Continuous Model Research Articles

Energy dissipation and evolutions of the nonlocal Cahn-Hilliard model and space fractional variants using efficient variable-step BDF2 method

In this work, an energy stable BDF2 scheme with general nonuniform time steps is developed for the nonlocal Cahn-Hilliard model to capture the multi-scale behavior of evolution efficiently and accurately. The fully discrete numerical scheme is demonstrated to inherit main physical properties of the continuous model, namely, mass conservation and energy dissipation. Recently, various variants of the Cahn-Hilliard model with nonlocal operators and fractional Laplacian have attracted great attention in terms of theoretical analysis and numerical approximation, while there is less emphasis on the comparisons among the different variant models. By comparing the impact of various parameters and coarsening behaviors, numerical results suggest that the nonlocal Cahn-Hilliard model bears a strong resemblance to the space fractional Cahn-Hilliard model derived from H−1 gradient flow of the nonlocal energy. Nevertheless, the order of the fractional Laplacian appears to affect only the rate of energy decay, without altering the profile of the solution for the fractional model relating to the H−β (0<β<1) gradient flow of the classical Ginzburg-Landau energy functional in one dimensional case.

Parameter identification of a reaction-diffusion predator-prey system based on optimal control theory

This paper takes a reaction-diffusion predator-prey system with ratio-dependent Holling III functional response function and Leslie-Gower term into consideration. First of all, the system model is proposed on the basis of basic biological assumptions and previous work, and the existence conditions of the equilibrium point of the system are discussed. Secondly, under the assumption of the existence of equilibrium point, the Turing instability necessary conditions induced by diffusion are investigated. Thirdly, optimal control theory is derived, and the adjoint system and the first-order optimization condition are established. Fourthly, parameter identification based on optimal control is studied, and the technique is extended to network structure. Finally, extensive numerical simulations, including Turing pattern, Normalized Population High Distribution Area (NPHDA) diagram and parameter identification, are carried out to illustrate and validate the analytical results. For the system dynamics phenomena, the results from different perspectives effectively demonstrate that the theoretical findings, numerical simulations and natural reality are identical. In terms of the parameter identification of continuous model and network model, the efficiency and accuracy of various algorithms are fully tested.

Half-quantized Hall states with C=3/2 exited by chiral photons

The topology of Hilbert space in semiconductor quantum wells (QW) can become non-trivial when excited by an electromagnetic wave. It means the quasi-energy bands acquire a nonzero integer Floquet-Chern number even if QW is trivial in the equilibrium. We analyze electron-photon interaction in the Floquet state and identify dynamical quantum phases characterized by half-quantized Floquet-Chern numbers. The non-integer topology depends on which equilibrium state is exposed to illumination. Trivial III-V semiconductor QW's such as AlGaAs and AlGaN, being resonantly illuminated, generate the dynamical index |CF|=1/2, similar to a gapless quantum anomalous semimetal (QAS) in equilibrium. Excitation of 2D topological insulator CdHgTe reveals |CF|=3/2 - the index stemmed exclusively from interaction with chiral photons. Comparing results obtained in continuous and full-Brillouin zone (BZ) models, we conclude that high-momentum regions in BZ contribute to the dynamical half-quantized topology. Results indicate that by manipulating parameters of external force, one can bring inverted-gap QW into a non-equilibrium state with a high topological non-integer charge |CF|=3/2. We present the phase diagram, which includes all dynamical states of non-trivial topology.

Fake Currency Detection System

Abstract: This project aims to develop a robust fake currency detection system leveraging image processing and machine learning techniques. Data cleaning involves image quality enhancement and handling of torn or dirty notes. The experimental setup includes a digital camera in a controlled lighting environment to capture currency images. MATLAB is used for software setup due to its extensive libraries. The algorithm involves pre-processing, feature extraction, and classification using machine learning algorithmslike decision trees or SVM. Continual model learning ensures adaptation to emerging counterfeit techniques. This system promises effective counterfeit detection with ongoing refinement, enhancing financial security.

