Constant Function Research Articles

Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the Biot system which consists of vector-valued displacements (geomechanics) coupled to a Darcy flow pressure equation. The MORe DWR method introduces a goal-oriented adaptive incremental proper orthogonal decomposition (POD) based-reduced-order model (ROM). The error in the reduced goal functional is estimated during the simulation, and the POD basis is enriched on-the-fly if the estimate exceeds a given threshold. This results in a reduction of the total number of full-order-model solves for the simulation of the porous medium, a robust estimation of the quantity of interest and well-suited reduced bases for the problem at hand. We apply a space-time Galerkin discretization with Taylor-Hood elements in space and a discontinuous Galerkin method with piecewise constant functions in time. The latter is well-known to be similar to the backward Euler scheme. We demonstrate the efficiency of our method on the well-known two-dimensional Mandel benchmark and a three-dimensional footing problem.

A mathematical model with uncertainty quantification for allelopathy with applications to real-world data

We revisit a deterministic model for studying the dynamics of allelopathy. The model is formulated in terms of a non-homogeneous linear system of differential equations whose forcing or source term is a piecewise constant function (square wave). To account for the inherent uncertainties present in this natural phenomenon, we reformulate the model as a system of random differential equations where all model parameters and the initial condition are assumed to be random variables, while the forcing term is a stochastic process. Taking extensive advantage of the so-called Random Variable Transformation (RVT) method, we obtain the solution of the randomized model by providing explicit expressions of the first probability density function of the solution under very general assumptions on the model data. We also determine the joint probability density function of the non-trivial equilibrium point, which is a random vector. If the source term is a time-dependent stochastic process, the RVT method might not be applicable since no explicit solution of the model is available. We then show an alternative approach to overcome this drawback by applying the Liouville–Gibbs partial differential equation. All the theoretical findings are illustrated through several examples, including the application of the randomized model to real-world data on alkaloid contents from leaching thornapple seed.

Spectral Reconstruction Improvement in a Cycloidal Coded-Aperture Mass Spectrometer.

Spatial aperture coding is a technique used to improve throughput without sacrificing resolution both in optical spectroscopy and sector mass spectrometry (MS). Previous work demonstrated that aperture coding combined with a position-sensitive array detector in a miniature cycloidal mass spectrometer was successful in providing high-throughput, high-resolution measurements. However, due to poor alignment and field nonuniformities, reconstruction artifacts were present. Recently, significant progress was made in eliminating most of the reconstruction artifacts with improved field uniformity and alignment. However, artifacts as large as 1/3 of the main peak were still observed at low mass (<17 u). Such artifacts will reduce accuracy in identification and quantification of analytes, reducing the impact of the throughput advantage gained by using a coded aperture. The artifacts were hypothesized to be a result of a mass dependent in curvature of ions in the ion source. Ions with higher mass (m/z > 17 u) and a larger curvature did not pass through all slits in the coded aperture. Therefore, when reconstructing with a system response derived from the aperture image from a higher mass m/z = 32 u ion, reconstruction artifacts appeared for m/z < 17 u. In this work, two methods were implemented to significantly reduce the presence of artifacts in reconstructed data. First, we modified the reconstruction algorithm to incorporate a mass-dependent system response function across the mass range (10-110 u). This method reduced the size of the artifacts by 82%. Second, to validate the hypothesis that the mass-dependent system response function was a result of differences in curvature of ions in the ion source, we modified the design of the ion source by shifting the coded aperture slits relative to the center of the ionization volume. This method resulted in ions of all masses passing through all slits in the coded aperture, a constant system response function across the entire mass range. Artifacts were reduced by 94%.

Modern technique to study Cauchy-type problem of fractional variable order differential equations with infinite delay via phase space

In this paper, we use a novel approach to study the existence, uniqueness, and stability of solutions (EUSS) to a Cauchy-type problem of nonlinear fractional differential equations (FrDiEq) of variable order with infinite delay (CPNFDEVOID). Contrary to the techniques taken in the literature, which were centered on the usage of the concept of generalized intervals and the idea of piecewise constant functions, our approach is straightforward and based on a novel fractional operator that is more appropriate and demonstrates the solvability and stability of the main problem under less restrictive presumptions. The results are achieved in this paper by using Fixed Point Theory (FPT). The application, which includes an example and supporting images, concludes the paper.

