Search Results (1,167)

Background: Patients undergoing dental treatment often experience psychological distress and social discomfort, yet longitudinal data on these changes are limited. Existing studies rely on cross-sectional designs or lengthy tools, reducing feasibility in routine practice. This study explored psychological and social trajectories during dental care, highlighting challenges and implications for patient wellbeing and care delivery. Methods: A prospective cohort study with repeated measures across three dental visits (V1–V3) was conducted. Participants completed a 21-item binary (yes/no) questionnaire assessing psychological (Q1–Q6) and social dimensions (Q7–Q14 at all visits; extended social domain Q7–Q21 at V2–V3). Composite scores were calculated, and longitudinal changes were analyzed using generalized estimating equations or mixed-effects models. Item-level trajectories were examined with multiple comparison adjustments. Results: Of 120 enrolled patients, 100 completed all visits. Psychological well-being consistently improved, while social outcomes showed more complex, domain-specific patterns. Item-level analyses revealed gains in appearance and satisfaction, whereas stigma, fear, and social integration remained relatively stable, underscoring the need to monitor multiple psychosocial dimensions. Conclusions: Psychosocial monitoring during dental care is feasible and potentially beneficial. The 21-item questionnaire was practical and well-accepted, with composite scores serving as simple indicators for tracking patient wellbeing and supporting a holistic, patient-centered approach. Further validation in larger and more diverse populations is needed. Full article

The skyhook inertance (SHI) control strategy facilitates the real-time adaptation of inertance parameters to dynamic loading conditions, consequently enhancing vehicle ride comfort. It features a simple algorithm and strong robustness. However, traditional skyhook inertance systems only adjust the magnitude of the control force by changing the inertance, without regulating the control force phase, which limits the control effect of the SHI control strategy. To solve this problem, this study introduces a fractional-order skyhook inertance (Fo-SHI) control approach. This method substitutes the second-order differential terms appearing in the conventional equation of motion of the fractional-order skyhook inertance system with fractional-order derivatives of the displacement. Consequently, the proposed strategy enables continuous and independent tuning of both the amplitude and phase of the generated control force. To achieve a realistic representation of the Fo-SHI forces, a fractional-order model integrating an adjustable damper and an inerter was developed. This model was subsequently validated through prototype testing, and its parameters were identified via a fitting process. The results of Hardware-in-the-Loop experiments demonstrate that the semi-active suspension employing the Fo-SHI control strategy achieves significant performance improvements over the conventional SHI-controlled suspension: the root mean square of body acceleration is reduced by up to 18.12% under full-load conditions, while suspension working space and dynamic tire load also show favorable responses. These findings clearly underscore the advantages and rationale for incorporating fractional-order control into vehicle suspension systems. Full article

This study presents a transient mathematical model and its numerical solution for the moving-boundary problem related to substrate diffusion and reaction in enzymatic catalytic particles. The main focus is on bioreactor startup, where the initial substrate concentration inside the particles is zero, forming a dead core that shrinks over time and makes the catalytic effectiveness factor time-dependent. The substrate mass balance leads to a partial differential equation with a moving boundary, solved using the method of lines coupled with Newton’s method (MLN), implemented in Wolfram Mathematica (WM). The proposed approach was validated for zero- and first-order kinetics at steady state, whose analytical solutions are available. Compared to the method of orthogonal collocation on finite elements, the MLN offers advantages such as not requiring an initial concentration profile and simple implementation in WM. The results demonstrate that the proposed method provides accurate and physically consistent solutions, contributing to a better understanding of dead-core dynamics and supporting the design of heterogeneous bioreactors with immobilized enzymes. Full article

In this study, we consider a potential expressed as a hyperbolic-sine function aiming to achieve the energy eigenvalues in a closed form, that is, as an analytical expression. Based on this, the Schrödinger equation is constructed within the framework of non-relativistic quantum mechanics and is tackled by using the Asymptotic Iteration Method. The potential in question was previously addressed in the literature. As an alternative, we obtain the complete energy spectrum in a closed form for the single-well regime of the potential function, by way of the quasi-exact solvability where the system has analytical energy eigenvalues once a certain condition is met, or a relation between the potential parameters is satisfied. This is provided by the applicability of the Asymptotic Iteration Method to both quasi-exact and numerical solutions. Thus, the effects of the potential parameters on the energy spectrum can be seen separately. We conclude that the accuracy of the obtained closed-form energy spectrum is quite high as evidenced by the strong agreement with the numerically obtained ones. Furthermore, it is seen that this consistency improves as the energy level increases. The obtained analytical expression can also be used as a simple analytical model for vibrational spectrum of molecular systems described by anharmonic single-well potentials. Full article

