Forward Scheme Research Articles

Control of new energy‐intensified triple column extractive distillation using feed split technique

AbstractBACKGROUNDHere, we investigated the control performance of extractive distillation intensified with ‘feed split’ (FS) technique – a process intensification technique that has not been widely applied to extractive distillation. Today, only a handful of studies have been reported on this topic, with only one focusing on the control performance and reporting the significant trade‐off between the steady‐state and dynamic performances. Nonetheless, the previous control study was based on the complex double column FS configuration. Recently, a new triple column FS configuration was reported (Sep. Purif. Technol. 2022 (297) 121467), but its control performance was not investigated. Hypothetically, the triple column FS configuration is less complex and does not involve any column integration and thus, may demonstrate a better dynamic performance. This study analyzed the control performances of the triple column FS configuration and the conventional configuration for the binary azeotropic separation of tetrahydrofuran and ethanol.RESULTSTwo types of control structures were examined for both configurations, i.e., the basic temperature control structure and the different feed forward temperature control schemes. The best control structure from each configuration is compared and findings showed that the conventional configuration provides better controllability performance.CONCLUSIONOur results suggested that the conventional configuration can bring the product qualities closer to their setpoint, while providing a lower transient deviation. © 2023 Society of Chemical Industry (SCI).

Numerical study of the solitary wave shoaling phenomena using KdV Equation

In this paper, we use a mathematical model to study the amplification of solitary wave height as water depth decreases. When considering solitary waves, it is necessary to incorporate nonlinear and dispersive effects into the model. As a consequence, we consider Korteweg–De Vries (KdV) to accurately examine this shoaling solitary wave phenomenon. The challenge in solving KdV equations is numerical approximation due to the presence of higher order derivative terms. In this section, we define a fourth-order forward time-centered space numerical scheme. Additionally, we compare our numerical results to the analytical solution. The shallower the water, the greater the wave height amplification. This research may be used to forecast wave heights along the shoreline, which may aid in the design of coastal management.

Stability of non-linear flow in heterogeneous porous media simulations using higher order and continuity basis functions

Using isogeometric analysis, we present a highly optimized FORTRAN code for simulations of three-dimensional non-linear flow problem in heterogeneous media. This includes deriving the weak formulations, discretizing with the forward Euler scheme, and implementing computation of the right-hand side. Some properties of exact solutions of heat transport and non-linear flow in heterogeneous media problems have been derived to validate the numerical solution. Stability analysis of the employed explicit time-stepping scheme has been performed. First, the properties of the discrete form of the heat transfer problem have been systematically investigated, leading to the conjecture concerning the sufficient condition of stability of the scheme, which numerical computations have subsequently confirmed. A similar analysis has been carried out for the non-linear flow in heterogeneous media problem. For this problem, the bound on the time step was conjectured to decrease exponentially, which has been verified experimentally. The simulation’s behavior close to the stability limit has been investigated and found to be considerably more complex than for the heat transport problem. Detailed experimental analysis of the time complexity of the particular parts of the simulator algorithm has been described. In addition, dependence on both mesh size and order of continuity of B-spline basis has been investigated.

Modified unified critical state model for soils considering over-consolidation and cyclic loading behaviours

This paper presents a modified unified critical state model to predict the mechanical responses of both clays and sands under over-consolidation and cyclic loading conditions on the basis of clay and sand model (CASM), which is named as CASM-kII. Through the application of subloading surface concept, CASM-kII is able to describe the plastic deformation inside the yield surface and the reverse plastic flow, and is thus expected to capture the over-consolidation and cyclic loading behaviours of soils. CASM-kII is numerical implemented by the using of the forward Euler scheme with automatic substepping and error control. Then, a sensitivity study is carried out to check the influences of the three new parameters of CASM-kII on the mechanical response of soils in over-consolidation and cyclic loading conditions. Through the comparisons of experimental data and simulated results, it is found that CASM-kII is able to satisfactorily describe the mechanical responses of both clays and sands in over-consolidation and cyclic loading conditions.

