides a toolkit for addressing challenging cases in structural biology. Full article

The dynamics of open quantum systems play a crucial role in quantum information science. However, obtaining numerically exact solutions for the Lindblad master equation is often computationally expensive. Recently, machine learning techniques have gained considerable attention for simulating open quantum system dynamics. In this paper, we propose a deep learning model based on time series prediction (TSP) to forecast the dynamical evolution of open quantum systems. We employ the positive operator-valued measure (POVM) approach to convert the density matrix of the system into a probability distribution and construct a TSP model based on Transformer neural networks. This model effectively captures the historical evolution patterns of the system and accurately predicts its future behavior. Our results show that the model achieves high-fidelity predictions of the system’s evolution trajectory in both short- and long-term scenarios, and exhibits robust generalization under varying initial states and coupling strengths. Moreover, we successfully predicted the steady-state behavior of the system, further proving the practicality and scalability of the method. Full article

This study systematically verified the applicability and accuracy of the Probability Density Evolution Method (PDEM) in the probabilistic modeling of the dynamic response of anchored rock slopes under random seismic action through large-scale shaking table model tests. Across 144 sets of non-stationary random ground motions and 7 sets of white noise excitations, key response data such as acceleration, displacement, and changes in anchor axial force were collected. The PDEM was used to model the instantaneous probability density function (PDF) and cumulative distribution function (CDF), which were then compared with the results of normal distribution, Gumbel distribution, and direct sample statistics from multiple dimensions. The results show that the PDEM does not require a preset distribution form and can accurately reproduce the non-Gaussian, multi-modal, and time evolution characteristics of the response; in the reliability assessment of peak responses, its prediction deviation is much smaller than that of traditional parametric models; the three-dimensional probability density evolution cloud map further reveals the law governing the entire process of the response PDF from “narrow and high” in the early stage of the earthquake, “wide and flat” in the main shock stage, to “re-convergence” after the earthquake. The study confirms that the PDEM has significant advantages and engineering application value in the analysis of random seismic responses and the dynamic reliability assessment of anchored slopes. Full article

The environmental pollution caused by emerging organic contaminants—such as ibuprofen—is becoming increasingly a cause for alarm. New treatments for their removal are currently being developed, but the nature and toxicity of the transformation products (TPs) formed during the processes cannot be readily assessed experimentally. Atomistic simulations are thus of high interest in predicting the chemical structure of these TPs. In this paper, we demonstrate that the transformation of a contaminant molecule under irradiation can be studied using the threshold algorithm combined with the density functional-based tight-binding (DFTB) method. The fragmentation pathways of an ibuprofen molecule under irradiation are studied as a function of the energy added to the system. Specifically, the chemical structures of ibuprofen’s TPs, the paths between them, their stabilities, probabilities of occurrence, and the related mass spectra were obtained as a function of the amount of energy absorbed. We also simulated the evolution of the ibuprofen molecule as a function of the number of pulses, i.e., for a sequence of energy depositions. A dominant fragmentation scheme is identified, where first the OH group is released, followed by the loss of the CO group. The photon energy and the number of pulses are found to be key parameters for the selection of this degradation route among all identified fragmentation pathways. Full article

The quantizer–dequantizer method is employed. Using the construction of probability distributions describing density operators of a quantum system states, the connection between the Feynman path integral and the time evolution of the density operator (Landau density matrix) as well as the wave function of the stateconsidered. For single–mode systems with continuous variables, a tomographic propagator is introduced in the probability representation of quantum mechanics. An explicit expression for the probability in terms of the Green function of the Schrödinger equation is obtained. Equations for the Green functions defined by arbitrary integrals of motion are derived. Examples of probability distributions describing the evolution of state of a free particle, as well as states of systems with integrals of motion that depend on time (oscillator type) are discussed. Full article