Fluid–structure interaction (FSI) effects may significantly influence the dynamic response of blast-loaded structures, particularly in lightweight configurations where the structural motion modifies the pressure loading. Despite their relevance, FSI phenomena are often neglected in engineering practice, mainly due to the computational cost of fully coupled simulations and the lack of simple predictive tools. This study presents a semi-analytical framework for estimating FSI effects in free-standing blast-loaded plates. The framework relies on one-dimensional theories accounting for non-linear gas compressibility and includes both coupled and uncoupled formulations. Their comparison provides a direct quantification of the FSI contribution to the structural response. The framework was applied to two case studies from the literature, involving different blast intensities and plate areal masses. They were selected to highlight conditions in which the reflected pressure exhibits significant temporal decay while the plate is in motion, indicating relevant FSI effects. In both cases, the coupled formulation achieves excellent agreement with the observed reference data, whereas the uncoupled solution overestimates the plate velocity. These results validate the governing equations of the coupled formulation and demonstrate that they can be reliably applied to blast-loading scenarios characterised by time-decaying pressure profiles. Thus, unlike other methods in the literature, the framework extends beyond simplified loading assumptions and offers a robust basis for rapid and cost-effective estimation of FSI effects in blast-loaded plates. Full article

We revisit a hyperbolic wildfire model based on reaction–diffusion dynamics with relaxation effects and extend it by incorporating an advection transport term that accounts for wind-driven fire spread. After a planar two-dimensional reformulation and non-dimensionalization of the model, the analysis is restricted to the minimal ignition regime characterized by the presence of a logistic reaction term governing the evolution of the fire-affected tree fraction. The focus of the study is to assess the influence of the effective wind velocity on the propagation dynamics of the fire-affected tree fraction. For this purpose, analytical solutions of the extended wildfire model are derived by applying the Simple Equations Method (SEsM) in its (1,1) variant using a Riccati-type ordinary differential equation as a simple equation. The obtained families of exact solutions describe physically relevant transition fronts connecting fire-unaffected and fully fire-affected states, or vice versa. Numerical simulations of the derived analytical solutions are performed to demonstrate how the internal front thickness and the profile morphology depend on the specific variant of the Riccati-type solution and on the magnitude of the effective wind velocity. A phase-plane stability and bifurcation analysis of the reduced traveling wave system is carried out. Hopf bifurcation thresholds with respect to the effective wind velocity parameter are identified, revealing transitions between monotone front propagation and oscillatory regimes. A regime map is constructed in the parameter plane spanned by the effective wind velocity and the traveling wave speed. This regime diagram delineates regions of qualitatively different propagation behavior, including monotone advancing fronts, possible oscillatory regimes, and regimes in which traveling wave fronts cease to exist. Full article

Calculation of heat transfer in granular materials is an important task for many applications, from thermal management in electronics to exploring celestial soils. Usually, an effective thermal-conductivity model is employed to predict heat flux in unstructured granular media, such as a packed bed. However, a more advanced approach, the discrete element method (DEM), can capture the complex effects of mechanical loading and material mixtures on thermal transport coefficients, which traditional models struggle with. Pivotal for this approach is knowing the heat transfer coefficient between two adjacent particles. Currently, in most DEM-capable software, only particles in direct surface contact are considered to have non-zero heat conduction. We propose considering particles that are close to each other but don’t have a contact area with a non-zero surface area. We perform numerical modeling of the conductive heat transfer coefficient between equal spherical particles separated by media, assuming the fluid’s thermal conductivity is at least an order of magnitude lower. We use numerical solutions of differential equations to account for both thermal resistance within particles and through the gap between them. We found a simple generalized correlation for the heat transfer coefficient between particles and a general formula for the angular distribution of heat flux density across the particle surface. By employing a non-dimensional approach, the obtained formulas are constructed using non-dimensional parameters: the ratio of the particle’s thermal conductivity to that of the medium, and the ratio of the gap width between particles to their radius. The resulting formula is simple and convenient for DEM heat transfer calculations in packed and fluidized beds. Full article