FS-IBEKS: Forward secure identity-based encryption with keyword search from lattice

Public Key Encryption with Keyword Search (PEKS) makes it possible for a cloud server (CS) to match a trapdoor and a ciphertext. However, with the upgrowth of quantum techniques, most of the existing PEKS schemes will be broken by quantum computers in the coming future. Moreover, they are also under the threat of potential key exposure. Lattice-based forward secure PEKS scheme (FS-PEKS) overcomes the two problems above by combining the techniques of forward security and lattice-based cryptography. However, FS-PEKS schemes work in public key infrastructure (PKI), which will incur complicated certificate management procedures. In this work, to overcome the key management issue but still guarantee security even when attackers corrupt the keys, we extend the FS-PEKS scheme into the identity-based framework and present a forward secure identity-based encryption with keyword search (FS-IBEKS) scheme from lattice. The proposed scheme is secured under the selective identity against chosen plaintext attack (IND-sID-CPA) in the random oracle model. To further improve the security, we present another FS-IBEKS scheme into the standard model and give concrete security proof under the adaptive identity against chosen plaintext attack (IND-ID-CPA). The comprehensive performance evaluation demonstrates that our FS-IBEKS schemes are feasible for cloud computing.

Spatio-temporal numerical modeling of stochastic predator-prey model

In this article, the ratio-dependent prey-predator system perturbed with time noise is numerically investigated. It relates to the population densities of the prey and predator in an ecological system. The initial prey-predator models only depend on the time and a couple of the differential equations. We are considering a model where the prey-predator interaction is influenced by both space and time and the need for a coupled nonlinear partial differential equation with the effect of the random behavior of the environment. The existence of the solutions is guaranteed by using Schauder’s fixed point theorem. The computation of the underlying model is carried out by two schemes. The proposed stochastic forward Euler scheme is conditionally stable and consistent with the system of the equations. The proposed stochastic non-standard finite difference scheme is unconditionally stable and consistent with the system of the equations. The graphical behavior of a test problem for different values of the parameters is shown which depicts the efficacy of the schemes. Our numerical results will help the researchers to consider the effect of the noise on the prey-predator model.

One‐Dimensionl Inversion of Magnetotelluric Field Data by SIS and Occam's Inversion Technique: A Case Study from the Indian Himalaya

AbstractElectromagnetic method is one of the most effective geophysical methods in earth crust and mantle structure studies. Magnetotelluric (MT) data are used to obtain resistivity image of earth's surface on the depth scale of few hundred of meters to several tens of km. One‐dimensional (1D) MT inversion is carried out to estimate electrical resistivity variation of earth's surface with depth. In the present research paper one‐dimensional inversion of MT sounding curves is carried out on nine sites in foothill of Himalaya near Roorkee to Hardwar region. A non‐iterative and minimum norm estimator based algorithm Straight forward Inversion Scheme (SIS) is used to obtain continuous smoothest resistivity depth model. Another iterative and minimum norm estimator based algorithm Occam's inversion scheme is also used to obtain smoothest one‐dimensional inversion model. The data is inverted for both TE‐ and TM‐mode of polarization. The inverted data shows one‐dimensional behavior of subsurface resistivity up to depth about 0–15 km with resistivity variation ≈10–100 ohm‐m in both modes of polarization and after that the subsurface structure is two‐dimensional in both modes. 1D inversion of data provides a good starting model to reduce the computational cost of two‐dimensional inversion.

Finite-Time Fuzzy Adaptive PPC for Nonstrict-Feedback Nonlinear MIMO Systems.

This article addresses the issue of the fuzzy adaptive prescribed performance control (PPC) design for nonstrict feedback multiple input multiple output (MIMO) nonlinear systems in finite time. Unknown nonlinear functions are handled via fuzzy-logic systems (FLSs). By combining the adaptive backstepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which can not only avoid the computational complexity issue but also improve the control performance in contrast to the traditional DSC control methods. Furthermore, to make the tracking errors have the prescribed performance in finite time, a new Lyapunov function is constructed by considering the transform error constraint. Based on the designed Lyapunov functions, it is proved that all the signals of the controlled systems are semiglobal practical finite-time stability (SGPFS). Finally, a simulation example is provided to illustrate the feasibility and validity of the put forward control scheme.

Numerical‐discrete‐scheme‐incorporated recurrent neural network for tasks in natural language processing

AbstractA variety of neural networks have been presented to deal with issues in deep learning in the last decades. Despite the prominent success achieved by the neural network, it still lacks theoretical guidance to design an efficient neural network model, and verifying the performance of a model needs excessive resources. Previous research studies have demonstrated that many existing models can be regarded as different numerical discretizations of differential equations. This connection sheds light on designing an effective recurrent neural network (RNN) by resorting to numerical analysis. Simple RNN is regarded as a discretisation of the forward Euler scheme. Considering the limited solution accuracy of the forward Euler methods, a Taylor‐type discrete scheme is presented with lower truncation error and a Taylor‐type RNN (T‐RNN) is designed with its guidance. Extensive experiments are conducted to evaluate its performance on statistical language models and emotion analysis tasks. The noticeable gains obtained by T‐RNN present its superiority and the feasibility of designing the neural network model using numerical methods.

