Nonlinear Formula Research Articles

Networked Control System Based on PSO-RBF Neural Network Time-Delay Prediction Model

To satisfy the requirement of real-time and accurate control of the system, a time-delay prediction control system based on the PSO-RBF neural network model is established to solve the effect of time delay on the control system’s performance. Firstly, a network control model with a time delay is established to predict the control system’s output to solve the uncertainty of the output time delay. Secondly, an improved offline prediction model of RBF networks is proposed to solve the problem of the low accuracy of time-delay prediction in PSO-RBF networks. To solve the problem that the PSO algorithm is prone to fall into local optimality, a nonlinear adjustment formula for the parameters of the PSO algorithm based on the number of iterations is proposed, and the TS algorithm is used to make the optimal global solution. Finally, in order to compensate for the problem of time delay, an online RBF network prediction controller is designed, the parameters of the online RBF network are adjusted by the gradient descent method, and a target function with the differential component is proposed to evaluate the optimization effect of the rolling optimization stage. The results from the true-time simulation platform show that the delay prediction control system based on the PSO-RBF network model proposed in this paper improves the IAE by 59.9% and 31.7%, respectively, compared to the traditional PID controller and fuzzy PID control under the influence of uncertainty disturbances. Therefore, the time-delay prediction control system proposed in this paper has good control capability for the time-delay compensation problem and system output.

Effective removal of hexavalent chromium from water by sustainable nano-scaled waste avocado seeds: adsorption isotherm, thermodynamics, kinetics, and error function

In the current investigation, an efficient low-cost nano-scaled material was prepared from waste avocado seeds (NASs) and employed as a sustainable nanosorbent for removal of hexavalent chromium ions. The adsorption and surface characteristics with respect to the availability of functional groups, basic component elements, and structural properties of NASs were achieved by different techniques. Analysis of NASs referred to the presence of carbon and oxygen contents providing 97.21%. The NASs particles were homogenously identified and ranged between 18.68 and 19.05 nm. The impact of various affecting adsorption parameters on hexavalent chromium ions removal was elaborated and optimized at pH 2.0, NASs dose 10 mg, contact time 30 min, and temperature 25 °C by the batch adsorption assay. Fifteen linear and nonlinear modeling tests were applied to evaluate the adsorption isotherms and arranged in the following fitting order: Tempkin < BET < Dubinin-Radushkevich < Generalized < Halsey ˂ Flory–Huggins < Freundlich < Harkins–Jura ˂ Langmuir for linear formulas and Weber-van Vliet < Langmuir < Generalized < Radke–Prausnitz (II) < Radke–Prausnitz (III) < Fritz-Schlunder IV < Baudu < Multilayer < Fritz-Schlunder V < Toth for nonlinear formulas with 2 to 5 parameters. Linear and nonlinear pseudo-second-order models, intraparticle diffusion, and Elovich models were also scrutinized, and both pore diffusion and film were similarly involved in the rate-limiting step. The values of ΔS° (0.21 kJ/mol), ΔH° (− 41.02 kJ/mol) and ΔG° (− 28.30 to − 19.97 kJ/mol) at high concentration of hexavalent chromium (50 mg L−1) and a temperature range of 20–60 °C reflected the disordering, spontaneously exothermic adsorption process. The activation energy (Ea) was also confirmed to include the diffusion process at the activation energy in the rate-limiting step. The potential application of NASs in hexavalent chromium removal from wastewater, seawater, and tap water as real aqueous matrices referred to excellent percentage removal values in the range from 98.44 to 98.86%. Based on the outlined results, one can deduce that excellent performance and efficiency for removal of high hexavalent chromium concentration at high temperature, low nanosorbent mass, and low pH from different aqueous matrices were accomplished by the evaluated NAS nanosorbent. Accordingly, the investigated NAS nanosorbent is recommended to apply in high stress industrial and wastewater treatment plants.

