Solution Of Problem Research Articles

Integrated analytical, experimental, and numerical study of vibrational response in clamped circular plates with pressurised air cavities

This paper presents a comprehensive investigation, comprised of analytical, experimental and numerical approaches, into the interaction between the sound field produced within a pressurised air-filled back cavity and the vibration of a thin clamped circular plate subjected to its pressure. Previous investigations into the interaction of sound fields with vibrating boundaries have primarily been restricted to non-pressurised cavities. We extend the application of the weak modal coupling method to derive a solution for this unexplored physical problem by utilising classic plate theory, Fourier-Bessel series formulation and the uncoupled solutions for a pressurised cylindrical sound field and a thin clamped circular plate with uniform radial tension. We describe the vibration response of the coupled system in terms of the uncoupled cavity and plate modes. Using a set of geometric and physical properties for the system, the resonance frequencies and response functions are calculated and the coupling between the sound field and the plate is investigated as a function of cavity pressure, providing novel fundamental insights into the physical system. We construct an experimental rig to embody the conditions of the analytical investigation for the purpose of validation. Finite element analysis (FEA), employing modal analysis and transient dynamic analysis, is used to further validate and extend the analytical insights while more accurately mirroring the experimental conditions. The response functions, mode shapes, resonance frequencies and their dependence on the cavity pressure were experimentally measured and numerically simulated, with direct comparisons made with the analytical model. A high degree of accuracy for the analytical model is validated along with its ability to describe the underlying physical phenomena. The validated analytical model is then leveraged to perform fundamental explorations into the modal contributions as a function of cavity pressure and a parametric sensitivity analysis on the effects of plate radii and plate thickness on the coupled system resonance frequencies.

On the convergence of local solutions for the method quADAPT

ABSTRACT A classical solution approach to semi-infinite programming, which is easy to implement, is based on discretizing the semi-infinite index set. The Blankenship and Falk algorithm adaptively chooses a small discretization. On every iteration, a solution based on the current discretization is calculated. In a second step, the most violated constraint is determined and added to the discretization. In a previous work, the authors showed that the algorithm has a slow convergence and introduced a new method that exhibits a quadratic rate [Seidel and Küfer, An adaptive discretization method solving semi-infinite optimization problems with quadratic rate of convergence. Optimization. 2022;71(8):2211–2239]. In this paper, we further investigate the introduced method. The method implements new constraints that can cut off parts of the feasible set. We will study the effect on local minima. We assume that in each iteration local solutions to the discretized problems are computed. We will give an example showing that in general a limit point is not necessarily a local solution of the original semi-infinite problem, but only of an approximate problem. We then study second-order conditions and show that they coincide for both problems. We use this to develop conditions under which local solutions converge to a local solution in the limit. Finally, we present quadratic convergence results for the case of local solutions.

On crack simulation by mixed‐dimensional coupling in GFEM with global‐local enrichments

AbstractA strategy that combines the global‐local version of the generalized finite element method (GFEM) with a mixed‐dimensional coupling iterative method is proposed to simulate two‐dimensional crack propagation in structures globally represented by Timoshenko‐frame models. The region of interest called the local problem, where the crack propagates, is represented by a 2D elasticity model, where a fine mesh of plane stress/strain elements and special enrichment functions are used to describe this phenomenon accurately. A model of Timoshenko‐frame elements simulates the overall behavior of the structure. A coarse mesh of plane stress/strain elements provides a bridge between these two representation scales. The mixed‐dimensional coupling method imposes displacement compatibility and stress equilibrium at the interface between the two different element types by an iterative procedure based on the principle of virtual work. After establishing the constraint equations for the interface, the 2D elasticity model is related to the small‐scale model by the global‐local enrichment strategy of GFEM. In such a strategy, the numerical solutions of the local problem subjected to boundary conditions derived from the global‐scale problem enrich the approximation of this same global problem in an iterative procedure. Each step of the crack propagation requires a new sequence of this iterative global‐local procedure. On the other hand, the constraint equation for the interface is defined only once. The crack representation in a confined region by the global‐local strategy avoids a remeshing that would require new constraint equations. Two numerical problems illustrate the proposed strategy and assess the influence of the analysis parameters.