Predicting post-fire hydrological and erosive catchment response during rainfall events. A comparison of OpenLISEM and MOHID Land models

Wildfires are a source of instability for the natural water cycle in forested watersheds, endangering the water quantity and quality reaching downstream water bodies. The faster hydrological response of a burned area leads to increased runoff and transport of sediment and ash particles during and after rainfall events. Therefore, the use of an adequate spatiotemporal resolution in hydrological models is necessary to properly estimate post-fire impacts. Especially when addressing hydrological events such as flash floods and debris flows, which are highly unpredictable and are characterized by short duration and high impact outside the burned area.This study aims to compare the ability of two hydrological models to simulate the hydrological response and sediment transport during the first year after a fire to ultimately understand which one would best serve as a post-fire hydrological predicting tool at event scale. To achieve this goal, OpenLISEM, an event-based hydrological model, and MOHID Land, a continuous model with variable timestep, were compared. Driven by several limitations identified in previous modeling exercises at this scale during the calibration phase, this work performed a parametrization through the variation in boundary conditions characterizing each event.OpenLISEM and MOHID Land models exhibited similar capabilities in simulating runoff during the first post-fire year. However, the larger erosion input parameters required by MOHID Land increase the complexity of erosion prediction and increase equifinality. In addition, MOHID Land limited capacity to perform sensitivity and uncertainty analyses emerged as a major disadvantage, hindering the assessment of the reliability of the model's predictions. Despite its limitations for not integrating subsurface flow and base flow, OpenLISEM is the most suitable model for assessing post-fire impacts on runoff and sediment production at the event scale, because of its ease of implementation and its reduced computational requirements.

Relationship between effective blood flow rate and clinical outcomes in maintenance hemodialysis patients: a single-center study

The association between blood flow rate (BFR) and clinical outcomes in patients undergoing maintenance hemodialysis (MHD) is inconclusive. This retrospective study included 175 patients undergoing MHD treatment between July 2015 and March 2022, divided into two groups based on time-averaged effective blood flow rate (eBFR) median value. We investigated arteriovenous fistula (AVF) outcomes and the association of eBFR with all-cause mortality and new major adverse cardiovascular events (MACE). Mean ± SD and median time-averaged eBFR values were 276 ± 24 and 275 mL/min, respectively. After adjusting for relevant factors including age, sex, vintage, diabetes, CVD, receiving hemodiafiltration (HDF) treatment and spKt/V, Cox models indicated a low time-averaged eBFR (≤ 275 ml/min) was associated with increased risks of all-cause mortality (hazard ratio [HR] 14.18; 95% confidence interval [CI], 3.14–64.1) and new MACE (HR 3.76; 95% CI, 1.91–7.40) in MHD patients. Continuous Cox models demonstrated each 20 ml/min increase in eBFR linked to a 63% decrease in the risk of all-cause mortality (HR: 0.37, 95% CI: 0.23–0.59) and a 38% decrease in the occurrence of new MACE (HR: 0.62, 95% CI: 0.46–0.84). There was no significant difference in AVF outcomes between the two groups. Our study noted higher eBFR (>275 mL/min) is associated with lower risks of both all-cause mortality and new MACE compared with low eBFR (≤275 mL/min). Increased eBFR is not associated with a higher risk of AVF failure.

Grid Cells in Cognition: Mechanisms and Function.

The activity patterns of grid cells form distinctively regular triangular lattices over the explored spatial environment and are largely invariant to visual stimuli, animal movement, and environment geometry. These neurons present numerous fascinating challenges to the curious (neuro)scientist: What are the circuit mechanisms responsible for creating spatially periodic activity patterns from the monotonic input-output responses of single neurons? How and why does the brain encode a local, nonperiodic variable-the allocentric position of the animal-with a periodic, nonlocal code? And, are grid cells truly specialized for spatial computations? Otherwise, what is their role in general cognition more broadly? We review efforts in uncovering the mechanisms and functional properties of grid cells, highlighting recent progress in the experimental validation of mechanistic grid cell models, and discuss the coding properties and functional advantages of the grid code as suggested by continuous attractor network models of grid cells.