Robust Feedback Linearization Control Design for Five-Link Human Biped Robot with Multi-Performances

The study first proposes the difficult nonlinear convergent radius and convergent rate formulas and the complete derivations of a mathematical model for the nonlinear five-link human biped robot (FLHBR) system which has been a challenge for engineers in recent decades. The proposed theorem simultaneously has very distinctive superior advantages including the stringent almost disturbance decoupling feature that addresses the major deficiencies of the traditional singular perturbation approach without annoying “complete” conditions for the discriminant function and the global exponential stability feature without solving the impractical Hamilton–Jacobi equation for the traditional H-infinity technique. This article applies the feedback linearization technique to globally stabilize the FLHBR system that greatly improved those shortcomings of nonlinear function approximator and make the effective working range be global for whole state space, whereas the traditional Jacobian linearization technique is valid only for areas near the equilibrium point. In order to make some comparisons with traditional approaches, first example of the representative ones, that cannot be addressed well for the pioneer paper, is shown to demonstrate the fact that the effectiveness of the proposed main theorem is better than the traditional singular perturbation technique. Finally, we execute a second simulation example to compare the proposed approach with the traditional PID approach. The simulation results show that the transient behaviors of the proposed approach including the peak time, the rise time, the settling time and the maximum overshoot specifications are better than the traditional PID approach.

On the generalized nonlinear mechanics of compressible, incompressible, isotropic, and anisotropic hyperelastic membranes

The aim of this paper is to develop a generalized formula for the finite deformation analysis of hyperelastic membranes under various geometry, material, and loading conditions that can be applied to the mechanics of polymer or biological membranes. To do so, the kinematics of deformation in three-dimensional space is formulated and basic kinematic and kinetic quantities are introduced. Set of differential equations governing the deformation of hyperelastic membranes are expressed in a variational framework. Due to inherently nonlinear characteristics of governing equations at large regimes of deformations, a Total Lagrangian (TL) nonlinear finite element formula is developed. The formulation accounts for isotropic as well as anisotropic with transverse isotropy hyperelastic materials. Moreover, both compressible and incompressible cases of membranes are considered. Particular emphasis is on compressible case, where an additional nonlinear equation is solved to obtain the stretch of the membrane in the thickness direction. Furthermore, a study about the effect of participation of fourth and fifth invariants in transversely isotropic strain energy functions is performed. In several cases, introducing transversely isotropic strain energy is unavoidable. As observed in this paper, in the case of biological membranes, the existence of a preferred direction is necessary to predict its behavior in different directions, correctly. Eventually, various examples are solved and excellent results in comparison to those available in the literature are achieved.

A Piezoelectrically Excited ZnO Nanowire Mass Sensor with Closed-Loop Detection at Room Temperature.

One-dimensional nanobeam mass sensors offer an unprecedented ability to measure tiny masses or even the mass of individual molecules or atoms, enabling many interesting applications in the fields of mass spectrometry and atomic physics. However, current nano-beam mass sensors suffer from poor real-time test performance and high environment requirements. This paper proposes a piezoelectrically excited ZnO nanowire (NW) mass sensor with closed-loop detection at room temperature to break this limitation. It is detected that the designed piezo-excited ZnO NW could operate at room temperature with a resonant frequency of 417.35 MHz, a quality factor of 3010, a mass sensitivity of -8.1 Hz/zg, and a resolution of 192 zg. The multi-field coupling dynamic model of ZnO NW mass sensor under piezoelectric excitation was established and solved. The nonlinear amplitude-frequency characteristic formula, frequency formula, modal function, sensitivity curve, and linear operating interval were obtained. The ZnO NW mass sensor was fabricated by a top-down method and its response to ethanol gas molecules was tested at room temperature. Experiments show that the sensor has high sensitivity, good closed-loop tracking performance, and high linearity, which provides great potential for the detection of biochemical reaction process of biological particles based on mechanics.

The Influence of Crest Width and Working States on Wave Transmission of Pile–Rock Breakwaters in the Coastal Mekong Delta

The coastline of the Ca Mau and Kien Giang provinces in the Vietnamese Mekong Delta has been severely eroded in recent decades. Pile–Rock Breakwaters (PRBWs) are among the most widely adopted structures for controlling shoreline erosion in this region. These structures are effective for wave energy dissipation, stimulating sediment accumulation, and facilitating the restoration of mangrove forests. These breakwaters are generally considered to be the best-engineering practice; however, there is currently insufficient scientific evidence with regard to specific structural design aspects. This can lead to PRBW structures being compromised when deployed in the field. This study used a physical model of a PRBW in a laboratory to investigate several design parameters, including crest width and working states (i.e., submerged, transition, and emerged), and investigated their relationship with the wave transmission coefficient, wave reflection coefficient, and wave energy dissipation. To investigate these relationships further, empirical formulas were derived for PRBWs under different sea states and crest widths to aid the design process. The results showed that the PRBW width had a significant influence on the wave energy coefficients. The findings revealed that the crest width of the breakwater was inversely proportional to the wave transmission coefficient (Kt) under the emerged state. The crest width was also proportional to the wave reduction efficiency and wave energy dissipation in both working states (i.e., the submerged and emerged states). The front wave disturbance coefficient (Kf) was found to be proportional to the wave reflection coefficient, and the wave height in front of the structure was found to increase by up to 1.4 times in the emerged state. The wave reflection coefficient requires special consideration to reduce the toe erosion in the structure. Lastly, empirical equations including linear and non-linear formulas were compared with previous studies for different classes of breakwaters. These empirical equations will be useful for understanding the wave transmission efficiency of PRBWs. The findings of this study provide important guidance for PRBW design in the coastal area of the Mekong Delta.

Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials

The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully developed. Here, we extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. This sensitivity to the energy derivatives is shown to produce unique nonlinear transport phenomena of mesoscopic systems including disordered and topological materials. By way of illustration, we investigate nonlinear conductance of disordered chains and identify their universal behavior according to symmetry. In particular, we find large singular nonlinear conductance for zero modes, including Majorana zero modes in topological superconductors. We also show the critical behavior of nonlinear response around the mobility edges due to the Anderson transitions. Moreover, we study nonlinear response of graphene as a prime example of topological materials featuring quantum anomaly. Furthermore, considering the geometry of electronic wave functions, we develop a scattering theory of the nonlinear Hall effect. We establish a new connection between the nonlinear Hall response and the nonequilibrium quantum fluctuations. We also discuss the influence of disorder and Anderson localization on the nonlinear Hall effect. Our work opens a new avenue in quantum physics beyond the linear-response regime.

Evaluating intraocular lens power formula constant robustness using bootstrap algorithms.

Bootstrapping is a modern technique mostly used in statistics to evaluate the robustness of model parameters. The purpose of this study was to develop a method for evaluation of formula constant uncertainties and the effect on the prediction error (PE) in intraocular lens power calculation with theoretical-optical formulae using bootstrap techniques. In a dataset with N=888 clinical cases treated with the monofocal aspherical intraocular lens (Vivinex, Hoya) constants for the Haigis, the Castrop and the SRKT formula were optimised for the sum of squared PE using nonlinear iterative optimisation (interior point method), and the formula predicted spherical equivalent refraction (predSEQ) and the PE were derived. The PE was bootstrapped NB=1000 times and added to predSEQ, and formula constants were derived for each bootstrap. The robustness of the constants was calculated from the NB bootstrapped models, and the predSEQ was back-calculated from the NB formula constants. With bootstrapping, the 90% confidence intervals for the a0/a1/a2 constants of the Haigis formula were -0.8317 to -0.5301/0.3203 to 0.3617/0.1954 to 0.2100, for the C/H/R constants of the Castrop formula they were 0.3113 to 0.3272/0.1237 to 0.2149/0.0980 to 0.1621, and for the A constant of the SRKT formula they were 119.2320 to 119.3028. The back-calculated PE from the NB bootstrapped formula constants standard deviation for the mean/median/mean absolute/root mean squared PE were 5.677/5.735/0.401/0.318 e-3 dpt for the Haigis formula, 5.677/5.735/0.401/0.31829 e-3 dpt for the Castrop formula and 14.748/14.790/0.561/0.370 e-3 dpt for the SRKT formula. We have been able to prove with bootstrapping that nonlinear iterative formula constant optimisation techniques for the Haigis, the Castrop and the SRKT formulae yield consistent results with low uncertainties of the formula constants and low variations in the back-calculated mean, median, mean absolute and root mean squared formula prediction error.

An Improved Component-Wise WENO-NIP Scheme for Euler System

As is well known, due to the spectral decomposition of the Jacobian matrix, the WENO reconstructions in the characteristic-wise fashion (abbreviated as CH-WENO) need much higher computational cost and more complicated implementation than their counterparts in the component-wise fashion (abbreviated as CP-WENO). Hence, the CP-WENO schemes are very popular methods for large-scale simulations or situations whose full characteristic structures cannot be obtained in closed form. Unfortunately, the CP-WENO schemes usually suffer from spurious oscillations badly. The main objective of the present work is to overcome this drawback for the CP-WENO-NIP scheme, whose counterpart in the characteristic-wise fashion was carefully studied and well-validated numerically. The approximated dispersion relation (ADR) analysis is performed to study the spectral property of the CP-WENO-NIP scheme and then a negative-dissipation interval which leads to a high risk of causing spurious oscillations is discovered. In order to remove this negative-dissipation interval, an additional term is introduced to the nonlinear weights formula of the CP-WENO-NIP scheme. The improved scheme is denoted as CP-WENO-INIP. Accuracy test examples indicate that the proposed CP-WENO-INIP scheme can achieve the optimal convergence orders in smooth regions even in the presence of the critical points. Extensive numerical experiments demonstrate that the CP-WENO-INIP scheme is much more robust compared to the corresponding CP-WENO-NIP or even CH-WENO-NIP schemes for both 1D and 2D problems modeled via the Euler equations.