Monte Carlo tree search control scheme for multibody dynamics applications

There is considerable interest in applying reinforcement learning (RL) to improve machine control across multiple industries, and the automotive industry is one of the prime examples. Monte Carlo Tree Search (MCTS) has emerged and proven powerful in decision-making games, even without understanding the rules. In this study, multibody system dynamics (MSD) control is first modeled as a Markov Decision Process and solved with Monte Carlo Tree Search. Based on randomized search space exploration, the MCTS framework builds a selective search tree by repeatedly applying a Monte Carlo rollout at each child node. However, without a library of available choices, deciding among the many possibilities for agent parameters can be intimidating. In addition, the MCTS poses a significant challenge for searching due to the large branching factor. This challenge is typically overcome by appropriate parameter design, search guiding, action reduction, parallelization, and early termination. To address these shortcomings, the overarching goal of this study is to provide needed insight into inverted pendulum controls via vanilla and modified MCTS agents, respectively. A series of reward functions are well-designed according to the control goal, which maps a specific distribution shape of reward bonus and guides the MCTS-based control to maintain the upright position. Numerical examples show that the reward-modified MCTS algorithms significantly improve the control performance and robustness of the default choice of a constant reward that constitutes the vanilla MCTS. The exponentially decaying reward functions perform better than the constant value or polynomial reward functions. Moreover, the exploitation vs. exploration trade-off and discount parameters are carefully tested. The study’s results can guide the research of RL-based MSD users.

Dynamics of a Conformable Fractional Order Generalized Richards Growth Model on Star Network with N=20 Nodes

In this study, we analyze dynamical behavior of the conformable fractional order Richards growth model. Before examining the analysis of the dynamical behavior of the fractional continuous time model, the model is reduced to the system of difference equations via utilizing piecewise constant functions. An algebraic condition that ensures the stability of the positive fixed point of the system is obtained. With the center manifold theory, the existence of a Neimark-Sacker bifurcation at the fixed point of the discrete-time system is proven and the direction of this bifurcation is determined. In addition, the discrete dynamical system is also studied on the star network with N=20 nodes. Analysis complex dynamics of Richards growth model into coupled dynamical network shows that the complex star network with N=20 nodes also exhibits Neimark-Sacker bifurcation about the fixed point concerning with parameter c. Numerical simulations are performed to demonstrate the stability, bifurcations and dynamic transition of the coupled network.

Green synthesis of Ag/Yb2O3 nanostructures based-MIP for tamoxifen detection: Advancing from refractometers to sensor

This study presents a novel optical fiber refractometer based on a single smart functional layer of Ag/Yb2O3 nanostructure, synthesized by a green chemistry method using oak fruit extract. The optical phenomena of surface plasmon resonance (SPR) and lossy mode resonance (LMR) were investigated based on the performance of the real and imaginary parts of the dielectric constant function of nanoparticles and nanostructures coated on the optical fiber. The Ag/Yb2O3 nanostructure enhances the LMR phenomenon and acts as an electron mediator for the detection of tamoxifen (TAM) drug, a widely used anticancer agent. The Ag/Yb2O3 nanostructure was coated on a curved optical fiber surface along with a molecularly imprinted polymer (MIP) layer, which provided selective recognition of TAM molecules. The sensor probe showed rapid and reversible adsorption/desorption of TAM, with a high sensitivity of 5.3611 nm/µM and a limit of detection (LOD) and limit of quantification (LOQ) of 0.0987 μM and 0.32902 μM, respectively. The sensor also exhibited good recovery rate and effectiveness in real samples, demonstrating its potential for sensivity applications.

Comparing machine learning potentials for water: Kernel-based regression and Behler-Parrinello neural networks.