Dynamic examination of closed cylindrical shells utilizing the differential transform method

This article presents an innovative approach using the Differential Transform Method (DTM) to analyze the vibration characteristics of cylindrical shells, integrating Taylor's series with Sander's classical theory. It demonstrates DTM's efficiency, accuracy, and potential as an alternative method. The study introduces a novel application of the DTM in exploring the free vibration of cylindrical shells, detailing a technique to address challenges such as normalization, linear solution methodologies, and parameter derivative modifications. A dimensionless parameter analysis evaluates the impact of length, radius, thickness, and modulus of elasticity. Comparative analysis with Hybrid Finite Element Method (FEM) data and validation against existing literature highlights DTM's precision and reliability. In conclusion, DTM offers a robust solution for the eigenvalue problem in coupled differential equations, providing accurate vibration parameters. Additionally, an important relationship between the modulus of elasticity and frequency in the dimensionless state was obtained.

New computational methods using seventh-derivative type for the solution of first-order initial value problems

This study uses finite power series as the basis function and interpolation and collocation techniques to study a class of implicit block methods of a seventh-derivative type. Discrete schemes are implicit two-point block methods that are obtained by selecting collocation points carefully and unevenly in order to improve the stability of the methods through testing. Nevertheless, in contrast to other current numerical equations, these methods require seventh-derivative functions. The novel techniques are identified, examined, and shown to be A-stable and convergent. Newton Raphson’s approach is used to accomplish method implementation. Trials demonstrated the effectiveness and precision of the derived equations in terms of computational time and absolute errors on a variety of first-order initial value issues, such as first-order, second-order linear differential systems and SIR model. When compared to similar methods that are currently in the literature, the suggested methods produce better numerical results.

Optimal Neumann control of the wave equation with L 1-control cost: the finite-time turnpike property

The finite-time turnpike property describes a situation where the optimal state reaches a steady state after finite time. The steady state is a solution of a static optimal control problem. We study an optimal control problem where the objective functional is the sum of an L 1 -norm control cost with a weight γ > 0 and a differentiable tracking term. We consider a vibrating string with homogeneous Dirichlet conditions at one end and Neumann control action at the other end. The tracking term is defined by the squared L 2 -norm of a non-collocated Neumann-observation. We show that the problem has a unique solution and that due to the non-smoothness of the L 1 -norm for sufficiently large T the optimal state reaches the desired state after a finite time that is equal to the minimal time where exact controllability holds. We also study the effect of smoothing of the control cost on the structure of the optimal control and show that the finite-time turnpike property also holds in the smoothing limit in a strong L 2 -sense.

Evaluation of Serum Kallistatin in Patients with Hepatocellular Carcinoma

Abstract Background Liver cirrhosis is the most frequent long-term consequence of all chronic liver diseases. Cirrhosis is often asymptomatic and unsuspected until complications. The annual incidence rates of liver cirrhosis and hepatocellular carcinoma is related with chronic hepatitis B or C all over the world. The majority of patients with liver cirrhosis or hepatocellular carcinoma die from complications, which happened relatively early in the course of the disease. Thus, the early diagnosis of liver diseases is the only solution for this great problem. Aim of the Work In the current study we aimed to evaluate serum kallistatin in Egyptian patients with hepatitis C virus related liver cirrhosis and hepatocellular carcinoma. Patients and Methods This case control study enrolled 90 Egyptian subjects aged ≥ 18 years old at Ain shams university hospitals, participants were classified into 3 groups as follow: Group 1: 30 patients with hepatocellular carcinoma (patients have been diagnosed with triphasic CT). Group 2: 30 patients with hepatitis C virus related liver cirrhosis (patients diagnosed according to clinical, laboratory and radiological findings. Group 3: 30 healthy subjects serving as a control group. Results This study found that patients with liver cirrhosis and HCC have lower levels of serum Kallistatin compared to a control group. In the HCC group, patients with more severe liver disease (Child class C) had lower Kallistatin levels than those with less severe disease (Child class A and B). Kallistatin was negatively correlated with certain markers of liver disease and inflammation in both groups, and positively correlated with hemoglobin and albumin. The study also tested the diagnostic accuracy of Kallistatin for detecting liver cirrhosis and HCC, and found that it had 66.5% accuracy for cirrhosis and 98% accuracy for HCC at specific cutoff points. Conclusion Serum Kallistatin has a potential rule as a new biomarker for the diagnosis and evaluation of liver cirrhosis and HCC. The present study was limited by the small sample size. Also, all participants were from the Egyptian population with liver disease induced by HCV- infection with no information if our findings would be valid for other population with different etiologies. Thus, further investigation should be carried out in order to validate these findings

Morphological diffculties in an anatomical pattern of the crystals

The study of minerals with modern electron microscopes requires the solution of anatomical problems of the crystals. To obtain consistent spectroscopic data from different instruments, it is necessary to point the microprobe directly to the same element of the crystal anatomy. This is diffcult to do unknown details of an anatomical pattern. The article provides the examples of complex arrangement of elements of crystal anatomy of different minerals to accumulate ontogenetic information for the formulation of the postulates.