This study proposed a cloud model-based framework for assessing the seismic robust-ness of water supply networks (WSN). A multi-scale robustness indicator system was developed, which considers physical-layer attributes (pipe material, length), topological-layer graph characteristics (node degree), and functional-layer hydraulic metrics (water supply adequacy rate). The cloud-probability density evolution method was employed to address parameter uncertainties, while Monte Carlo simulation was used to integrate these three indicators through the cloud composite weighting method to analyze the robustness qualitatively and quantitatively. The proposed method utilizes a forward cloud generator to generate the robustness distribution clouds for both net-work nodes and community-level systems, and its robustness level can be classified according to the standard cloud. A case study demonstrated the practical application of this assessment approach. The presented methodology for evaluating WSN robustness during seismic events provides critical insights for developing disaster prevention plans, formulating emergency response strategies, and implementing targeted seismic reinforcement measures. The integration of cloud theory with probabilistic assessment offers a novel paradigm for infrastructure resilience evaluation under uncertainty. Full article

Water environmental carrying capacity (WECC) is an important support for social and economic development and is closely related to regional production and consumption patterns. Exploring the level of WECC and its evolution trend is very urgent for the scientific formulation of targeted early warning control strategies. Therefore, this study first constructs the index system of WECC with a DPSIR model, and conducts the quantitative evaluation by combining the Kantiray Weighting method and the TOPSIS method. Then, the Kernel Density Estimation method and the Markov Chain model are applied to explore the spatiotemporal variation characteristics of WECC and predict its evolution trend. Finally, a case study of 17 municipal administrative regions in Hubei Province is carried out. The main findings are as follows: (1) The WECC status in Hubei Province during 2013–2022 was generally satisfactory and showed a trend of fluctuating improvement. (2) The spatial agglomeration effect of WECC in Hubei Province was significant, showing a distribution pattern of “high-high” agglomeration and “low-low” agglomeration. The improvement of the WECC in eastern Hubei was obvious, while that in central Hubei was slower, and the cities with a lower level of WECC had a more significant improvement effect. (3) Overall, the WECC of cities in Hubei Province tends to shift to a higher level. In a short period of time, the grade improvement of urban WECC in Hubei Province is more likely to occur between adjacent grades. With the increase in time span, the probability of this transition rises gradually. This study has proposed a set of methods for the evaluation and prediction of WECC status, which can provide important decision-making guidance for the early warning and regulation of regional differentiated WECC. Full article

More than a century ago, bacteriophages (phages) were discovered as entities that could both replicate and dramatically reduce bacterial culture turbidities. By the late 1940s, phage impact on broth turbidity was being studied using electronic detectors. This review examines such turbidimetric, also known as colorimetric or optical density means of studying phage biology. The focus is especially on relatively rapid and higher throughput phenotypic phage characterization versus methods that rely instead on phage plaques, spots, or genotype determinations. Topics covered include (i) the most probable number method along with Appelmans’ approach, (ii) estimation of phage growth parameters including especially that of phage lysis timing, (iii) consideration of lysis inhibition as a complicating factor, (iv) phage titering based on degrees of optical density change, (v) detection of both lysis from without and resistance to lysis from without, (vi) phage host-range determination, and (vii) study of post-lysis culture grow back, that is, of bacterial evolution of phage resistance. Based on over 30 years of experience using and studying optical density approaches to the exploration of broth-culture phage biology, the author takes a critical look at both the benefits and limitations of this increasingly common approach to phage biological characterization. Full article

Concrete creep and shrinkage are critical factors affecting the long-term performance of extradosed bridges, leading to deflection, stress redistribution, and potential cracking. Predicting these effects is challenging due to uncertainties in empirical models and a lack of long-term data. While beam element models are common in design, they often fail to capture complex stress fields in disturbed regions (D-regions), potentially leading to non-conservative assessments of crack resistance. This study presents a computationally efficient probabilistic framework that integrates the First-Order Second-Moment (FOSM) method with a high-fidelity solid element model to analyze these time-dependent effects. Our analysis reveals that solid element models predict 14% higher long-term deflections and 64% greater sensitivity to creep and shrinkage parameters compared to beam models, which underestimate both the mean and variability of deformation. The FOSM-based framework proves highly efficient, with its prediction for the standard deviations of bridge deflection falling within 7.1% of those from the more computationally intensive Probability Density Evolution Method. Furthermore, we found that time-varying parameters have a minimal effect on principal stress directions, validating a scalar application of FOSM with less than 3% error. The analysis shows that uncertainties from creep and shrinkage models increase the 95% quantile of in-plane principal stresses by 0.58MPa, which is approximately 23% of the material’s tensile strength and increases the cracking risk. This research underscores the necessity of using high-fidelity models and probabilistic methods for the reliable design and long-term assessment of complex concrete bridges. Full article