In this paper, we investigate the performance of different machine learning potentials (MLPs) in predicting key thermodynamic properties of water using RPBE + D3. Specifically, we scrutinize kernel-based regression and high-dimensional neural networks trained on a highly accurate dataset consisting of about 1500 structures, as well as a smaller dataset, about half the size, obtained using only on-the-fly learning. This study reveals that despite minor differences between the MLPs, their agreement on observables such as the diffusion constant and pair-correlation functions is excellent, especially for the large training dataset. Variations in the predicted density isobars, albeit somewhat larger, are also acceptable, particularly given the errors inherent to approximate density functional theory. Overall, this study emphasizes the relevance of the database over the fitting method. Finally, this study underscores the limitations of root mean square errors and the need for comprehensive testing, advocating the use of multiple MLPs for enhanced certainty, particularly when simulating complex thermodynamic properties that may not be fully captured by simpler tests.

Oxysulfide perovskites: reduction of the electronic band gap of RbTaO3 by sulfur substitution

In this study, the effects of sulfur substitution on the structural, mechanical, electronic, optical, and thermodynamic properties of RbTaO3−x S x have been investigated using the WIEN2k code in the framework of density functional theory (DFT). The cubic phase of RbTaO3 transforms to tetragonal for RbTaO2S and RbTaOS2; the latter transforms again to a cubic phase with added sulfur for RbTaS3. The results show that substituting S for O anions in RbTaO3 effectively decreased the band gap [calculated using TB-mBJ functional] from 2.717 eV to 1.438 eV, 0.286 eV, and 0.103 eV for the RbTaO3, RbTaO2S, RbTaOS2, and RbTaS3 compounds, respectively. The optical constants such as dielectric constant, refractive index, absorption coefficient, photoconductivity, reflectivity, and loss function have been calculated and analyzed. The elastic constants and moduli and their anisotropic nature were also investigated. Finally, the Debye temperature, thermal conductivity, melting temperature, specific capacities, and thermal expansion coefficients were computed and analyzed using established formalisms. The reduced band gap (1.438 eV) and high absorption coefficient (∼106 cm−1) of RbTaO2S, make it suitable for solar cell applications and for other visible light devices. Both ordered structure and super-cell have been used to cross-check results for RbTaO2S and RbTaOS2 compositions.

Convergence of Langevin-simulated annealing algorithms with multiplicative noise

We study the convergence of Langevin-Simulated Annealing type algorithms with multiplicative noise, i.e. for V : R d → R V : \mathbb {R}^d \to \mathbb {R} a potential function to minimize, we consider the stochastic differential equation d Y t = − σ σ ⊤ ∇ V ( Y t ) dY_t = - \sigma \sigma ^\top \nabla V(Y_t) d t + a ( t ) σ ( Y t ) d W t + a ( t ) 2 Υ ( Y t ) d t dt + a(t)\sigma (Y_t)dW_t + a(t)^2\Upsilon (Y_t)dt , where ( W t ) (W_t) is a Brownian motion, where σ : R d → M d ( R ) \sigma : \mathbb {R}^d \to \mathcal {M}_d(\mathbb {R}) is an adaptive (multiplicative) noise, where a : R + → R + a : \mathbb {R}^+ \to \mathbb {R}^+ is a function decreasing to 0 0 and where Υ \Upsilon is a correction term. This setting can be applied to optimization problems arising in Machine Learning; allowing σ \sigma to depend on the position brings faster convergence in comparison with the classical Langevin equation d Y t = − ∇ V ( Y t ) d t + σ d W t dY_t = -\nabla V(Y_t)dt + \sigma dW_t . The case where σ \sigma is a constant matrix has been extensively studied; however little attention has been paid to the general case. We prove the convergence for the L 1 L^1 -Wasserstein distance of Y t Y_t and of the associated Euler scheme Y ¯ t \bar {Y}_t to some measure ν ⋆ \nu ^\star which is supported by argmin ⁡ ( V ) \operatorname {argmin}(V) and give rates of convergence to the instantaneous Gibbs measure ν a ( t ) \nu _{a(t)} of density ∝ exp ⁡ ( − 2 V ( x ) / a ( t ) 2 ) \propto \exp (-2V(x)/a(t)^2) . To do so, we first consider the case where a a is a piecewise constant function. We find again the classical schedule a ( t ) = A log − 1 / 2 ⁡ ( t ) a(t) = A\log ^{-1/2}(t) . We then prove the convergence for the general case by giving bounds for the Wasserstein distance to the stepwise constant case using ergodicity properties.