Forecasting the waste production hierarchical time series with correlation structure

AbstractContinuous increase in society’s prosperity causes overwhelming growth of the produced municipal solid waste. Circular economy initiatives help to solve this problem by creating closed production cycles, where the produced waste is recycled, or its energy is recovered. An embedment of such principles requires implementation of new waste management strategies. However, these novel strategies must be based on the accurate forecasts of future waste flows. Municipal solid waste production data demonstrate behavior of hierarchical time series. Among all possible approaches to hierarchical times series forecasting, this article is focused on the reconciliation of the base waste generation forecasts. The novel method, that is based on the game-theoretically optimal reconciliation of hierarchical time series, is presented. The modified approach enables to incorporate interdependencies between time series using correlation matrix and to obtain the forecasts corresponding to the unique solution of the optimization problem. The potential of the proposed abstract approach is demonstrated on the waste production data of paper, plastics (both primarily sorted by households), and mixed municipal solid waste from the Czech Republic.

Water retention curves of sandy soils obtained from direct measurements, particle size distribution, and infiltration experiments

AbstractAccurate information about soil water retention curves (SWRCs) of sands is essential for evaluating groundwater recharge and vulnerability to contamination in many shallow sandy aquifers which are widespread on post glacial areas in Northern Europe and North America. Pedotransfer functions (PTFs) allow to estimate SWRC from basic physical characteristics of soils, such as textural composition. However, in the case of clean sands which are dominated by a single textural fraction, PTFs should be based on more detailed information given by the particle size distribution. In this study we evaluated three parametric PTFs, which estimate parameters of the van Genuchten SWRC based on empirical correlations to the parameters of soil particle size distribution, and five semi‐physical PTFs, which derive the pore size distribution from particle size distribution. PTFs were compared to SWRCs fitted to the results of drainage experiments on sandy soil samples from six locations in Gdańsk region (northern Poland). Although in all samples the content of silt and clay fractions was low (<3.5%), the differences in actual content of fines strongly influenced the shape of SWRC. In contrast, the amount of gravel fraction (varying from 1% to 35%) did not have significant effect on SWRC. Semi‐physical PTFs were found to be more accurate than parametric PTFs. The best overall performance was shown by the semi‐physical Chang and Cheng PTF. Among the parametric PTFs the best accuracy was obtained with the Schaap and Bouten method. However, all considered functions showed limited accuracy in higher suction range. Additionally, infiltration experiments were performed on four sites. SWRCs were obtained from ring infiltrometer tests using the Beerkan estimation of soil transfer parameters (BEST) method and from the tension infiltrometer (TI) tests using numerical solution of the inverse problem based on the Richards equation. In almost all cases the wetting SWRCs were characterized by higher values of the pressure scaling parameter α compared to SWRCs measured in drainage experiments, which is consistent with the well‐known phenomenon of hysteresis in soils. However, the BEST method resulted in significantly higher α and hydraulic conductivity Ks than TI, probably due to activation of the largest soil pores during ponded infiltration.

Exponential stabilization of linear systems with feedback optimization and its application to microgrids control

This paper proposes a feedback-optimization-based control method for linear time-invariant systems, which is aimed to exponentially stabilize the system and, meanwhile, drive the system output to an approximate solution of an optimization problem with convex set constraints and affine inequality constraints. To ensure the exponential stability of the closed-loop system, the original optimization problem is first reformulated into a counterpart that has only convex set constraints. It is shown that the optimal solution of the new optimization problem is an approximate optimal solution of the original problem. Then, based on this new optimization problem, the projected primal–dual gradient dynamics algorithm is used to design the controller. By using the singular perturbation method, sufficient conditions are provided to ensure the exponential stability of the closed-loop system. The proposed method is also applied to microgrid control.