Integrated elastic identification and LOS angular rate extraction for slender rockets: A continuous-discrete maximum correntropy Kalman filter approach

Slender rockets experience significant elastic deformation during flight due to aeroelastic forces, impacting their dynamic behavior and posing challenges for traditional line-of-sight (LOS) angular rate estimation methods. This paper addresses this challenge by proposing a novel and highly accurate line-of-sight angular rate extraction model. This model integrates elastic identification with line-of-sight angular rate extraction, employing estimated generalized coordinates to calculate seeker elastic deformation. After elastic decoupling of the seeker, the slender rocket's line-of-sight angular rate can be estimated accurately. Additionally, the model incorporates a continuous-discrete maximum correntropy Kalman filter (CD-MCKF) to effectively handle the non-Gaussian measurement noise and limitations associated with discretizing the continuous model. Simulations demonstrate that the proposed method achieves significantly higher accuracy compared to existing approaches. The improved accuracy of this method can provide more precise calculations for the design of slender rocket guidance and control systems, ultimately improving the flight stability and control accuracy of rockets, and laying a solid foundation for the integrated guidance and control research of slender rockets.

The chemostat reactor: A stability analysis and model predictive control

This contribution develops the model predictive control for an unstable chemostat reactor. Initially, we analyze the system’s model — a nonlinear first-order hyperbolic partial integro-differential equation (PIDE) — and carry the model linearization around an unstable operating condition. Employing the structure-preserving Cayley–Tustin transformation, we obtain a discrete-time model representation of the continuous model. Subsequently, we solve the operator Ricatti equations in the discrete-time setting to derive a full state feedback controller that stabilizes the closed-loop and design a Luenberger observer for state reconstruction given the system output measures. Finally, we formulate a dual-mode MPC ensuring constraint satisfaction and optimality, integrating the gain-based unconstrained full-state feedback optimal control obtained from the Ricatti equation. This dual-mode strategy describes an optimization problem where the predictive controller acts only if constraints become active within the control horizon. Simulation studies validate the controller performance, where the MPC only takes action if the constraints are predicted to be active within the control horizon while also guaranteeing closed-loop stabilization under only output feedback. This type of controller can be easily implemented with other control strategies and significantly decreases the computational costs of solving the optimal control problems when compared to other MPC approaches.

Experimental Research on the Floating Amount of Shield Tunnel Based on the Innovative Cumulative Floating Amount Calculation Method

The study of shield tunnel segment flotation is crucial for controlling the precision of underground excavation projects. Based on Winkler’s beam foundation theory, the load structure method, and the equivalent continuous beam model, and by considering the mechanical and spatial conditions that cause segment flotation, a novel theoretical calculation method for cumulative flotation is proposed using a simplified equivalent stiffness model of the tunnel. Additionally, a new concept of “equivalent flotation force” is introduced. The rationality and applicability of this theoretical calculation method are verified by comparing it with on-site construction data from the Yuanjiang River Crossing Tunnel Project in Changde, Hunan Province, China. The experimental results demonstrate that the theoretical calculation closely approximates the surface deformation monitoring data of the tunnel alignment in the eastern section of the project, and their deformation patterns are similar. Near the starting shaft, there is significant settlement influenced by stratum loss due to smaller tunnel flotation, with greater settlement occurring in the upper part. However, at approximately 45 m into both sections, they enter a deformation stability zone showing significant correlation in longitudinal deformation. Through comparison and verification of on-site experiments and theoretical model analysis, we preliminarily elucidate the feasibility of this innovative cumulative flotation theoretical calculation method which provides an important theoretical basis for assessing segment flotation issues in subsequent tunnel shield construction evaluations.

Association between visceral adiposity index and risk of diabetes and prediabetes: Results from the NHANES (1999-2018).

To investigate the association between the visceral adiposity index and the prevalence of diabetes and prediabetes in the US adult population. We conducted a cross-sectional study using data from the National Health and Nutrition Examination Survey (NHANES) from 1999 to 2018 for ten consecutive years, including 18745 eligible participants. The weighted multivariate logistic model and fitting curve were used to explore the correlation and dose-response relationship between visceral adiposity index (VAI) and diabetes (DM) and prediabetes in the general population and the prevalence of different subgroups. In the fully adjusted continuous model, the risk of diabetes and prediabetes in the general population increased 0.15 times [1.15 (1.10,1.20), p<0.0001] with every increase of 1 unit of VAI. In the fully adjusted classification model, with the lowest quartile array Q1 of VAI as the reference group, Q2 of the second Quantile group, Q3 of the third Quantile group, and Q4 of the Quartile group increased 0.26 times [1.26 (1.10,1.44), p<0.001], 0.65 times [1.65 (1.43,1.89), p<0.0001], 1.60 times [2.60 (2.28,2.97), p<0.0001] respectively with the risk of diabetes and prediabetes. The above results showed that VAI was positively associated with the prevalence of diabetes and prediabetes, and the fitted curves showed a non-linear trend. (P for non-linear = 0<0.05). The results of the subgroup population were consistent with the total population and a significant interaction was found in gender (P for interaction<0.0001). In conclusion, we found a non-linear positive association between VAI and the risk of diabetes and prediabetes in the US adult population and found that women have a higher risk of diabetes and prediabetes than men; therefore, we should focus on the female population, and we call for the use of VAI to manage the development of diabetes and prediabetes in the clinical setting.

