Dynamic Equations Research Articles

Friend Emotional Support and Dynamics of Adolescent Socioemotional Problems.

Emotional support from friends is a crucial source of social support for adolescents, significantly influencing their psychological development. However, previous research has primarily focused on how this support correlates with general levels of socioemotional problems among adolescents, neglecting the significance of daily fluctuations in these problems. The aim of this study was to explore the relationship between friend emotional support and both the average and dynamic indicators of daily emotional and peer problems in adolescents. These dynamic indicators include within-domain dynamics-such as inertia, which reflects the temporal dependence of experiences, and volatility, which indicates within-person variance-and cross-domain dynamics, such as transactional effects, which measure the strength of concurrent or lagged associations between daily emotional and peer problems. Participants were 315 seventh-grade Chinese adolescents (Mage = 13.05 years, SD = 0.77 years; 48.3% girls). Adolescents reported on their friends' emotional support at baseline and then completed measures of daily emotion and peer problems over a 10-day period. Using dynamic structural equation models, the results revealed that higher levels of friend emotional support were associated with fewer daily socioemotional problems. This was evident both in terms of average levels and dynamic aspects, characterized by lower mean levels of daily emotional and peer problems, reduced inertia and volatility of these problems, and a weaker spillover effect from daily emotional issues to peer problems. These findings highlight the significant role of friend-emotional support in mitigating adolescents' daily socioemotional challenges.

Strength-induced Peridynamic model for the dynamic failure of porous materials

Predicting the dynamic failure process of porous materials is a challenging task due to their complex structure. To minimize the use of time-consuming peridynamic (PD) models and to avoid surface effect issues in the dynamic failure of complex porous materials, this paper proposes a strength-induced PD model. The paper first presents the dynamic formula and relevant finite element discrete equation of the coupled PD and classical continuum mechanics (PD-CCM) model based on the Morphing method. The Morphing function is implemented to control the material parameters and enable the free transformation of PD and CCM models. Based on the coupled PD-CCM model, the strength-induced PD model is established to adaptively expand the PD subdomain in porous materials by controlling the Morphing function value through the strength state of the structure. This model enables the PD subdomain to appear automatically when the porous materials reach the critical stress state. The proposed model accurately predicts the location of crack initiation and path while minimizing computational costs and improving efficiency. Three two-dimensional numerical examples are used to verify the effectiveness, efficiency, and accuracy of the model. The results of the simulation suggest that the location where the crack initiates in the porous materials is strongly influenced by the amplitude of the dynamic load. Cracking is dependent on the pores and typically occurs through them.

Optimized Design of a Soft Actuator Considering Force/Torque, Bendability, and Controllability via an Approximated Structure

Abstract This paper introduces a novel design method that enhances the force/torque, bendability, and controllability of soft pneumatic actuators (SPAs). The complex structure of the soft actuator is simplified by approximating it as a cantilever beam. This allows us to derive approximated nonlinear kinematic models and a dynamical model, which is explored to understand the correlation between natural frequency and dimensional parameters of SPA. The design problem is then transformed into an optimization problem, using kinematic equations as the objective function and the dynamical equation as a constraint. By solving this optimization problem, the optimal dimensional parameters are determined. Six prototypes are manufactured to validate the proposed approach. The optimal actuator successfully generates the desired force/torque and bending angle, while its natural frequency remains within the constrained range. This work highlights the potential of using optimization formulation and approximated nonlinear models to boost the performance and dynamical properties of soft pneumatic actuators.

Asymptotic generalization errors in the online learning of random feature models

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the last layer is trainable, known as the random feature model. We study over-parametrization in the context of a student-teacher framework by deriving a set of differential equations for the learning dynamics. For any finite ratio of hidden layer size and input dimension, the student cannot generalize perfectly, and we compute the non-zero asymptotic generalization error. Only when the student's hidden layer size is exponentially larger than the input dimension, an approach to perfect generalization is possible. Published by the American Physical Society 2024