Applications of a variable anchoring iterative method to equation and inclusion problems on Hadamard manifolds

In this paper, we introduce a new iterative technique with a variable anchoring operator for reckoning the solution of a variational inequality problem over the set of the common fixed points of a nearly nonexpansive sequence of operators in the framework of Hadamard manifolds. We also establish a convergence result on the proposed algorithm for approximating a solution of the problem, under suitable assumptions. We apply our results for finding the solutions of a system of nonlinear equations, and of inclusion problems to support their utility Our work improves results in the recent literature. Numerical simulations are given for a better understanding of the effectiveness of our outcomes.

Doubly perturbed uncertain differential equations

In this paper, we study a class of doubly perturbed uncertain differential equations driven by canonical process that is the counterpart of Wiener process in the framework of uncertain theory. We give some sufficient conditions for the existence and uniqueness of solutions of the present problem under some weak conditions, where a convex combination of the Nagumo and Osgood conditions is considered. Subsequently, we consider the stability properties with regard to the initial value and coefficients. Finally, an example is provided to illustrate the effectiveness of our main results.

Development of an optimal adaptive finite element stabiliser for the simulation of complex flows

An optimal adaptive multiscale finite element method(AMsFEM) for numerical solutions of flow problems modelled by the Oldroyd B model is developed. Complex flows experience instabilities due to a phenomena known as the high Weissenberg number problem. The stabilisers are terms in-cooperated into the variational formulation when applying the finite element method. For the selected few stabilisers, numerical experiments are performed to study the convergence of the solutions. These demonstrate that adaptive strategies reduce the computational load of flow simulation. A best performing combination of choice of stabiliser and adaptive strategy is suggested.

Advances in Chitosan-based Drug Delivery Systems in Melanoma: A Narrative Review.

Melanoma accounts for the minority of skin cancer cases. However, it has the highest mortality rate among the subtypes of skin cancer. At the early stages of the disease, patients show a good prognosis after the surgery, but developing metastases leads to a remarkable drop in patients' 5-year survival rate. Despite the advances made in the therapeutic approaches to this disease, melanoma treatment is still facing several obstacles. Systemic toxicity, water insolubility, instability, lack of proper biodistribution, inadequate cellular penetration, and rapid clearance are some of the challenges that should be addressed in the field of melanoma treatment. While various delivery systems have been developed to circumvent these challenges, chitosan-based delivery platforms have indicated significant success. Chitosan that is produced by the deacetylation of chitin can be formulated into different materials (e.g., nanoparticle, film, and hydrogel) due to its characteristics. Both in vitro and in vivo studies have reported that chitosan-based materials can be used in drug delivery systems while offering a solution for the common problems in this area, such as enhancing biodistribution and skin penetration as well as the sustained release of the drugs. Herein, we reviewed the studies concerning the role of chitosan as a drug delivery system in melanoma and discussed how these drug systems are used for delivering chemotherapeutic drugs (e.g., doxorubicin and paclitaxel), genes (e.g., TRAIL), and RNAs (e.g., miRNA199a and STAT3 siRNA) successfully. Furthermore, we take a look into the role of chitosan-based nanoparticles in neutron capture therapy.

Inverse a time-dependent potential problem of a generalized time-fractional super-diffusion equation with a nonlinear source from a nonlocal integral observation

This paper focus on the problem of reconstructing the time-dependent potential in a class of generalized (including three special cases: the classical/multi-term/distributed order) time-fractional super-diffusion equations with nonlinear sources from a nonlocal integral observation. For such nonlinear equation, we investigate it for both the direct and inverse time-dependent potential problems. For the direct problem, given the time-dependent potential function p(t), we obtain the well-posedness of the corresponding initial–boundary value problem. For the inverse potential problem, by utilizing additional nonlocal measurement data and using the Arzelà–Ascoli theorem and Grönwall’s inequality, we prove the existence and uniqueness of the solution for such nonlinear problem. Meanwhile, we also demonstrate the ill-posedness of the inverse problem. Moreover, to validate the theoretical results, we numerically reconstruct the potential term from Bayesian perspective. Several numerical examples are presented to show the efficiency of the proposed method.