Digital Twin Concept Utilizing Electrical Resistivity Tomography for Monitoring Seawater Intrusion

Electrical resistivity tomography (ERT) has been seen as an appropriate instrument in several works to monitor and aid in the control of seawater intrusion (SWI) in coastal groundwater systems. This study seeks to discuss the synthesis of a digital twin that couples information between the physical space through ERT as a monitoring sensor and the digital space using SWI simulations to accurately model the behavior of SWI in the present and future settings. To showcase the concept, a Python-based simulation was presented that shows (a) the joint forward modeling-simulation scheme for calculating expected ERT apparent resistivity values from simulated SWI and (b) the calibration of the digital coastal aquifer system through genetic algorithm to accurately match the outputs of the SWI simulations with the ERT measurements.

BIFURCATION AND COMPARISON OF A DISCRETE-TIME HINDMARSH-ROSE MODEL

In this paper, a Hindmarsh-Rose model discretized by a nonstandard finite difference (NSFD) scheme is considered. Bifurcation behaviors are compared between the model obtained by the forward Euler scheme and the model obtained by the NSFD scheme. Through analytical and numerical comparisons, the Neimark-Sacker bifurcation of the model discretized by the NSFD method is closer to the Hopf bifurcation of the original continuous Hindmarsh-Rose model than that discretized by the forward Euler method. Moreover, due to the NSFD method's better stability and convergence, the integral step size can be chosen larger in the NSFD scheme. And much more dynamic behaviors can be obtained by using the NSFD scheme than those in the forward Euler scheme. These confirmed results can at least guarantee true available numerical results to investigate complex neuron dynamical systems.

The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting

Modeling the interaction between prey and predator plays an important role in maintaining the balance of the ecological system. In this paper, a discrete-time mathematical model is constructed via a forward Euler scheme, and then studied the dynamics of the model analytically and numerically. The analytical results show that the model has two fixed points, namely the origin and the interior points. The possible dynamical behaviors are shown analytically and demonstrated numerically using some phase portraits. We show numerically that the model has limit-cycles on its interior. This guarantees that there exists a condition where both prey and predator maintain their existence periodically.

On the fractional-order glucose-insulin interaction

<abstract><p>We consider a fractional-order model of glucose and insulin interaction based on the intra-venous glucose tolerance test (IVGTT). We show the existence of the model's solution, uniqueness, non-negativity, and boundadness. In addition, for the proposed fractional-order model, we establish sufficient conditions for stability or instability. Some conditions for bifurcation in the proposed model are presented using bifurcation theory. Further, in the case of first order the model is discretized by applying the forward Euler scheme. We investigate how small the time step size must be chosen to guarantee that the steady state solution is an attractive fixed point of the discretized model. Numerical simulations that we provided support the analytical results.</p></abstract>

Forward and Backward Secure Searchable Encryption Scheme Supporting Conjunctive Queries Over Bipartite Graphs

Forward and Backward Secure Searchable Encryption Scheme Supporting Conjunctive Queries Over Bipartite Graphs

3-D Forward Modeling of Transient EM Field in Rough Media Using Implicit Time-Domain Finite-Element Method

In a heterogeneous medium (usually called a rough medium) with fractured formations, the propagation of an electromagnetic (EM) field is a type of subdiffusion. Current mainstream geophysical EM data processing methods cannot be applied to data acquired on heterogeneous Earth, as they are not governed by the classic diffusion theory. To evaluate the influence of roughness on the transient EM (TEM) signal for a complex model and contribute to data inversion, we proposed a novel three-dimensional (3-D) forward modeling scheme for TEM in rough media. First, we derived the governing equation with a fractional-order time derivative for the subdiffusion of EM waves in rough media. Then, we proposed a novel time discretization using an unequal step length for the Caputo operator, which significantly reduces the total number of time steps. Finally, an implicit time-domain finite-element method using unstructured tetrahedron discretization was adopted to solve the 3-D forward problem. Furthermore, an efficient time segmentation strategy combined with parallel RHS construction was proposed to accelerate modeling. The numerical results prove that the proposed method is accurate and efficient, and will be a powerful numerical method for analyzing TEM wave propagation and processing TEM data in areas with multiscale fractures or porosity.