A continuum model for describing pseudo-turbulent flows of a dispersed phase is developed using a statistical approach based on the kinetic equation for the probability density of particle velocity and temperature. The introduction of the probability density function enables a statistical description of the particle ensemble through equations for the first and second moments, replacing the dynamic description of individual particles derived from Langevin-type equations of motion and heat transfer. The lack of detailed dynamic information on individual particle behavior is compensated by a richer statistical characterization of the motion and heat transfer within the particle continuum. A numerical simulation of the unsteady flow of a gas–particle suspension generated by the interaction of a shock wave with a particle cloud is performed using an interpenetrating continua model and equations for the first and second moments of both gas and particles. Numerical methods for solving the two-phase gas dynamics equations—formulated using a two-velocity and two-temperature model—are discussed. Each phase is governed by conservation equations for mass, momentum, and energy, written in a conservative hyperbolic form. These equations are solved using a high-order Godunov-type numerical method, with time discretization performed by a third-order Runge–Kutta scheme. The study analyzes the influence of two-dimensional effects on the formation of shock-wave flow structures and explores the spatial and temporal evolution of particle concentration and other flow parameters. The results enable an estimation of shock wave attenuation by a granular backfill. The extended pressure relaxation region is observed behind the cloud of particles. Full article

Economic dispatch using wind power plants plays a role in reducing the price of electricity production by dispatching power among different generating units for thermal and wind power plants, and supplying load demand while meeting the power system equality and inequality constraints. Adding wind power plants to the economic dispatch model can significantly reduce electricity production costs and reduce carbon dioxide emissions. In this paper, fuel cost and emission minimization are considered as the objective function of the economic dispatch problem, taking into account transmission loss using the B matrix. The quadratic model of the fuel cost and emission criterion functions is modeled without considering a valve-point loading effect. The real power generation limits for both wind and conventional generating units are considered. In addition, a closed-form expression based on the incomplete gamma function is provided to define the impact of wind power, which includes the cost of wind energy, including overestimation and underestimation of available wind power using a Weibull-based probability density function. In this research work, Lagrange’s algorithm is proposed to solve the Wind–Thermal Economic Emission Dispatch (WTEED) problem. The developed Lagrange classical optimization algorithm for the WTEED problem is validated using the IEEE test systems with 6-, 10-, and 40-generation unit systems. The proposed Lagrange optimization method for WTEED problem solutions demonstrates a notable improvement in both economic and environmental performance compared to other heuristic optimization methods reported in the literature. Specifically, the fuel cost was reduced by an average of 4.27% in the IEEE 6-unit system, indicating more economical power dispatch. Additionally, the emission cost was lowered by an average 22% in the IEEE 40-unit system, reflecting better environmental compliance and sustainability. These results highlight the effectiveness of the proposed approach in achieving a balanced trade-off between cost minimization and emission reduction, outperforming several existing heuristic techniques such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Differential Evolution (DE) under similar test conditions. The research findings report that the proposed Lagrange classical method is efficient and accurate for the convex wind–thermal economic emission dispatch problem. Full article

The novel engines nowadays with high efficiency are operated under the superpressure, supercritical, and supersonic extreme conditions that are situated in the broken reaction zone regime. In this article, the propagation and heat/radical diffusion physics of a high-pressure dimethyl ether (DME)/air turbulent lean-premixed flame are investigated numerically by direct numerical simulation (DNS). A wide range of statistical and diagnostic methods, including Lagrangian fluid tracking, Joint Probability Density Distribution (JPDF), and chemical explosive mode analysis (CEMA), are applied to reveal the local combustion modes and dynamics evolution, as well as the roles of heat/mass transport and cool/hot flame interaction in the turbulent combustion, which would be beneficial to the design of novel engines with high performances. It is found that the three-staged combustion, including cool-flame, warm-flame, and hot-flame fronts, is a unique behavior of DME flame under the elevated-pressure, lean-premixed condition. In the broken reaction zone regime, the reaction zone thickness increases remarkably, and the heat release rate (HRR) and fuel consumption rate in the cool-flame zone are increased by 16% and 19%, respectively. The diffusion effect not only enhances flame propagation, but also suppresses the local HRR or fuel consumption. The strong turbulence interplaying with diffusive transports is the underlying physics for the enhancements in cool- and hot-flame fronts. The dominating diffusive sub-processes are revealed by the aid of the diffusion index. Full article