Correlation and validity of imputed PaO2/FiO2 and SpO2/FiO2 in patients with invasive mechanical ventilation at 2600m above sea level.

To establish the correlation and validity between PaO2/FiO2 obtained on arterial gases versus noninvasive methods (linear, nonlinear, logarithmic imputation of PaO2/FiO2 and SpO2/FiO2) in patients under mechanical ventilation living at high altitude. Ambispective descriptive multicenter cohort study. Two intensive care units (ICU) from Colombia at 2600m a.s.l. Consecutive critically ill patients older than 18 years with at least 24h of mechanical ventilation were included from June 2016 to June 2019. None. Variables analyzed were demographic, physiological messures, laboratory findings, oxygenation index and clinical condition. Nonlinear, linear and logarithmic imputation formulas were used to calculate PaO2 from SpO2, and at the same time the SpO2/FiO2 by severe hypoxemia diagnosis. The intraclass correlation coefficient, area under the ROC curve, sensitivity, specificity, positive predictive value, negative predictive value, positive and negative likelihood ratio were calculated. The correlation between PaO2/FiO2 obtained from arterial gases, PaO2/FiO2 derived from one of the proposed methods (linear, non-linear, and logarithmic formula), and SpO2/FiO2 measured by the intraclass correlation coefficient was high (greater than 0.77, p<0.001). The different imputation methods and SpO2/FiO2 have a similar diagnostic performance in patients with severe hypoxemia (PaO2/FiO2 <150). PaO2/FiO2 linear imputation AUC ROC 0,84 (IC 0.81-0.87, p<0.001), PaO2/FiO2 logarithmic imputation AUC ROC 0.84 (IC 0.80-0.87, p<0.001), PaO2/FiO2 non-linear imputation AUC ROC 0.82 (IC 0.79-0.85, p<0.001), SpO2/FiO2 oximetry AUC ROC 0.84 (IC 0.81-0.87, p<0.001). At high altitude, the SaO2/FiO2 ratio and the imputed PaO2/FiO2 ratio have similar diagnostic performance in patients with severe hypoxemia ventilated by various pathological conditions.

Correlation and validity of imputed PaO2/FiO2 and SpO2/FiO2 in patients with invasive mechanical ventilation at 2600 m above sea level

ObjectiveTo establish the correlation and validity between PaO2/FiO2 obtained on arterial gases versus noninvasive methods (linear, nonlinear, logarithmic imputation of PaO2/FiO2 and SpO2/FiO2) in patients under mechanical ventilation living at high altitude. DesignAmbispective descriptive multicenter cohort study. SettingTwo intensive care units (ICU) from Colombia at 2600m a.s.l. Patients or participantsConsecutive critically ill patients older than 18 years with at least 24h of mechanical ventilation were included from June 2016 to June 2019. InterventionsNone. VariablesVariables analyzed were demographic, physiological messures, laboratory findings, oxygenation index and clinical condition. Nonlinear, linear and logarithmic imputation formulas were used to calculate PaO2 from SpO2, and at the same time the SpO2/FiO2 by severe hypoxemia diagnosis. The intraclass correlation coefficient, area under the ROC curve, sensitivity, specificity, positive predictive value, negative predictive value, positive and negative likelihood ratio were calculated. ResultsThe correlation between PaO2/FiO2 obtained from arterial gases, PaO2/FiO2 derived from one of the proposed methods (linear, non-linear, and logarithmic formula), and SpO2/FiO2 measured by the intraclass correlation coefficient was high (greater than 0.77, p<0.001). The different imputation methods and SpO2/FiO2 have a similar diagnostic performance in patients with severe hypoxemia (PaO2/FiO2 <150). PaO2/FiO2 linear imputation AUC ROC 0,84 (IC 0.81–0.87, p<0.001), PaO2/FiO2 logarithmic imputation AUC ROC 0.84 (IC 0.80–0.87, p<0.001), PaO2/FiO2 non-linear imputation AUC ROC 0.82 (IC 0.79–0.85, p<0.001), SpO2/FiO2 oximetry AUC ROC 0.84 (IC 0.81–0.87, p<0.001). ConclusionsAt high altitude, the SaO2/FiO2 ratio and the imputed PaO2/FiO2 ratio have similar diagnostic performance in patients with severe hypoxemia ventilated by various pathological conditions.

