First-order Time Research Articles

The 36-Item Yoni Task: Normative Data for the Clinical Assessment of Theory of Mind

Background: The evaluation of Theory of Mind (ToM) in the clinical setting remains limited due to the lack of valid instruments for a quick and reliable assessment. In this study, the psychometric properties of the Yoni-36 task were tested, and correction grids, equivalence scores, and normative data were computed. Methods: In total, 318 healthy subjects (169 females; mean age = 42.22 ± 18.11 years; mean education = 15.01 ± 3.43 years) were enrolled and administered the Yoni-36 task. Results: Statistical analysis showed good-to-high internal consistency, split-half reliability, and discrimination ability (especially for the second-order items) of the Yoni-36 task. Regression models highlighted the predictive role of age and education on second-order, affective, cognitive accuracy, and response time scores. Education influenced the first-order ToM response time score as well. Based on β values of the regressions, raw scores of the Yoni task were adjusted for sex, age, and education, and correction grids were computed. The equivalent scores indicated an accuracy index score < 0.69 and a response time index score < 0.83 as cut-off points for ToM competence. Normative data reported a mean accuracy and response time index score of 0.90 ± 0.11 and 0.91 ± 0.05 in the Italian population, respectively. Conclusions: The Yoni-36 proved to be a valid instrument for a quick and reliable ToM assessment, suitable to be included in neuropsychological batteries and to be used in routine clinical practice.

Temporal error monitoring: Does agency matter?

Error monitoring is the ability to report one's errors without relying on feedback. Although error monitoring is investigated mostly with choice tasks, recent studies have discovered that participants parametrically also keep track of the magnitude and direction of their temporal, spatial, and numerical judgment errors. We investigated whether temporal error monitoring relies on internal generative processes that lead to the to-be-judged first-order timing performance. We hypothesized that if the endogenous processes underlie temporal error monitoring, one can monitor timing errors in emitted but not observed timing behaviors. We conducted six experiments to test this hypothesis. The first two experiments showed that confidence ratings were negatively related to error magnitude only in emitted behaviors, but error directionality judgments of observed behaviors were more precise. Experiment 3 replicated these effects even after controlling for the motor aspects of first-order timing performance. The last three experiments demonstrated that belief of agency (i.e., believing that the error belongs to the self or someone else) was critical in accounting for the confidence rating effects observed in the first two experiments. The precision of error directionality judgments was higherin thenon-agency condition. These results show that confidence is sensitive to belief, and short-long judgment is sensitive to the actual agency of timing behavior (i.e., whether the behavior was emitted by the self or someone else).

A thermodynamics-consistent spatiotemporally-nonlocal model for microstructure-dependent heat conduction

The spatiotemporally-nonlocal phenomena in heat conduction become significant but challenging for metamaterials with artificial microstructures. However, the microstructure-dependent heat conduction phenomena are captured under the hypothesis of spatiotemporally local equilibrium. To capture the microstructure-dependent heat conduction phenomena, a generalized nonlocal irreversible thermodynamics is proposed by removing both the temporally-local and spatially-local equilibrium hypotheses from the classical irreversible thermodynamics. The generalized nonlocal irreversible thermodynamics has intrinsic length and time parameters and thus can provide a thermodynamics basis for the spatiotemporally-nonlocal law of heat conduction. To remove the temporally-local equilibrium hypothesis, the generalized entropy is assumed to depend not only on the internal energy but also on its first-order and high-order time derivatives. To remove the spatially local equilibrium hypothesis, the thermodynamics flux field in the dissipation function is assumed to relate not only to the thermodynamics force at the reference point but also to the thermodynamics force of the neighboring points. With the developed theoretical framework, the thermodynamics-consistent spatiotemporally-nonlocal models can then be developed for heat transfer problems. Two examples are provided to illustrate the applications of steady-state and transient heat conduction problems.

The localized RBF interpolation with its modifications for solving the incompressible two-phase fluid flows: A conservative Allen–Cahn–Navier–Stokes system

In this research work, we apply a numerical scheme based on the first-order time integration approach combined with the modifications of the meshless approximation for solving the conservative Allen–Cahn–Navier–Stokes equations. More precisely, we first utilize a first-order time discretization for the Navier–Stokes equations and the time-splitting technique of order one for the dynamics of the phase-field variable. Besides, we use the local interpolation based on the Matérn radial function for spatial discretization. We should solve a Poisson equation with the proper boundary conditions to have the divergence-free property during the numerical algorithm. Accordingly, the applied numerical procedure could not give a stable and accurate solution. Instead, we solve a regularization system in a discrete form. To prevent the instability of the numerical solution concerning the convection term, a biharmonic term with a small coefficient based on the high-order hyperviscosity formulation has been added, which has been approximated by a scalable interpolation based on the combination of polyharmonic spline with polynomials (known as the PHS+poly). The obtained full-discrete problem is solved using the biconjugate gradient stabilized method considering a proper preconditioner. We investigate the potency of the numerical scheme by presenting some simulations via uniform, hexagonal, and quasi-uniform nodes on rectangular and irregular domains. Besides, we have compared the proposed meshless method with the standard finite element method due to the used CPU time.