Stability and causality of rest frame modes in second-order spin hydrodynamics

We analyze the low- and high-momentum rest frame modes in the second-order spin hydrodynamics and check the asymptotic causality of the theory. A truncation scheme of the Israel-Stewart formalism derived in our earlier work is proposed that extends the minimal causal formulation. It consists of altogether 40 interconnected relaxation-type dynamical equations—16 (24) of them correspond to the independent components of the energy-momentum (spin) tensor. Similarly to previous studies, we find that the stability of the perturbations and asymptotic causality require using the spin equation of state that satisfies the generalized Frenkel condition demanding that the “electric” and “magnetic” components of the spin density tensor have opposite signs. For low-momentum modes this behavior is similar to that found earlier for the first-order (Navier-Stokes) spin hydrodynamics. Published by the American Physical Society 2024

A novel game-based belief rule base

Establishing an initial belief rule base (BRB) expert system typically relies on expert knowledge. However, the heterogeneity in knowledge arising from variations in expert cognition directly impacts the accuracy and robustness of BRB. Furthermore, the existing research lacks a discussion on building the initial BRB under multi-expert knowledge. In response to this challenge, a novel game-based belief rule base (GBRB) is proposed in this paper. First, a consensus matrix is introduced to formalize the interaction among expert knowledge, which is the foundation for constructing a multi-expert evolutionary game. Subsequently, the replicator equation for population dynamics is employed to simulate the dynamic process of the multi-expert evolutionary game. Finally, optimal expert knowledge, which refers to referential values and belief degrees, is determined based on the evolution results to participate in establishing GBRB. Case studies are conducted to illustrate the construction process and effectiveness of the GBRB. The experimental results are compared with machine learning-related methodologies. The comparative results demonstrate the good performance of GBRB in modeling effectiveness and prediction accuracy.

A tripartite model of the psychotherapy relationship: Interrelations among its components and their unfolding across sessions.

The tripartite model of the therapy relationship, which includes the working alliance, real relationship, and transference-countertransference configuration, has been a useful way to conceptualize the complexity of the connection between a therapist and a client. However, little research has focused on the interrelationships between these three components over time. This study sought to replicate the findings of Bhatia and Gelso (2018) by examining the between-person relationships among each of the three elements averaged across all sessions. Additionally, we extended earlier work by examining the within-person relationship between the working alliance, the real relationship, and transference-countertransference with themselves as well as with each of the other elements across sessions. Using 5,931 sessions across 142 clients and 36 therapists, we examined time-ordered associations among the cocreated working alliance, cocreated real relationship, and the therapist-rated transference-countertransference configuration using latent variable dynamic structural equation modeling. Results replicated the findings of Bhatia and Gelso (2018), demonstrating that in one session, the working alliance and the real relationship were positively related, and both the working alliance and the real relationship were negatively related to the transference-countertransference configuration. Regarding the interrelations over time, the findings revealed that the working alliance in the previous session had a significant and positive relationship with real relationship in the current session, and the real relationship in the previous session was related to reduced transference-countertransference in the current session. These findings provide support for complex interrelations among the components over time. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Kinematic modelling of three link robot manipulator and joint torque optimization using genetic algorithm in MATLAB

This research article presents the non-linear dynamic of a three-link robotic manipulator formulated by the Newton-Euler method. The planar manipulator is composed of three links and three revolute joints rotating about the z-axis. The three nonlinear non-homogeneous dynamic equations have been solved graphically with the help of MATLAB by phase variable method. The work represents the graphical solution of the transient response of angular position, and angular velocity of each link member for a predetermined interval of time. With the help of simulated value from MATLAB, torque characteristics have been determined for different torque ratios and optimum torque has been derived using a genetic algorithm to move the manipulator in a proper direction.

Cosmological time crystals from Gauss-Bonnet gravity in four dimensions

We investigate various cosmological aspects of a 4-Dimensional Gauss-Bonnet Lagrangian, which is integrated into the Einstein Lagrangian with an arbitrary sign, using the Friedman-Lemaître-Robertson-Walker (FLRW) metric. We consider a general potential term, V(a), that depends on the scale factor a, and we analyze several scenarios by investigating the critical points of the dynamical equations and stability conditions to understand how the universe's behavior is affected by the Gauss-Bonnet term. Our research suggests that choosing the negative sign, this integration allows for the spontaneous breaking of time reflection symmetry. This can lead to the generation of a wall-bounce universe even with a normal matter sector, marking a significant departure from traditional theories. Furthermore, we examine the possibility of a time-crystal universe, showing that under certain circumstances, the theory might give rise to cyclic universes.