Intuitionistic fuzzy generalized eigenvalue proximal support vector machine

Generalized eigenvalue proximal support vector machine (GEPSVM) has attracted widespread attention due to its simple architecture, rapid execution, and commendable performance. GEPSVM gives equal significance to all samples, thereby diminishing its robustness and efficacy when confronted with real-world datasets containing noise and outliers. In order to reduce the impact of noises and outliers, we propose a novel intuitionistic fuzzy generalized eigenvalue proximal support vector machine (IF-GEPSVM). The proposed IF-GEPSVM assigns the intuitionistic fuzzy score to each training sample based on its location and surroundings in the high-dimensional feature space by using a kernel function. The solution of the IF-GEPSVM optimization problem is obtained by solving a generalized eigenvalue problem. Further, we propose an intuitionistic fuzzy improved generalized eigenvalue proximal support vector machine (IF-IGEPSVM) by solving the standard eigenvalue decomposition resulting in simpler optimization problems with less computation cost which leads to an efficient intuitionistic fuzzy-based model. We conduct a comprehensive evaluation of the proposed IF-GEPSVM and IF-IGEPSVM models on UCI and KEEL benchmark datasets. Moreover, to evaluate the robustness of the proposed IF-GEPSVM and IF-IGEPSVM models, label noise is introduced into some UCI and KEEL datasets. The experimental findings showcase the superior generalization performance of the proposed IF-GEPSVM and IF-IGEPSVM models when compared to the existing baseline models, both with and without label noise. Our experimental results, supported by rigorous statistical analyses, confirm the superior generalization abilities of the proposed IF-GEPSVM and IF-IGEPSVM models over the baseline models. Furthermore, we implement the proposed IF-GEPSVM and IF-IGEPSVM models on the USPS recognition dataset, yielding promising results that underscore the models’ effectiveness in practical and real-world applications. The source code of the proposed IF-GEPSVM and IF-IGEPSVM models are available at https://github.com/mtanveer1/IF-GEPSVM.

Multi‐objective terminal trajectory optimization based on hybrid genetic algorithm pseudospectral method

AbstractDuring terminal guidance, the attack platform is provided with a high‐resolution image of the target area through the application of synthetic aperture radar. Additionally, the stealth trajectory with low observability can significantly impact mission success. This paper considers both the performance of missile‐borne synthetic aperture radar imaging and stealth performance as influencing factors for terminal trajectory optimization, which is modelled as a constrained multi‐objective optimization problem. The application of the pseudospectral method in the solution of optimal control problems has led to the proposal of the hybrid genetic algorithm pseudospectral optimization framework. The problem is decomposed into several single‐objective optimal control problems, which can generate a specific initial population for the genetic algorithm to obtain a set of Pareto‐optimal solutions. Finally, the numerical simulations demonstrate the effectiveness of the proposed optimization approach compared with the benchmark scheme.

On the choice of physical constraints in artificial neural networks for predicting flow fields

The application of Artificial Neural Networks (NNs) has been extensively investigated for fluid dynamic problems. A specific form of ANNs are Physics-Informed Neural Networks (PINNs). They incorporate physical laws in the training and have increasingly been explored in the last few years. In this work, prediction accuracy of PINNs is compared with that of conventional Deep Neural Networks (DNNs). The accuracy of a DNN depends on the amount of data provided for training. The change in prediction accuracy of PINNs and DNNs is assessed using a varying amount of training data. To ensure the correctness of the training data, they are obtained from analytical and numerical solutions of classical problems in fluid mechanics. The objective of this work is to quantify the fraction of training data relative to the maximum number of data points available in the computational domain, such that the accuracy gained with PINNs justifies the increased computational cost. Furthermore, the effects of the location of sampling points in the computational domain and noise in training data are analyzed. In the considered problems, it is found that PINNs outperform DNNs when the sampling points are positioned in the Regions of Interest. The PINNs for the potential flow around the Rankine oval have shown better robustness against noise in training data compared to DNN. Both models show higher prediction accuracy when sampling points are randomly positioned in the flow domain as compared to a prescribed distribution of sampling points. The findings reveal new insights on the strategies to massively improve the prediction capabilities of PINNs with respect to DNNs.

The unified transformation approach to higher-order Gerdjikov-Ivanov model and Riemann-Hilbert problem

In this paper, a higher-order Gerdjikov-Ivanov (HOGI) model with cubic dispersion and quintic nonlinearity terms will be researched, which is a 3-order flow model of the well known GI system. The initial-boundary value problems of the HOGI model on the half-line will be given by the unified transformation approach. The solutions of the HOGI model will be expressed by forms of the solutions of a matrix Riemann-Hilbert problem (RHP). The relevant jump matrices of the RHP will be explicitly found by the two scattering matrices s(ϵ) and S(ϵ). Finally, the so-called global relation will be given.