Analytical trajectory prediction of high-eccentricity spacecraft transfer orbits considering J2 perturbation

Using the perturbation method, the problem of high-accuracy rapid prediction for high-eccentricity spacecraft transfer orbit considering the J2 perturbation is solved. First, an auxiliary geocentric coordinate system is constructed based on the main flight plane of the spacecraft, and a generalized dynamics model considering the J2 perturbation is established by introducing the auxiliary longitude as the independent variable in that coordinate system. Since the J2 term is quite small, using the perturbation method, the dynamics model is decomposed into a zeroth-order system and a first-order system, where the solution of the zeroth-order system is just the analytical solution of the Kepler orbit, but the first-order system is complex and thus difficult to solve. The exact solutions for the first-order heading angle and auxiliary latitude are derived successfully. The approximate analytical solutions for first-order speed, flight path angle, and auxiliary longitude are obtained using a collocation method. Finally, Chebyshev polynomials are employed to derive an approximate analytical solution for the first-order flight time. Simulation results affirm the superiority of the proposed analytical solutions over Kozai's mean elements method and Biria's improved intermediary method.

Relay feedback identification and PI-PD control of asymmetrical heating and cooling processes

A common type of nonlinear system in the field of process industry is asymmetrical heating and cooling processes. These systems have two operating modes, heating and cooling, each with a particular dynamic feature. This study deals with identifying and controlling such processes. The relay feedback identification method based on the state-space approach, which results in exact estimates, is used in the identification procedure to achieve two first-order plus dead time (FOPDT) process models. Following process identification, two sets of PI-PD controller parameters are acquired in line with the user-defined gain and phase margin specifications, and the system is controlled using a gain-scheduled PI-PD control method. Some simulation examples are provided to demonstrate the use and profitability of the suggested identification and control approaches. Comparisons with a similar study are provided for both identification and control approaches to clearly demonstrate the benefits of the suggested procedures.

A switched system approach to exponential stabilization of interval type-2 fuzzy nonlinear systems with packet dropouts

This paper investigates the exponential stabilization problem for interval type-2 (IT2) fuzzy system with parameter uncertainties and packet dropouts. The sample-and-hold characteristic is simulated by employing an input delay methodology, and we present a model for the packet dropout phenomenon using switched approach. Some novel two-side delay-dependent looped-functionals are proposed by considering state information in the intervals from tr to t and t to tr+1 which relaxes the monotonic constraint of the Lyapunov–Krasovskii functional (LKF) and enhances the utilization of the actual sampling pattern. Additionally, some free-weighting matrices, slack matrices, the bound information in membership functions (MFs) and the signs of the first-order time derivative of fuzzy MFs are used to obtain a novel relaxed sufficient conditions for exponential stabilization of interval type-2 fuzzy systems (IT2 FS). Based on the LKF theory, new relaxed sufficient conditions with linear matrix inequalities (LMIs) constraints are derived. According to the criterion, sampled-data controller is devised to ensure that the closed-loop system is exponential stabilization. Finally, an illustrative example is presented to demonstrate the practicality and effectiveness of the method proposed. Comparative analysis highlights the simplicity and practicality of the suggested algorithm.

Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport

The purpose of this paper is to study the fundamental solution of the time-space bi-fractional diffusion equation incorporating an additional kinetic source term in semi-infinite space. The equation is a generalization of the integer-order model ∂tρ(x,t)=∂x2ρ(x,t)-ρ(x,t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\partial _{{t}} {\\rho (x,t)}} = {\\partial ^2_{{x}} {\\rho (x,t)}} - { \\rho (x,t)}$$\\end{document} (also known as the Debye–Falkenhagen equation) by replacing the first-order time derivative with the Caputo fractional derivative of order 0<α<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<\\alpha < 1$$\\end{document}, and the second-order space derivative with the Riesz-Feller fractional derivative of order 0<β<2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0< \\beta <2$$\\end{document}. Using the Laplace-Fourier transforms method, it is shown that the parametric solutions are expressed in terms of the Fox’s H-function that we evaluate for different values of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}.