Evolution and stability of bubbles in cement-based materials under low air pressure: A Theoretical and experimental Study

In recent years, more and more infrastructures are being built in high-altitude regions where the atmospheric pressure is lowered. However, low atmospheric pressure affects bubble stability, which deteriorates the frost resistance of concrete and the sustainability of civil infrastructures in high-altitude regions. Currently, the evolution of bubbles in cement-based materials under low air pressure is unclear. Therefore, we developed the bubble dynamic differential equation which considering the viscosity of cement paste to describe bubble evolution and stability in cement-based materials; investigated the effect of nano-bubble water (NBW) on bubble stability in cement-based materials; and revealed the stabilization mechanism of bubbles reinforced by NBW. An experimental apparatus that integrates pressure regulating, bubbling, observation, and data recording is designed. The high-precision microscope and air-void analyzer are employed to study the dynamic evolution of bubble distribution over time and the hardened air-void parameters. The bubble dynamic differential equation indicates that the decrease of initial bubble size can improve bubble stability. The experimental results show that the average bubble diameter at low air pressure (0.5P) is larger than that at standard air pressure (P), and bubbles evolve more rapidly at 0.5P; when NBW is used, the average bubble diameter at P and 0.5P is reduced by 24.5% and 48.8%, respectively, and bubbles evolve more slowly. The stabilization principle of bubbles reinforced by NBW is discussed. It is proved that low atmospheric pressure affects the generation and evolution of bubbles, while NBW can reduce initial bubble size and improve bubble stability in cement-based materials. This research not only establishes bubble dynamic differential equation in cementitious materials, but also proposes an effective approach to improve bubble stability of cement-based materials at low atmospheric pressure, which promotes the sustainable development of infrastructures in high-altitude regions.

Analysis of optical solitons propagation in the dual-mode resonant nonlinear Schrödinger dynamical equation with assorted nonlinear interactions

Analysis of optical solitons propagation in the dual-mode resonant nonlinear Schrödinger dynamical equation with assorted nonlinear interactions

Online estimation of vertical velocity for deep-sea carriers based on depth data

Seabed residential stations are essential for the future exploration of the deep-sea exploration. Deep-sea carriers accompany transport equipment for underwater resident stations. To accommodate the low-energy consumption and low-cost nature of deep-sea carriers, an online vertical velocity estimation method based on depth data is proposed. This method serves as a cost-effective alternative to the expensive acoustic and inertial velocity measurement equipment conventionally used in underwater navigation systems. To meet the demand for low-cost online velocity measurements, a dynamic model was created for buoyancy-driven vehicles such as deep-sea carriers during unpowered ascent. Two distinct methods were used to process depth sensor data: one involves central differencing followed by low-pass filtering, and the other entails the differentiation of the data after fitting it to dynamic equations. This approach yields two different types of estimated velocities. A sliding window was defined and used the variance of the velocity and fitting coefficient within the window as indicators to assess the uncertainty of the velocity data. Based on this evaluation, an adaptive weight allocation rule for the fusion process was formulated. This approach allows us to derive the weighted estimated velocity. Through lake trials, the weighted estimated velocity was validated to closely match the ideal velocity data and showed a substantial reduction in velocity variance compared to the differenced estimated velocity that was not fused. This indicates that the fluctuations in the velocity data were significantly reduced. In addition, the integrated displacement showed an average absolute error of 0.1769 m compared with the measured displacement. This indicates that the weighted estimated velocity effectively reflects the true state of motion of the deep-sea carrier. Furthermore, when unexpected motion occurs in deep-sea carriers, the weighted estimated velocity can prevent falling into the "smoothness trap.” This demonstrated the robustness of the proposed algorithm.