The exact response theory, also known as Transient Time Correlation Function formalism, is a powerful method concerning how observables respond to a given perturbation of the dynamics of the systems of interest, and it extends linear response theory to generic (autonomous) dynamical systems. Its main ingredient is the so-called dissipation function. In this paper, we adapt this theory for time-lagged systems, and we illustrate its applicability considering simple examples of delay equations, with different memory terms. Adopting the technique already used for time deterministic as well as stochastic time-dependent perturbations, the dynamics is described in a higher dimensional phase space, in which the delay-dependent dynamics is mapped into an augmented phase space: the new dynamics is proven to be autonomous and suitable for the exact responses to be computed. In addition, we explore the comparison between linear and exact approaches for a specific kernel choice. Full article

Time delays are inherent in modern motion-control and electric-drive loops due to sensing, filtering, sampling and computation, communication, and actuation scheduling. When such delays are only partially known, they can markedly reduce stability margins and narrow the admissible range of state-feedback gains, especially in high-bandwidth servo applications. This paper develops a design-oriented state-feedback framework for delay-affected plants based on the Manabe polynomial concept and the Coefficient Diagram Method (CDM). The plant is represented as a chain of integrators of order two to four with an effective input gain, and the feedback gain is synthesized for the nominal delay-free model by matching a standard Manabe/CDM characteristic polynomial using the classical CDM stability-index pattern. When an unmodeled input delay is present, the closed loop is governed by a delay-dependent characteristic equation. By introducing a normalized representation, the analysis yields explicit delay-stability limits that directly translate into a lower bound on the equivalent time constant used for tuning. The degradation of the phase margin and gain margin with increasing normalized delay is quantified as design charts, and a simple phase-margin-based inequality is proposed for selecting the tuning time constant, with gain-margin checks recommended as a verification step. Full article

Petroleum hydrocarbons remain major environmental contaminants, and understanding the mechanisms governing their biodegradation is essential for designing effective remediation plans. The strategy in this article is slightly different from other cases in the literature. Such literature models require, for their elaboration, a significant number of experiments; the number of experimental determinations is at least proportional to the square of the number of constants introduced in the mathematical expressions. For this reason, the strategy followed in this article is different—starting from a set of experiments carried out and presented in a coherent and published manner, a simple methodology for building specific and minimal models, which will allow solving specific problems, was effectively developed. This study develops a nonlinear mathematical structure, expressed as a system of coupled differential equations, that simultaneously describes the degradation of petroleum hydrocarbons and the dynamics of hydrocarbon-degrading bacteria and fungi in soil–sludge mixtures. The model was calibrated using experimental data obtained from biopiles prepared with different volumetric ratios of contaminated soil and sewage sludge. Approximate analytical solutions were derived and the distributed constants were evaluated. For a consistent discussion, the analytical solutions were assessed against numerical desk simulations performed with a classical fourth-order Runge–Kutta method, which accurately reproduced the nonlinear behavior of the specific system. This numerical approach was chosen in order to overcome the proper difficulties encountered in this strategy implementation. The results show that the soil–sludge ratio strongly influences biodegradation efficiency, while kinetic parameters determine whether microbial communities evolve toward a stationary regime or accelerated contaminant removal. The combined analytical–numerical framework provides a robust predictive tool for optimizing mixture composition and improving the design of bioremediation treatments for petroleum-contaminated soils. Full article

To estimate leaf area, the length-width method, also called the Montgomery equation, has been widely used. It is an empirical formula stating that within a given species, the area of a leaf is proportional to the product of its length and width. Although the formula is known to be applicable to a variety of simple leaves and leaflets, its applicability to compound leaves has only been investigated on a limited range of leaf forms and economically important crops. In this study, we investigated whether this method is broadly applicable to compound leaves of diverse forms. We measured 20 compound-leaved species including various leaf shapes (ternate, biternate, triternate, palmate, pedate, and pinnate leaves) as well as life forms (trees, herbs, and woody and herbaceous lianas). Our data cover diverse taxa, including both Ranunculales and core eudicots (Fabales, Rosales, Fagales, Vitales, Apiales, Lamiales, Asterales, and Dipsacales). The results show that the length-width method is applicable to all types of compound leaves investigated (slope [i.e., Montgomery parameter]: 0.298–1.035; R² = 0.928–0.996). These results indicate that a compound leaf can be considered equivalent to a simple lobed leaf when applying the length-width method. Full article