Binary Newton Calculation Method of Residual Stress Based on the Indentation Energy Difference Theory

Residual stress is a key parameter to evaluate the structural reliability of energy equipment. The indentation method has the characteristics of being nondestructive and easy to operate to calculate the residual stress of test materials, which has a broad application prospect in the field testing of energy equipment. However, because of the effect of preloading and data acquisition delay, the problem of indentation data fluctuation is prominent, and the indentation energy coefficient fitted by the traditional least square method is not consistent with the theoretical law, making it difficult to carry out stable calculations. In this paper, the Newton iteration formula of a binary nonlinear formula is derived based on the univariate Newton iteration formula, which is introduced into the data processing of residual stress, which increases the weight of the data in the stability stage and reduces the influence of the fluctuation data on the fitting results, so that the indentation energy coefficient is accurately calculated. Combined with the basic principle of indentation energy difference theory, the precise and efficient measurement of residual stress is realized.

Deep neural networks based temporal-difference methods for high-dimensional parabolic partial differential equations

Solving high-dimensional partial differential equations (PDEs) is a long-standing challenge, for which classical numerical methods suffer from the well-known curse of dimensionality. In this paper, we propose deep neural networks (NN) based temporal-difference (TD) learning methods for numerically solving high-dimensional parabolic PDEs. To this end, we approximate the solution of the original PDE with an NN function. To calculate this neural network function, we first transform the deterministic parabolic PDE to a forward-backward stochastic differential equations (FBSDE) system with the nonlinear Feynman-Kac formula, and then transform the forward updating process of FBSDE as a Markov reward process (MRP). On this basis, we approximate the solution of the PDE by training an NN function with a reinforcement learning technique described as below: we first discretize the temporal interval to a finite number of time steps and then at each time step, we generate many trajectories and design the loss function as the mean square of temporal difference error on all trajectories. With this loss function, we update the parameters of the NN function with the stochastic gradient descent (SGD) method. Numerical experiments show that comparing to some other existed deep learning methods, our method not only accelerates the computational speed but also improves the computational accuracy. In particular, the relative errors of our algorithm achieve the order of O(10−4) even the dimension of the problem is as high as 100.

Nonlinear Differential Equations in Preventing Financial Risks

Abstract The nonlinear differential equation option pricing formula is invaluable in financial derivatives investment risk assessment. This article applies the theory of nonlinear differential equations to deal with financial risks in commodity and currency markets. Through this condition, we obtain the fair price process of contingent rights under the classic Black-Scholes model and the price process of the optimal growth investment strategy. The results show that the risk measurement under stable distribution is suitable for investors to manage risk.

Empirical formulas for groundwater use under wheat growth conditions in the Huaibei Plain of China

Abstract Using groundwater for crop growth plays a key role in the sustainable management of water resources and irrigation and drainage design. Some studies did not consider the influence of different crop growth stages and the non-linear effect of the groundwater depth on groundwater use. In this study, three types of formulae for groundwater use were developed by referencing the phreatic evaporation formula without crops. According to the observation data, groundwater depth and use, and wheat evapotranspiration were fitted using these three non-linear formulae in each crop growth stage. The Accelerated Gene Algorithm (AGA) was used to optimize the parameters, and their performance indices were calculated. We observed that groundwater use increased gradually as the decrease in groundwater depth and the increase in wheat evapotranspiration; the correlation coefficients of wheat evapotranspiration and groundwater use were small (such as 0.539, 0.428) in the seedling stage and mature stage and large (such as 0.631, 0.625) in other stages. The performance of the Aviriyanover formula was the best with a correlation coefficient of 0.686 between the simulation and observation; therefore, this formula was recommended to determine groundwater use.