Quantitative analysis and stochastic modeling of osteophyte formation and growth process on human vertebrae based on radiographs: a follow-up study

Osteophytes are frequently observed in elderly people and most commonly appear at the anterior edge of the cervical and lumbar vertebrae body. The anterior osteophytes keep developing and will lead to neck/back pain over time. In clinical practice, the accurate measurement of the anterior osteophyte length and the understanding of the temporal progression of anterior osteophyte growth are of vital importance to clinicians for effective treatment planning. This study proposes a new measuring method using the osteophyte ratio index to quantify anterior osteophyte length based on lateral radiographs. Moreover, we develop a continuous stochastic degradation model with time-related functions to characterize the anterior osteophyte formation and growth process on cervical and lumbar vertebrae over time. Follow-up data of anterior osteophytes up to 9 years are obtained for measurement and model validation. The agreement test indicates excellent reproducibility for our measuring method. The proposed model accurately fits the osteophyte growth paths. The model predicts the mean time to onset of pain and obtained survival function of the degenerative vertebrae. This research opens the door to future quantification and mathematical modeling of the anterior osteophyte growth on human cervical and lumbar vertebrae. The measured follow-up data is shared for future studies.

A Continuous Non-Invasive Blood Pressure Prediction Method Based on Deep Sparse Residual U-Net Combined with Improved Squeeze and Excitation Skip Connections.

Arterial blood pressure (ABP) serves as a pivotal clinical metric in cardiovascular health assessments, with the precise forecasting of continuous blood pressure assuming a critical role in both preventing and treating cardiovascular diseases. This study proposes a novel continuous non-invasive blood pressure prediction model, DSRUnet, based on deep sparse residual U-net combined with improved SE skip connections, which aim to enhance the accuracy of using photoplethysmography (PPG) signals for continuous blood pressure prediction. The model first introduces a sparse residual connection approach for path contraction and expansion, facilitating richer information fusion and feature expansion to better capture subtle variations in the original PPG signals, thereby enhancing the network's representational capacity and predictive performance and mitigating potential degradation in the network performance. Furthermore, an enhanced SE-GRU module was embedded in the skip connections to model and weight global information using an attention mechanism, capturing the temporal features of the PPG pulse signals through GRU layers to improve the quality of the transferred feature information and reduce redundant feature learning. Finally, a deep supervision mechanism was incorporated into the decoder module to guide the lower-level network to learn effective feature representations, alleviating the problem of gradient vanishing and facilitating effective training of the network. The proposed DSRUnet model was trained and tested on the publicly available UCI-BP dataset, with the average absolute errors for predicting systolic blood pressure (SBP), diastolic blood pressure (DBP), and mean blood pressure (MBP) being 3.36 ± 6.61 mmHg, 2.35 ± 4.54 mmHg, and 2.21 ± 4.36 mmHg, respectively, meeting the standards set by the Association for the Advancement of Medical Instrumentation (AAMI), and achieving Grade A according to the British Hypertension Society (BHS) Standard for SBP and DBP predictions. Through ablation experiments and comparisons with other state-of-the-art methods, the effectiveness of DSRUnet in blood pressure prediction tasks, particularly for SBP, which generally yields poor prediction results, was significantly higher. The experimental results demonstrate that the DSRUnet model can accurately utilize PPG signals for real-time continuous blood pressure prediction and obtain high-quality and high-precision blood pressure prediction waveforms. Due to its non-invasiveness, continuity, and clinical relevance, the model may have significant implications for clinical applications in hospitals and research on wearable devices in daily life.