Reflect-Push Methods Part I: Two Dimensional Techniques

We determine all maximum weight downsets in the product of two chains, where the weight function is a strictly increasing function of the rank. Many discrete isoperimetric problems can be reduced to the maximum weight downset problem. Our results generalize Lindsay's edge-isoperimetric theorem in two dimensions in several directions. They also imply and strengthen (in several directions) a result of Ahlswede and Katona concerning graphs with maximal number of adjacent pairs of edges. We find all optimal shifted graphs in the Ahlswede-Katona problem. Furthermore, the results of Ahlswede-Katona are extended to posets with a rank increasing and rank constant weight function. Our results also strengthen a special case of a recent result by Keough and Radcliffe concerning graphs with the fewest matchings. All of these results are achieved by applications of a key lemma that we call the reflect-push method. This method is geometric and combinatorial. Most of the literature on edge-isoperimetric inequalities focuses on finding a solution, and there are no general methods for finding all possible solutions. Our results give a general approach for finding all compressed solutions for the above edge-isoperimetric problems.&#x0D; By using the Ahlswede-Cai local-global principle, one can conclude that lexicographic solutions are optimal for many cases of higher dimensional isoperimetric problems. With this and our two dimensional results we can prove Lindsay's edge-isoperimetric inequality in any dimension. Furthermore, our results show that lexicographic solutions are the unique solutions for which compression techniques can be applied in this general setting.

Error estimates of characteristic finite elements for bilinear convection–diffusion optimal control problems

This paper investigates a fully discrete characteristic finite element approximation of bilinear unsteady convection–diffusion optimal control problems. The characteristic line method is used to treat the convection term and the finite element method is adopted to treat the diffusion term. The state and adjoint state are discretized by piecewise linear functions, the control is approximated by piecewise constant functions. A priori error estimates are derived for the state, adjoint state and control variables. Some numerical examples are provided to confirm our theoretical findings.

Vertical-axis turbine performance enhancement with physics-informed blade pitch control. Basic principles and proof of concept with high-fidelity numerical simulation

In this study, we developed active physics-informed turbine blade pitch control methods to conquer the inconsistent energy harvesting efficiency challenges encountered by the vertical-axis turbines (VATs) technology. Specifically, individual turbine blades were pitched by actuators following commands from the physics-informed controllers, and the turbine performance improvements as a result of the blade pitch control mechanism and the associated flow physics were studied. The aim of the blade pitch control was to maintain constant effective angles of attack (AoAs) experienced by turbine blades through active blade pitch, and the constant AoA function was designed to facilitate control mechanism implementation into real-world VATs. To gain in-depth understanding of the capability of the control, flow physics was studied for different constant AoA control strategies across a wide range of tip speed ratios and wind speeds and was compared with that from the corresponding baselines without control, and that from the sinusoidal AoA control strategy. The comparison between the turbine performance with constant AoA control and that without control showed a consistent increase in the time-averaged net power coefficient, a measure of energy harvesting efficiency taking out of the actuator loss, ranging from 27.4% to 704.0% across a wide spread of wind speeds. The superior turbine performance with constant AoA control was largely attributed to blade dynamic stall management during the blade upstream and downstream cycles and the transition between the two cycles.

Cauer Ladder Network With Constant Basis Functions for Eddy Current Problems Involving Conductor Movement

Cauer Ladder Network With Constant Basis Functions for Eddy Current Problems Involving Conductor Movement

Charger-Mediated Energy Transfer for Quantum Battery With Constant Time Dependent Step Function and Open System Approach

The energy charging of quantum battery is analysed by open quantum approach. The modelled of the charger and battery are described by harmonic oscillator model. We choose this model because the harmonic oscillator battery gives the largest maximum energy albeit having the longest maximum time. In this paper, the interaction as actual quantum system whose dynamic is determined by Lindblad Master Equation in terms of constant is a step function to set the time when energy flow and what time that energy stop to flow or the interaction between charger and battery has stopped. The energy equation was determined by solving the master equation with second order differential equation to find the first momenta from charger and battery. Based on the equation, the energy of charger will not be zero which mean after interaction in several times, the charger will not one hundred percent lose its energy when the energy storage in battery already done.