Modeling gas flow in low-permeability formations: An efficient combination of mixed finite elements and high order time integration schemes

Numerical simulation of gas flow in low permeability formations is a challenging task due to the high nonlinearity induced by (i) the compressibility of the gas, (ii) the Klinkenberg slippage effect and (iii) the Langmuir adsorption of the gas on the pore surface. Because of these nonlinearities, modeling gas flow in low permeability formations requires a great deal of computational effort. In this work, we develop an efficient numerical model using advanced spatial and temporal discretization methods for a simultaneous solution of the coupled equations of gas flow, cubic Peng-Robinson equation of state, slippage effect and Langmuir adsorption. The spatial discretization is performed with the lumped hybrid formulation of the mixed finite element method which is well adapted for fluid flow in heterogeneous porous media. The time integration is performed with high-order methods via the method of lines (MOL) which allows large time steps and efficient solution of the nonlinear system of equations. Numerical experiments, performed for gas extraction in a heterogeneous domain, point out the high efficiency of the new model since it can be until 10 times more efficient than the classical first-order time discretization method. Results of global sensitivity analysis show that the intrinsic gas-phase permeability and the Klinkenberg factor are the most influential parameters controlling the pumping rate in the case of gas extraction in a homogeneous domain.

Convergence of a TPFA finite volume scheme for nonisothermal immiscible compressible two-phase flow in porous media

This paper presents and analyzes a finite volume scheme for a fully degenerate parabolic system modeling the compressible two-phase flow, such as water-gas, problem in porous media considering the effects of temperature. The problem is written in terms of the phase formulation, i.e. the saturation of one phase, the pressure of the second phase and the temperature are primary unknowns. We use a first-order time implicit Euler scheme. The spatial discretization uses a fully coupled fully implicit cell-centered two-point flux approximation scheme where upwinding of the flux across an interface between two control volumes is performed for each fluid phase. Under physically relevant assumptions on the data, we prove the maximum principle for both saturation and temperature. We obtain a priori estimates and we show that the discrete problem is well posed. Also, we exploit various a priori estimates as well as compactness arguments to establish the convergence of the numerical scheme toward the weak solution. The open-source platform DuMuX was employed for the implementation of the developed algorithm based on the above scheme. Numerical result are presented to demonstrate the efficiency of this scheme. The test addresses the evolution in 2D of CO2 injection into a layered aquifer. The algorithm's convergence with first order is validated by our numerical results, which support the theoretical results. To our best knowledge, this is the first convergence result of a finite volume scheme in the case of nonisothermal immiscible compressible two-phase flow in porous media.

Trajectory tracking for non-holonomic mobile robots: A comparison of sliding mode control approaches

This paper implements and compares the performance of three controllers based on Sliding Mode Control (SMC) applied to the motion control of mobile robots. The controllers include a standard SMC controller and two variations, namely Dynamic Sliding Mode Control (D-SMC) and Dual Sliding Mode Control (DM-SMC). The three controllers differ from conventional SMC approaches since they are designed based on a generic reduced-order empirical model that can represent any system that exhibits behavior akin to a First-Order Plus Delay Time (FOPDT) system. In this study, the comparison of controllers focuses on the Trajectory Tracking Problem (TTP) of a Nonholonomic Mobile Robot (NMR). Performance indices are employed to quantify the controllers' results across three trajectory types. Simulation results evidence that if a smooth curvature trajectory is tracked, the best performance (in terms of minimizing trajectory tracking error and controller effort) can be obtained by using a DM-SMC. On the other hand, if there are discontinuities in the curvature, the results suggest that a better alternative is the D-SMC since it compensates for abrupt changes as in the case of tracking a square trajectory. Overall, the findings from this work demonstrated that the use of simplified empirical models to design SMC-based motion controllers can be successfully applied to solve the TTP of NMR.

Analysis on a High Accuracy Fully Implicit Solution for Strong Nonlinear Diffusion Problem - Convergence, Stability, and Uniqueness

Some fundamental properties are analyzed for a fully implicit finite difference (FIFD) solution of conservative strong nonlinear diffusion problem. The scheme is constructed by combining a second-order backward difference temporal discretization and a central finite difference spatial discretization, and therefore highly nonlinear. Theoretical analysis is carried out under a coercive condition according with the diffusion feature of the strong nonlinear diffusion model. Benefiting from the boundedness estimates of the FIFD solution itself and its first- and second-order spatial difference quotients, some novel argument techniques are developed to overcome the difficulties coming from the nonlinear approximation for the strong nonlinear conservative diffusion operator. Consequently, it is proved rigorously that the FIFD scheme is unconditionally stable, its solution is unique and convergent to the exact solution of the original problem with second-order space-time accuracy. Numerical examples are provided to confirm its advantages on precision and efficiency over its first-order time accurate counterpoint.