Non-smooth dynamics of impacting viscoelastic pipes conveying pulsatile fluid

This paper aims to investigate the stability and nonlinear dynamics of an initially curved viscoelastic clamped–clamped pipe conveying pulsatile fluid, with special attention to the non-smooth dynamics of this gyroscopic system under the influence of initial curvature and gravity. In this study, the impacting contact is modeled as a trilinear repulsive force. Based on the Euler–Bernoulli beam theory, the nonlinear governing equations, which take into account geometric, curvature, and damping nonlinearities, are developed using Hamilton’s principle. The continuous model is discretized using the Galerkin method and then solved using the arc-length technique and a time integration method. A linear analysis of the natural frequency and complex mode shape shows the unexpected frequency intersection and modal asymmetry. The qualitative changes in the nonlinear dynamics of the impacting pipe in both sub- and super-critical regions are examined and presented in the form of bifurcation diagrams, frequency–amplitude curves, force–amplitude curves, time histories, and phase portraits. Numerical results show that some complex dynamical behaviors can occur in different impact constraint cases, including a grazing bifurcation, sticking, period doubling, and chaos at the impact location, may occur. The initial curvature and gravity result in different behaviors, such as the asymmetry change of the equilibrium configuration and the occurrence of the flutter instability. The current analysis is significant to understand the non-smooth dynamic mechanisms and also provide design and technology guidance for the pipe system with motion-limiting constraints.

Service-aware real-time slicing for virtualized beyond 5G networks

Edge Intelligence is expected to play a vital role in the evolution of 5G networks, empowering them with the capability to make real-time decisions regarding various allocations related to their management and service provisioning to end-users. This shift facilitates the transition from a network-aware approach, where applications are developed to manage network quality fluctuations, to a service-aware network that self-adjusts based on the hosted applications. In this paper, we design and implement a service-aware network managed from the network edge. We utilize and assess various Machine Learning models to classify cellular network traffic flows in the backhaul, aiming to predict their future impact on network load. Leveraging these predictions, the network can proactively and autonomously reallocate slices in the Radio Access Network via programmable APIs, ensuring the demands of the traffic-generating applications are met. The approach integrates innovative MLOps methodologies for distributed and online training, enabling continuous model refinement and adaptation to evolving network dynamics. Our framework was tested in a real-world environment with realistic traffic scenarios, and the results were evaluated in real-time, down to a granularity of 10ms. Our findings indicate that the network can swiftly adjust to traffic, providing users with slices tailored to their application needs. Notably, our experiments show that under the studied settings, the users experienced up to 4 times lower latency (jitter) and nearly 4 times higher throughput when interacting with various applications, compared to the standard non-AI/ML unit. Furthermore, our dynamic scheme significantly optimizes resource allocation, ensuring energy efficiency by avoiding over- and under-provisioning of resources.

Effect of discretization choices when modeling the thermo-chemical history of the accreting core

Different discretizations methods applied to models of core/mantle segregations are tested (single stage, multistage accretion, results of N-body simulations) in order to test the sensitivity of the thermo-chemical coupling to the type of discretization used. We found that while single stage and large discretization of segregation steps yield very different core temperature, multistage models of accretion and core mantle segregation, at least for the model presented in this paper, tend to yield similar results, whether it is for the light element concentrations or the final temperature of the core. As long as a magma ocean existence throughout the entire process of core/mantle segregation is posited, and that only the impactor's masses of metal and silicate are re-equilibrated at each step, the degree of discretization of continuous model does not matter as long as it encompasses more than 10 steps of calculations.

Cholinergic neuromodulation of prefrontal attractor dynamics controls performance in spatial working memory.