Generalized extended (2+1)-dimensional Kadomtsev-Petviashvili equation in fluid dynamics: analytical solutions, sensitivity and stability analysis

Generalized extended (2+1)-dimensional Kadomtsev-Petviashvili equation in fluid dynamics: analytical solutions, sensitivity and stability analysis

Advanced Thick FGM Plates-Cylindrical Shells in Linear Unsteady Supersonic Flow

Introduction:: Thick functionally graded (FG) plates-cylindrical shells with third-order shear deformation theory (TSDT) of displacement models under thermal vibration in linear unsteady supersonic flow are investigated by using the generalized differential quadrature (GDQ) method. Method:: The nonlinear coefficient term of TSDT models and the advanced nonlinear shear correction coefficient expression are used to study the thermal vibration of thick FG plates and cylindrical shells in linear unsteady supersonic flow. At the intersection of FG plates-cylindrical shells, the displacements, stress resultants, and moment resultants could be reasonably assumed in the continuity condition for the differential volume in linear unsteady supersonic flow, respectively. Result:: The dynamic equilibrium differential equations of thick FG plates and cylindrical shells in linear unsteady supersonic flow, respectively in terms of partial derivatives of displacements and shear rotations subjected to partial derivatives of thermal loads, mechanical loads consist of the linear supersonic aerodynamic pressure and inertia terms can be presented. Two parametric effects including environment temperature and functionally graded material (FGM) power law index on the thermal stress and center displacement of thick FG plates-cylindrical shells in linear unsteady supersonic flow are investigated. Conclusion:: The linear unsteady supersonic flow over the outer surface of thick FG platescylindrical shells provides the additional aerodynamic effect on the values of displacements and stresses.

Idiographic bidirectional associations of stressfulness of events and negative affect in daily life as indicators for mental health: An experience sampling study.

Evidence suggests that complex micro-dynamics occurring in daily life underly the development of mental distress. We aimed to (1) study the cross-lagged association between stressful events and negative affect (NA), (2) show that there is substantial between-person variability in idiographic associations and (3) show that idiographic associations are indicative of mental health. Experience sampling study assessing perceived stressfulness of events (PSE) and NA four times per day for 2weeks in a non-clinical convenience sample (N=70, mean age=22.9, 61% female, 69% German). Bivariate vector autoregressive model implemented in dynamic structural equation modelling to model the associations between stressful events and NA and obtain idiographic associations. Stressfulness of events and NA were significantly reciprocally associated. Autocorrelations and cross-lagged associations from PSE to NA showed substantial variability and were significantly related with trait measures of depression, anxiety, well-being, and perceived stress. Contrary to expectations, cross-lagged associations from NA to stressfulness of events were not related to trait mental health. The approach outlined in this article is useful for studying idiographic dynamics in daily life. The findings increase our understanding of micro-dynamics underlying mental health and individual differences in these processes.

Applications of Structural Nabla Derivatives on Time Scales to Dynamic Equations

We present here more general concepts of Hausdorff derivatives (structural Nabla derivatives) on a timescale. We examine structural Nabla integration on temporal scales. Using the fixed-point theorem, we establish adequate criteria for the question of existence and uniqueness of the solution to an initial value problem characterized by structural Nabla derivatives on timescales. Furthermore, some features of the new operator are proven and illustrated by using concrete examples.

Towards accelerating particle‐resolved direct numerical simulation with neural operators

AbstractWe present our ongoing work aimed at accelerating a particle‐resolved direct numerical simulation model designed to study aerosol–cloud–turbulence interactions. The dynamical model consists of two main components—a set of fluid dynamics equations for air velocity, temperature, and humidity, coupled with a set of equations for particle (i.e., cloud droplet) tracing. Rather than attempting to replace the original numerical solution method in its entirety with a machine learning (ML) method, we consider developing a hybrid approach. We exploit the potential of neural operator learning to yield fast and accurate surrogate models and, in this study, develop such surrogates for the velocity and vorticity fields. We discuss results from numerical experiments designed to assess the performance of ML architectures under consideration as well as their suitability for capturing the behavior of relevant dynamical systems.