Partial isospectrality of a matrix pencil and circularity of the c-numerical range

We study when functions of the eigenvalues of the pencil(1)Re(e−itA)=cos⁡(t)ReA+sin⁡(t)ImA are constant functions of t. The results are then applied to questions regarding the numerical range, the higher rank numerical range and the c-numerical range, and we derive trace type conditions for when these numerical ranges are disks centered at 0. The theory of symmetric polynomials plays an important part in the proofs.

Singular integral based closed-form solutions for modified EMPS models in semipermeable magneto-electro-elastic materials

The singular integral equation method is applied to present analytical solutions for modified electric-magnetic-polarization saturation (EMPS) models subjected to semipermeable center cracked magneto-electro-elastic (MEE) materials. A generalized methodology is presented to explicitly solve the EMPS model under any arbitrary saturated electric and magnetic conditions using the distributed dislocation method (DDM) and finding the analytical solutions for developed singular integral equations. The explicit expressions are derived for distributed dislocation densities, crack opening displacement (COD), crack opening potential (COP), crack opening induction (COI), saturated zone lengths, and local stress intensity factor (LSIF) for particular cases of the generalized EMPS model such as constant, linear, quadratic and cubic polynomial varying saturated electric and magnetic conditions. Using an iterative scheme and the explicit solutions of COD, COP, and COI, the exact semipermeable crack-face conditions are evaluated at the center of the crack, and the same applies throughout the crack-surface for the study of semipermeable modified EMPS models. A comparative analysis of the fracture parameters has also been carried out between the results of exact semipermeable crack-face conditions and the results of semipermeable crack-face conditions of the center crack problem to analyze the impact of polynomial varying saturated conditions on the crack-face conditions. Numerical studies performed under different electromagnetic-mechanical loadings, volume fractions, and crack-face conditions demonstrate the increasing effects in the fracture parameters' values with the degree of the polynomial varying saturated conditions.

On the Exact Solution of a Scalar Differential Equation via a Simple Analytical Approach

The existence of the advance parameter in a scalar differential equation prevents the application of the well-known standard methods used for solving classical ordinary differential equations. A simple procedure is introduced in this paper to remove the advance parameter from a special kind of first-order scalar differential equation. The suggested approach transforms the given first-order scalar differential equation to an equivalent second-order ordinary differential equation (ODE) without the advance parameter. Using this method, we are able to construct the exact solution of both the transformed model and the given original model. The exact solution is obtained in a wave form with specified amplitude and phase. Furthermore, several special cases are investigated at certain values/relationships of the involved parameters. It is shown that the exact solution in the absence of the advance parameter reduces to the corresponding solution in the literature. In addition, it is declared that the current model enjoys various kinds of solutions, such as constant solutions, polynomial solutions, and periodic solutions under certain constraints of the included parameters.

Global output‐feedback adaptive regulation for planar time‐delay nonlinear systems with polynomial growth

AbstractThis paper addresses the problem of the global adaptive regulation via output feedback for a class of uncertain planar time‐varying delay nonlinear systems with an unknown control coefficient and unmeasured states dependent growth. The growth rate is the form of an unknown constant multiplying polynomial of output, and the upper bounds of unknown control coefficient and unknown time‐varying delay are both not required to be known. A systematic non‐identifier‐based output‐feedback control scheme is developed by combining the idea of universal control, backstepping technique, and Lyapunov–Krasovskii theorem. The global regulation of nonlinear systems and the global boundedness of the closed‐loop system can be simultaneously achieved by the designed controller based on a dynamic high‐gain observer and a proper update law. A practical example illustrates the efficiency of the proposed method.

Spectral subspaces of Sturm-Liouville operators and variable bandwidth

We study spectral subspaces of the Sturm-Liouville operator f↦−(pf′)′ on R, where p is a positive, piecewise constant function. Functions in these subspaces can be thought of as having a local bandwidth determined by 1/p. Using the spectral theory of Sturm-Liouville operators, we make the reproducing kernel of these spectral subspaces more explicit and compute it completely in certain cases. As a contribution to sampling theory, we then prove necessary density conditions for sampling and interpolation in these subspaces and determine the critical density that separates sets of stable sampling from sets of interpolation.