The behavioral and neural effects of the endogenous release of acetylcholine following stimulation of the Nucleus Basalis of Meynert (NB) have been recently examined in two male monkeys (Qi et al. 2021). Counterintuitively, NB stimulation enhanced behavioral performance while broadening neural tuning in the prefrontal cortex (PFC). The mechanism by which a weaker mnemonic neural code could lead to better performance remains unclear. Here, we show that increased neural excitability in a simple continuous bump attractor model can induce broader neural tuning and decrease bump diffusion, provided neural rates are saturated. Increased memory precision in the model overrides memory accuracy, improving overall task performance. Moreover, we show that bump attractor dynamics can account for the nonuniform impact of neuromodulation on distractibility, depending on distractor distance from the target. Finally, we delve into the conditions under which bump attractor tuning and diffusion balance in biologically plausible heterogeneous network models. In these discrete bump attractor networks, we show that reducing spatial correlations or enhancing excitatory transmission can improve memory precision. Altogether, we provide a mechanistic understanding of how cholinergic neuromodulation controls spatial working memory through perturbed attractor dynamics in PFC.Significance statement Acetylcholine has been thought to improve cognitive performance by sharpening neuronal tuning in prefrontal cortex. Recent work has shown that electrical stimulation of the cholinergic forebrain in awake-behaving monkeys induces a reduction in prefrontal neural tuning under stimulation conditions that improve performance. To reconcile these divergent observations, we provide network simulations showing that these derive consistently from specific conditions in prefrontal attractor dynamics: firing rate saturation leads to increased storage precision and reduced neural tuning upon cholinergic activation via an increase in neural excitability, a reduction in neural correlations, and an increase in excitatory transmission. Our study integrates previously reported data into a consistent mechanistic view of how acetylcholine controls spatial working memory via attractor network dynamics in prefrontal cortex.

Developing a continuous SIR epidemic model and its discrete version using Euler method: Analyzing dynamics with analytical and numerical methods

Developing a continuous SIR epidemic model and its discrete version using Euler method: Analyzing dynamics with analytical and numerical methods

Multibody dynamics in robotics with focus on contact events

Abstract Multibody dynamics methodologies have been fundamental tools utilized to model and simulate robotic systems that experience contact conditions with the surrounding environment, such as in the case of feet and ground interactions. In addressing such problems, it is of paramount importance to accurately and efficiently handle the large body displacement associated with locomotion of robots, as well as the dynamic response related to contact-impact events. Thus, a generic computational approach, based on the Newton–Euler formulation, to represent the gross motion of robotic systems, is revisited in this work. The main kinematic and dynamic features, necessary to obtain the equations of motion, are discussed. A numerical procedure suitable to solve the equations of motion is also presented. The problem of modeling contacts in dynamical systems involves two main tasks, namely, the contact detection and the contact resolution, which take into account for the kinematics and dynamics of the contacting bodies, constituting the general framework for the process of modeling and simulating complex contact scenarios. In order to properly model the contact interactions, the contact kinematic properties are established based on the geometry of contacting bodies, which allow to perform the contact detection task. The contact dynamics is represented by continuous contact force models, both in terms of normal and tangential contact directions. Finally, the presented formulations are demonstrated by the application to several robotics systems that involve contact and impact events with surrounding environment. Special emphasis is put on the systems’ dynamic behavior, in terms of performance and stability.

Simulation of Solidification Structure in the Vacuum Arc Remelting Process of Titanium Alloy TC4 Based on 3D CAFE Method

Vacuum arc remelting is the main production method of titanium alloy ingots at present. In order to obtain good quality ingots, it is of great significance to study the formation of the solidification structure of ingots via vacuum arc remelting. In order to select and optimize the nucleation parameters for the solidification microstructure simulation of an ingot, a 3D CAFE model for microstructure evolution during vacuum arc remelting was established, taking into account heat transfer, flow, and solute diffusion. The Gaussian distribution continuous nucleation model and extended KGT model were used to describe the grain nucleation and dendrite tip growth rates, respectively. The multi-point mass source and moving boundary method were used to simulate the ingot growth. The results show that there are three typical crystal regions in the solidification structure of vacuum arc remelting titanium alloy ingots, namely the surface fine crystal region, columnar crystal region, and central equiaxed crystal region. The proportion of the columnar crystal region in the solidification structure of an ingot increases gradually with the increase in the undercooling of the maximum bulk nucleation. With an increase in the maximum bulk nucleation density, the equiaxed grain zone gradually increases, and the grain size gradually decreases. The proportion of the columnar crystal region in the solidification structure of an ingot increases gradually with an increase in the undercooling of the maximum bulk nucleation. The maximum volume nucleation variance has no obvious effect on the change in the solidification structure. When the maximum volume nucleation undercooling is 5.5 K, the maximum volume nucleation standard deviation is 4 K, and the maximum volume nucleation density is 5 × 108. The solidification structure simulation results are in good agreement with the experimental results.