Research on the influence of flexible wheelset rotation effect on wheel rail contact force

PurposeUnder the high-speed operating conditions, the effects of wheelset elastic deformation on the wheel rail dynamic forces will become more notable compared to the low-speed condition. In order to meet different analysis requirements and selecting appropriate models to analyzing the wheel rail interaction, it is crucial to understand the influence of wheelset flexibility on the wheel-rail dynamics under different speeds and track excitations condition.Design/methodology/approachThe wheel rail contact points solving method and vehicle dynamics equations considering wheelset flexibility in the trajectory body coordinate system were investigated in this paper. As for the wheel-rail contact forces, which is a particular force element in vehicle multibody system, a method for calculating the Jacobian matrix of the wheel-rail contact force is proposed to better couple the wheel-rail contact force calculation with the vehicle dynamics response calculation. Based on the flexible wheelset modeling approach in this paper, two vehicle dynamic models considering the wheelset as both elastic and rigid bodies are established, two kinds of track excitations, namely normal measured track irregularities and short-wave irregularities are used, wheel-rail geometric contact characteristic and wheel-rail contact forces in both time and frequency domains are compared with the two models in order to study the influence of flexible wheelset rotation effect on wheel rail contact force.FindingsUnder normal track irregularity excitations, the amplitudes of vertical, longitudinal and lateral forces computed by the flexible wheelset model are smaller than those of the rigid wheelset model, and the virtual penetration and equivalent contact patch are also slightly smaller. For the flexible wheelset model, the wheel rail longitudinal and lateral creepages will also decrease. The higher the vehicle speed, the larger the differences in wheel-rail forces computed by the flexible and rigid wheelset model. Under track short-wave irregularity excitations, the vertical force amplitude computed by the flexible wheelset is also smaller than that of the rigid wheelset. However, unlike the excitation case of measured track irregularity, under short-wave excitations, for the speed within the range of 200 to 350 km/h, the difference in the amplitude of the vertical force between the flexible and rigid wheelset models gradually decreases as the speed increase. This is partly due to the contribution of wheelset’s elastic vibration under short-wave excitations. For low-frequency wheel-rail force analysis problems at speeds of 350 km/h and above, as well as high-frequency wheel-rail interaction analysis problems under various speed conditions, the flexible wheelset model will give results agrees better with the reality.Originality/valueThis study provides reference for the modeling method of the flexible wheelset and the coupling method of wheel-rail contact force to the vehicle multibody dynamics system. Furthermore, by comparative research, the influence of wheelset flexibility and rotation on wheel-rail dynamic behavior are obtained, which is useful to the application scope of rigid and flexible wheelset models.

Steady Solutions to Equations of Viscous Compressible Multifluids

For the differential equations of the barotropic dynamics of compressible viscous multifluids in a bounded three-dimensional domain with an immobile rigid boundary, a study of the solvability of the boundary value problem is made. Weak generalized solutions to the boundary value problem are shown to exist with weak constraints on the types of viscosity matrices and constitutive equations for pressure and momentum exchange.

Asymptotically safe cosmology with non-canonical scalar field

We investigate the quantum modified cosmological dynamical equations in a Friedmann–Lemaître–Robertson–Walker universe filled with a barotropic fluid and a general non-canonical scalar field characterized by a Lagrangian similar to k-essence model but with a potential term. Quantum corrections are incorporated by considering the running of the gravitational and potential couplings, employing the functional renormalization group approach. Covariant conservation of the non-canonical scalar field and the background barotropic fluid is considered separately, imposing a constraint resulting from the Bianchi identity. This constraint determines the evolution of the cut-off scale with the scale factor and also reveals the cosmic fixed points, depending on whether the flow ceases or continues to evolve. We explore how the general non-canonical scalar field parameter affects the different types of cosmic fixed points and how it differs from the canonical case. Furthermore, we establish a bound on the ratio of the renormalization group parameters involving the non-canonical parameter for which the universe may exhibit accelerated expansion for mixed fixed points. This bound indicates the non-canonical scalar field includes larger sets of asymptotically safe renormalization group fixed point which may give rise to an accelerated universe.