Unsteady State Temperature Distribution Inside House Based on Slope Roof

The house is a building that serves as a place to gather with family and also to get comfort. The house is designed so the occupants can feel aesthetically and functionally comfortable. It will be interesting to discuss the temperature inside the house as one of the comfort factors. The study aims to analyze the temperature conditions inside the house, which are influenced by the slope of the roof. A two-dimensional unsteady state heat equation represents this temperature since the temperature distribution satisfies the heat transfer concept and changes over time. This governing equation will be approximated by the forward time center space scheme as one finite difference method and completed by the quadratic ghost point method since the house domain is an irregular shape. Van Neumann criteria are applied here to analyze the stability of the computational approach for this numerical scheme. Furthermore, these schemes are implemented in MATLAB application to quantitatively and visually display temperature dynamics. Some simulations completed these approximations to see temperature variations over time. The results show that the bigger slope causes the average temperature to be cooler. In other words, the temperature in the house will be more comfortable when the roof slope gets bigger.

Generation of ultrafast laser with 11 MW peak power from a gain-managed nonlinear tapered fiber amplifier

A gain-managed nonlinear (GMN) tapered fiber amplifier with a monolithic configuration is experimentally demonstrated. Both the forward and backward pumping scheme were investigated, and the results indicate that the latter is advantageous in suppressing the unwanted stimulated Raman scattering and the resulting mode distortion while boosting the pulse energy with a shortest pulse width of sub-50 fs. Specifically, a maximum single pulse energy of 707 nJ and a peak power of 11 MW with a fundamental Gaussian distribution beam profile were respectively realized without temporally stretching the seed pulse. In addition, the backward pumped amplifier was further examined through changing its seeding power, and it is found that a relatively low input power is preferable for obtaining high performance laser pulses with shorter duration while without compromise on the output single pulse energy. It is believed that the combination of the GMN amplification and the large mode area tapered fiber provides a promising scheme for realizing high energy ultrafast lasers with a monolithic and concise structure.

Spectral treatment for the fractional-order wave equation using shifted Chebyshev orthogonal polynomials

This paper will examine the approximate solution for the fractional-order wave equation. The method used for this purpose fundamentally is based on the second kind of Chebyshev polynomials besides the Chebyshev collocation mechanism in addition to the forward finite difference scheme. The fractional-order terms are expressed through Caputo’s fractional-order derivative definition. With these tools, the problem will be converted into an algebraic system of equations that are solved numerically. The accuracy and applicability of the proposed technique are demonstrated through some given numerical applications.

Acceleration of RBF-FD meshless phase-field modelling of dendritic solidification by space-time adaptive approach

• A novel meshless approach for phase-field modelling of dendritic growth. • Reduction of discretisation-induced anisotropy by the scattered nodes. • Increase in computational efficiency by a space-time adaptive approach. A novel adaptive numerical approach is developed for an accurate and computationally efficient phase-field modelling of dendritic solidification. The adaptivity is based on the dynamic quadtree domain decomposition. A quadtree decomposes the computational domain into rectangular sub-domains of different sizes. Each sub-domain is extended to ensure overlap communication between neighbouring sub-domains. In each sub-domain, uniform distribution of computational nodes is generated. The product between the node density and the sub-domain area is fixed to ensure the h-adaptivity. The adaptive approach provides the highest density of computational nodes at the solid-liquid interface and the lowest density in the bulk of the phases. The meshless radial basis function generated finite difference (RBF-FD) method is applied for the spatial discretisation of the partial differential equations which arise from the phase-field model. The RBF-FD method is especially appealing since it allows straightforward spatial discretisation of partial differential equations on scattered node distributions. The use of scattered node distribution reduces the discretisation-induced anisotropy in the phase-field modelling of dendritic growth. The forward Euler scheme is used for temporal discretisation. The adaptive time-stepping is employed to speed up the calculations further. The performance of the novel numerical approach is tested for dendritic solidification of supercooled pure melts and supersaturated dilute binary alloys at arbitrary preferential growth directions. The impact of the numerical parameters on the accuracy and computational efficiency is thoroughly analysed. It is shown that the RBF-FD method, defined on scattered node distribution, together with the space-time adaptive approach, represents an accurate and efficient technique for solving the phase-field models of dendritic solidification.

Speeding up mesoscale thermal simulations of powder bed additive manufacturing thanks to the forward Euler time-integration scheme: A critical assessment

This work addresses the mesoscale conduction-based modelling of Powder Bed Fusion for metallic materials. The forward Euler (explicit) time integration strategy is thoroughly benchmarked for the first time in a Powder Bed Fusion simulation. We also compare the computational times of explicit and implicit schemes when applied to an experimentally validated Powder Bed Fusion simulation. We demonstrate that the use of the former scheme results in considerable speedups (20 to 100) without noticeable loss of accuracy. We furthermore propose a Powder Bed Fusion-dedicated procedure to estimate the maximum allowable time step size of the explicit scheme.