Explicit P1 Finite Element Solution of the Maxwell-Wave Equation Coupling Problem with Absorbing b. c.

In this paper, we address the approximation of the coupling problem for the wave equation and Maxwell’s equations of electromagnetism in the time domain in terms of electric field by means of a nodal linear finite element discretization in space, combined with a classical explicit finite difference scheme for time discretization. Our study applies to a particular case where the dielectric permittivity has a constant value outside a subdomain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this subdomain, Maxwell’s equations hold. Outside this subdomain, the wave equation holds, which may correspond to Maxwell’s equations with a constant permittivity under certain conditions. We consider as a model the case of first-order absorbing boundary conditions. First-order error estimates are proven in the sense of two norms involving first-order time and space derivatives under reasonable assumptions, among which lies a CFL condition for hyperbolic equations. The theoretical estimates are validated by numerical computations, which also show that the scheme is globally of the second order in the maximum norm in time and in the least-squares norm in space.

Feedback control strategy of Fischer–Tropsch process in a micro-GtL plant

Gas-to-liquid technology monetizes flared natural gas to produce green fuel while reducing carbon emissions. In the first step, oxygen reforms methane to CO and H2 followed by Fischer–Tropsch synthesis (FTS), which is highly exothermic and requires a tight temperature control to avoid thermal runaway. Bench-scale units are insufficient to generate basic data to design dynamic control systems for pilot-plants, particularly for intensified processes, because of uncertainties related to heat losses and the spatial and temporal reaction rates. Here, we propose a simulation-based feedback controller design strategy to initially estimate the parameters of a proportional Integral (PI) controller. We applied a power law model to design the controller in Aspen V12 and tested its robustness with a fractional lumped model as an alternative. An Excel ‘solver module’ estimated heat exchange parameters considering the fluidized bed hydrodynamics at steady state. Then, through dynamic simulation, we identified the parameters of a ‘first-order plus dead time’ model via a step response of the reactor temperature to design the PI temperature controller. The controller parameters were characterized by the internal model control (IMC) approach, which is robust to upstream disturbances, kinetic model mismatch, and heat exchange uncertainties.

Pharmacokinetic Modeling of Bepotastine for Determination of Optimal Dosage Regimen in Pediatric Patients with Allergic Rhinitis or Urticaria.

Bepotastine, a second-generation antihistamine for allergic rhinitis and urticaria, is widely used in all age groups but lacks appropriate dosing guidelines for pediatric patients, leading to off-label prescriptions. We conducted this study to propose an optimal dosing regimen for pediatric patients based on population pharmacokinetic (popPK) and physiologically based pharmacokinetic (PBPK) models using data from two previous trials. A popPK model was built using NONMEM software. A one-compartment model with first-order absorption and absorption lag time described our data well, with body weight incorporated as the only covariate. A PBPK model was developed using PK-Sim software version 10, and the model well predicted the drug concentrations obtained from pediatric patients. Furthermore, the final PBPK model showed good concordance with the known properties of bepotastine. Appropriate pediatric doses for different weight and age groups were proposed based on the simulations. Discrepancies in recommended doses from the two models were likely due to the incorporation of age-dependent physiological factors in the PBPK model. In conclusion, our study is the first to suggest an optimal oral dosing regimen of bepotastine in pediatric patients using both approaches. This is expected to foster safer and more productive use of the drug.

Reaction Curve-Assisted Rule-Based PID Control Design for Islanded Microgrid

In a renewable energy-based islanded microgrid system, frequency control is one of the major challenges. In general, frequency oscillations occur in islanded microgrids due to the stochastic nature of load and variable output power of distributed generating units (DGUs). In the presented research proposal, frequency oscillations are suppressed by implementing the proportional integral derivative (PID) controller-based control design strategy for an islanded microgrid. The modeling of the islanded microgrid is firstly presented in the form of a linearized transfer function. Further, the derived transfer function is approximated into its equivalent first-order plus dead time (FOPDT) form. The approximated FOPDT transfer function is obtained by employing the reaction curve method to calculate the parameters of the FOPDT transfer function. Furthermore, the desired frequency regulation is achieved for the manifested FOPDT transfer function by incorporating PID control design. For PID controller tuning, different rule-based methods are implemented. Additionally, comparative analysis is also performed to ensure the applicability of the comparatively better rule-based tuning method. The Wang–Chan–Juang (WCJ) method is found effective over other rule-based tuning methods. The efficacy of the WCJ method is proved in terms of transient response and frequency deviation. The tabulated data of tuning parameters, time domain specifications, and error indices along with responses are provided in support of the presented control strategy.