Traditional methods for geostressfield inversion face issues such as weak physical interpretability and insufficient generalization ability. This study pioneers the application of Physics-Informed Neural Network (PINN) to this problem, developing a data- and physics-driven inversion algorithm. The framework incorporates a constitutive-equation-based regularized loss function as a hard constraint during training to ensure physical consistency. To address boundary load uncertainty, two quantification approaches—Bayesian linear regression and surrogate model optimization—are proposed to establish 95% confidence intervals for boundary coefficients. Verification based on simple three-dimensional models and actual geological models of mines shows that PINN inversion achieves a mean absolute relative error as low as 0.0772%, with an error of 15.67% under sparse sampling conditions—significantly lower than the 31.07% error of the traditional Back propagation neural network. This demonstrates excellent robustness and data efficiency. In the practical engineering application of complex geological bodies, the average error of principal stress inversion is 9.35% with a minimum error of 0.137%. All inversion results fall within the permissible accuracy range of engineering, and the stress distribution conforms to basic laws, with an average error of 0.453 in the constitutive relation. Compared with BP neural network and multiple linear regression methods, it shows obvious accuracy advantages. This method provides a new solution for intelligent ground stress prediction with high accuracy, high efficiency, and strong physical interpretability, and also lays the foundation for early identification of geological disasters. Full article

An advanced frequency study in thick-walled functionally graded material (FGM) spherical shells is investigated with advanced shear correction. The values of advanced shear correction can be greater than one, be a negative value, and be affected by a nonlinear term of third-order shear deformation theory (TSDT) of displacements, FGM power law index, and temperature. It is novel and interesting to consider using TSDT and advanced shear correction to derive a simple homogeneous equation with reasonable simplifications into a symmetrical sparse matrix subjected to free vibration. The zero determinant of the symmetrical sparse matrix can be expressed to calculate the natural frequency by Newton’s method. The parameter effects of advanced shear correction, a nonlinear TSDT term, temperature, and the FGM power-law index on the natural frequencies of thick-walled FGM spherical shells are presented. The natural-frequency data for the axial and circumferential mode shapes are obtained. This is a new finding, as the assumed simplification in a sparse matrix causes a numerical truncation error; the natural-frequency values of the presented sparse matrix are much greater than those in a full matrix for thick-walled FGM spherical shells. Full article

Measurement models that have a chemical composition as one of the arguments require special attention when used with the law of propagation of uncertainty from the Guide to the expression of uncertainty in measurement. The constraint that the amount fractions in a composition add exactly to unity not only affects the covariance matrix associated with the composition, but also impacts the differentiation of the measurement model to obtain the expressions and values of the sensitivity coefficients. Differentiating the measurement model with respect to each variable individually is not possible as it involves evaluating the model for infeasible inputs, leading to an undefined output. In this work, a numerical method for constrained partial differentiation is presented, enabling the use of the law of propagation of uncertainty for measurement models with compositions as one of their arguments. The numerical method enables treating the measurement model as a black box and using it with measurement models in the form of an algorithm. The numerical method is demonstrated by showing how the uncertainty associated with composition, temperature and pressure can be propagated through an equation of state, in this case, the GERG-2008 equation of state. It is shown that this differentiation can be completed in a few simple steps, requiring only a valid implementation of the measurement model that provides an output value for given input quantities. The numerical differentiation method applies in principle to all differentiable functions of a composition. Full article

Optimal tracking control for high-order partially unknown nonlinear systems poses significant challenges, particularly in deriving tractable solutions without requiring persistent excitation (PE) conditions or precise system models. This study develops an adaptive optimal tracking control law using neural network (NN)-based reinforcement learning (RL) for high-order partially unknown nonlinear systems. By designing a cost function associated with the sliding mode variable (SMV), the original tracking control problem is equivalently transformed into solving the optimal control problem related to the tracking Hamilton–Jacobi–Bellman (HJB) equation. Since the analytical solution of the HJB equation is generally intractable, we employ a policy iteration algorithm derived from the HJB equation, where both the partial derivative of the optimal tracking cost function and the optimal control law are approximated by NNs. The proposed RL framework achieves simplification through actor–critic training laws derived under the condition that a simple function is zero. Finally, both a numerical example and a single-link robotic arm application are provided to demonstrate the effectiveness and advantages of the proposed adaptive optimal tracking control method. Full article