Measuring free surface elevation of shoaling waves with pressure transducers

An assessment of formulas to recover wave surface elevation from pressure measurements was carried out in the present study. The investigation focused on the formulas’ performance in the shoaling region, i.e. where the wave nonlinearity gradually increases as the wave travels towards shallower waters. Formulas based on linear wave theory alongside nonlinear reconstructions were considered. Experiments in a large-scale wave flume provided with a concrete beach profile were performed, in which regular waves were generated and surface elevation was measured with acoustic, resistive and pressure gauges. The considered formulas require the application of a cutoff frequency to the wave signal in order to avoid high frequencies amplification that progressively arise as wave shoaling occur. A simple but effective method to obtain a reference cutoff frequency is proposed in the present work; the method is based on a polynomial fitting of the unfiltered wave energy spectrum. A sensitivity analysis of each formula to the variation of this cutoff frequency was carried out. Results showed that all the investigated formulas recover wave elevation fairly well for low-nonlinearity waves, whereas overestimating wave crest height as nonlinearity increases. Wave reconstruction of the linear formulation performance was comparable to nonlinear formulations in terms of wave crest height reconstruction, although tending to amplify frequencies in the wave trough. Moreover, the performance of the formulas to correctly recover the asymmetry and flatness of the surface elevation distribution was assessed by analysing third- and fourth-order moment statistics. In this sense, nonlinear reconstruction formulas performed better in recovering the asymmetric distribution of the wave elevation, with the formula based on linear wave theory underestimating skewness and kurtosis for large nonlinearity waves.

Nonlinear Dynamic Model for Parameter Estimation of Li-Ion Batteries Using Supply–Demand Algorithm

The parameter extraction of parameters for Li-ion batteries is regarded as a critical topic for assessing the performance of battery energy storage systems (BESSs). The supply–demand algorithm (SDA) is used in this work to identify a storage system’s unknown parameters. The parameter-extracting procedure is represented as a nonlinear optimization task in which the state of charge (SOC) is approximated using nonlinear features related to the battery current and the initial SOC condition. Furthermore, the open-circuit voltage is approximated using the resulting SOC, which is performed in a nonlinear formula, as well. When used in the dynamic nonlinear BESS model, the SDA was used to verify the fitness values and standard deviation error. Furthermore, the results that were acquired using SDA are compared to recently developed approaches, which are the gradient-based, tuna swarm, jellyfish, heap-based, and forensic-based optimizers. Simulated studies were paired with experiments for the 40 Ah Kokam Li-ion battery and the ARTEMIS driving-cycle pattern. The numerical outcomes showed that the proposed SDA is an approach which is excellent at identifying the parameters. Furthermore, when compared to the other current optimization techniques, for both the Kokam Li-ion batteries and the ARTEMIS drive-cycle pattern, the suggested SDA exhibited substantial precision.

Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs

In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional Itô (or path-dependent) calculus, the relationship between the systems and related path-dependent quasi-linear stochastic partial differential equations (SPDEs in short) is established, and the well-known nonlinear stochastic Feynman-Kac formula of Pardoux and Peng [Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Relat. Fields 98 (1994), pp. 209–227.] is developed to the non-Markovian situation. Moreover, we obtain the differentiability of the solution to the forward-backward doubly stochastic systems and some properties of solutions to the path-dependent SPDEs.

Adjustable arch-beam combination structural strengthening system for reinforced concrete beam bridge

A new adjustable and combined reinforcement method consisting of arch rib and steel beam is proposed in this paper. The principle is to redistribute the internal forces of the structure through the support of the arch rib and to form a combined structure by using steel and concrete. Symmetrically loaded bending tests were carried out with five different combined strengthening schemes. The analysis of the test process was conducted adopting a FEM model, and the equations for calculating the RC beam's load capacity under combined strengthening were derived while considering the slip effect. The experimental results indicated that the combined reinforcement method had a synergistic effect when the ultimate load capacity had increased by more than 95% after reinforcement. As the size of the arch ribs and profile beams increased, a better reinforcement effect was seen. However, beyond a certain range, the RC beams had already broken down and had failed before the reinforcement material could yield. The combined reinforcement method changes the force system of the original RC beam, resulting in a smaller angular inclination trend of the cracks in the original purely curved section and a smaller crack extension. The non-linear finite element results are generally consistent with experimental loads, displacements, and ductility, while the average ratio of experimental to calculated ultimate Load capacity is 0.95, demonstrating that non-linear finite elements and theoretical formulas are accurate.

Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations

In this paper, we first study the connection between mass-conserving SPDEs on a bounded domain and backward doubly stochastic differential equations, which is a new extension of nonlinear Feynman-Kac formula to mass-conserving SPDEs. Then the infinite horizon mass-conserving SPDEs and their stationary solutions are considered without monotonic conditions, while the Poincare inequality plays an important role. Finally, the existence and the stationarity to solutions of non-Lipschitz mass-conserving stochastic Allen-Cahn equations are obtained.