Efficient numerical methods for semilinear one dimensional parabolic singularly perturbed convection-diffusion systems

In this work we deal with the numerical solution of one dimensional semilinear parabolic singularly perturbed systems of convection-diffusion type. We assume that the coupling in the convection terms is weak and also that the coupling reaction terms are nonlinear. In the case of considering different small diffusion parameters at each equation with different orders of magnitude, the exact solution usually shows overlapping boundary layers on the outflow of the spatial domain. To approximate it, we construct a numerical scheme which combines the upwind finite difference scheme, defined on a piecewise uniform Shishkin mesh, to discretize in space and a linearized version of the fractional implicit Euler method together with an appropriate splitting by components to discretize in time. Then, the fully discrete method is uniformly convergent with respect to both diffusion parameters, having first order in time and almost first order in space. The choice of this time integrator provokes that only tridiagonal linear systems must be solved at each time step; in this way, the computational cost of the algorithm is considerably lower than this one associated to classical implicit methods. The numerical results obtained for different test problems corroborate in practice the good performance of the numerical algorithm.

Theory of moment propagation for quantum dynamics in single-particle description.

We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle wave functions as generally done in time-dependent density functional theory, we describe an approach for reducing the high computational cost of simulating the quantum dynamics. The equation of motion is given for the moments by deriving analytical expressions for the first-order and second-order time derivatives of the moments, and a numerical scheme is developed for performing quantum dynamics by expanding the moments in the Taylor series as done in classical molecular dynamics simulations. We propose a few numerical approaches using this theoretical formalism on a simple one-dimensional model system, for which an analytically exact solution can be derived. The application of the approaches to an anharmonic system is also discussed to illustrate their generality. We also discuss the use of an artificial neural network model to circumvent the numerical evaluation of the second-order time derivatives of the moments, as analogously done in the context of classical molecular dynamics simulations.

Dynamic Optimization of Lactic Acid Production from Grape Stalk Solid-State Fermentation with Rhizopus oryzae Applying a Variable Temperature Profile

Lactic acid is widely used in the food industry. It can be produced via chemical synthesis or biotechnological pathways by using renewable resources as substrates. The main challenge of sustainable production lies in reaching productivities and yields that allow for their industrial production. In this case, the application of process engineering becomes a crucial tool to improve the performance of bioprocesses. In this work, we performed the solid-state fermentation of grape stalk using Rhizopus oryzae NCIM 1299 to obtain lactic acid, employing three different temperatures (22, 35, and 40 °C) and a relative humidity of 50%. The Logistic and First-Order Plus Dead Time models were adjusted for fungal biomass growth, and the Luedeking and Piret with Delay Time model was used for lactic acid production, obtaining higher R2 values in all cases. At 40 °C, it was observed that Rhizopus oryzae grew in pellet form, resulting in an increase in lactic acid productivity. In this context, the effect of temperature on the kinetic parameters was evaluated with a polynomial correlation. Finally, using this correlation, a smooth and continuous optimal temperature profile was obtained by a dynamic optimization method, improving the final lactic acid concentration by 53%.

Partitioned schemes for the blood solute dynamics model by the variational multiscale method

In this paper, we consider a heterogeneous model of solute absorption processes by the arterial wall. This model is based on an advection-diffusion equation describing the solute dynamics in the vascular lumen, the convective field being provided by the blood velocity. A pure diffusive model coupled with this equation is considered for the solute dynamics inside the arterial wall. The two subdomains are physically separated by the endothelial layer, which acts as a selectively permeable membrane and the interface condition matching the two subproblems follow from the nature of this membrane. To compute the approximate solutions, we propose two partitioned schemes for this model by the variational multiscale method. Stability and convergence results are proved for both schemes. We derive error bounds of the fully discrete solution which are first order in time. The optimal error estimates in space could be achieved for the velocity and concentration in the H1-norm, and pressure in the L2-norm with the proper choosing of stabilized parameters. Theoretical results are supported by numerical examples, and two model problems from the physiological interest are also considered.