Aimed at dealing with the problems of high reliability solution cost and low solution accuracy under random excitation, especially Gaussian white noise excitation, this paper proposes a probability density evolution and reliability analysis method for nonlinear gear transmission systems under Gaussian white noise excitation based on the path integration method. This method constructs an efficient probability density evolution framework by combining the path integration method, the Chapman–Kolmogorov equation, and the Laplace asymptotic expansion method. Based on Rice’s theory and combined with the adaptive Gauss–Legendre integration method, the transient and cumulative reliability of the system are path integration method calculated. The research results show that in the periodic response state, Gaussian white noise leads to the diffusion of probability density and peak attenuation, and the system reliability presents a two-stage attenuation characteristic. In the chaotic response state, the intrinsic dynamic instability of the system dominates the evolution of the probability density, and the reliability decreases more sharply. Verified by Monte Carlo simulation, the method proposed in this paper significantly outperforms the traditional methods in both computational efficiency and accuracy. The research reveals the coupling effect of Gaussian white noise random excitation and nonlinear dynamics, clarifies the differences in failure mechanisms of gear systems in periodic and chaotic states, and provides a theoretical basis for the dynamic reliability design and life prediction of nonlinear gear transmission systems. Full article

The paper innovatively studies the impact of dual randomness of structural parameters and seismic excitation on the seismic reliability of highway pile–slab structures using the probability density evolution method. A nonlinear stochastic dynamic model was established through the platform, integrating, for the first time, the randomness of concrete material properties and seismic motion variability. The main findings include the following: Under deterministic seismic input, the displacement angle fluctuation range caused by structural parameter randomness is ±3%, and reliability decreases from 100% to 65.26%. For seismic excitation randomness, compared to structural parameter randomness, reliability at the 3.3% threshold decreases by 7.99%, reaching 92.01%. Dual randomness amplifies the variability of structural response, reducing reliability to 86.38% and 62%, with a maximum difference of 20.5% compared to single-factor scenarios. Compared to the Monte Carlo method, probability density evolution shows significant advantages in computational accuracy and efficiency for large-scale systems, revealing enhanced discreteness and irregularity under combined randomness. This study emphasizes the necessity of addressing dual randomness in seismic design, advancing probabilistic seismic assessment methods for complex engineering systems, thereby aiding the design phase in enhancing facility safety and providing scientific basis for improved design specifications. Full article

Water transportation is a critical component of the overall transportation system. However, the gradual increase in traffic density has led to a corresponding rise in accident occurrences. This study proposes a quantitative framework for analyzing the evolutionary paths of maritime traffic accident risks by integrating complex network theory and link prediction methods. First, 371 maritime accident investigation reports were analyzed to identify the underlying risk factors associated with such incidents. A risk evolution network model was then constructed, within which the importance of each risk factor node was evaluated. Subsequently, several node similarity indices based on node importance were proposed. The performance of these indices was compared, and the optimal indicator was selected. This indicator was then integrated into the risk evolution network model to assess the interdependence between risk factors and accident types, ultimately identifying the most probable evolution paths from various risk factors to specific accident outcomes. The results show that the risk evolution path shows obvious characteristics: “lookout negligence” is highly correlated with collision accidents; “improper route selection” plays a critical role in the risk evolution of grounding and stranding incidents; “improper on-duty” is closely linked to sinking accidents; and “illegal operation” show a strong association with fire and explosion events. Additionally, the average risk evolution paths for collisions, groundings, and sinking accidents are relatively short, suggesting higher frequencies of occurrence for these accident types. This research provides crucial insights for managing water transportation systems and offers practical guidance for accident prevention and mitigation. Full article