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In this work, we investigate a divergence-free, nonconforming virtual element method for the numerical approximation of the Stokes eigenvalue problems using polygonal unstructured meshes on polygonal domain. By employing an elliptic projection operator, we "enhance" the definition of the virtual element space to make the L 2 -projection operator computable with optimal order. Furthermore, we prove the optimal order of convergence of the eigenfunction approximation and the double order of convergence of the eigenvalue approximation through compactness arguments for the solution operator (Babuška-Osborn Theory). Finally, we present a set of numerical experiments to assess the good approximation behavior of the method and show its computational performance. [ABSTRACT FROM AUTHOR]

A C 0 nonconforming virtual element method (VEM) is employed for the discretization of nonselfadjoint fourth-order eigenvalue problems derived from the transmission eigenvalue problem on general polygonal meshes. Further, we linearize the model problem by introducing an auxiliary variable and thus the variational problem becomes double in size. We discretize the modified scheme by using suitable projection operators and acquire the convergence analysis under standard assumptions on the polygonal meshes. We establish that the resulting discretization provides a correct approximation of the spectrum and conclude the convergence of the eigenfunctions and eigenvalues. A variety of representative examples are examined to justify the theoretical estimates. [ABSTRACT FROM AUTHOR]

We approximate the solution of the stream function formulation of the Oseen equations on general domains by designing a nonconforming Morley-type virtual element method. Under a suitable assumption on the continuous problem's coefficients, the discrete scheme is well-posed. By introducing an enriching operator, we derive an a priori estimate of the error in a discrete H2 norm. By post-processing the discrete stream function, we compute the discrete velocity and vorticity fields. Furthermore, we recover an approximate pressure field by solving a Stokes-like problem in a nonconforming Crouzeix–Raviart-type virtual element space that is in a Stokes-complex relation with the Morley-type space of the virtual element approximation. Finally, we confirm our theoretical estimates by solving benchmark problems that include a convex and a nonconvex domain. [ABSTRACT FROM AUTHOR]

In this work, we have designed conforming and nonconforming virtual element methods (VEM) to approximate non-stationary nonlocal biharmonic equation on general shaped domain. By employing Faedo–Galerkin technique, we have proved the existence and uniqueness of the continuous weak formulation. Upon applying Brouwer's fixed point theorem, the well-posedness of the fully discrete scheme is derived. Further, following [J. Huang and Y. Yu, A medius error analysis for nonconforming virtual element methods for Poisson and biharmonic equations, J. Comput. Appl. Math. 386 (2021) 113229], we have introduced Enrichment operator and derived a priori error estimates for fully discrete schemes on polygonal domains, not necessarily convex. The proposed error estimates are justified with some benchmark examples. [ABSTRACT FROM AUTHOR]

In this article, we have developed the mixed virtual element formulation for the nonlocal parabolic problem. A priori error estimates for the semi‐discrete and the fully‐discrete schemes are derived and analyzed. The spatial discretization is based on the mixed virtual element framework, and the backward Euler method is used for the time discretization. Using Brouwer's fixed point argument, we have proved the existence and uniqueness of a fully‐discrete scheme. A set of representative numerical examples investigates such theoretical results. [ABSTRACT FROM AUTHOR]

In this work, a new Virtual Element Method (VEM) of arbitrary order k ≥ 2 for the time dependent Navier–Stokes equations in stream-function form is proposed and analyzed. Using suitable projection operators, the bilinear and trilinear terms are discretized by only using the proposed degrees of freedom associated with the virtual space. Under certain assumptions on the computational domain, error estimations are derived and shown that the method is optimally convergent in both space and time variables. Finally, to justify the theoretical analysis, four benchmark examples are examined numerically. [ABSTRACT FROM AUTHOR]

This article deals with the development of the virtual element method for the approximation of semilinear hyperbolic problems. For the space discretization, two different operators are used: the energy projection operator and an internal -projection operator . In order to deal with the time derivative, a Newmark scheme is employed; and the resulted fully discrete scheme is analysed. Moreover, with the help of projection operators, optimal error estimates are derived for both semi- and fully discrete schemes in -norm and -norm. We have conducted numerical experiments on polygonal meshes to illustrate the performance of the proposed scheme and validate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this article, we discuss and analyze new conforming virtual element methods (VEMs) for the approximation of semilinear parabolic problems on convex polygonal meshes in two spatial dimension. The spatial discretization is based on polynomial and suitable nonpolynomial functions, and a Euler backward scheme is employed for time discretization. The discrete formulation of both the proposed schemes—semidiscrete and fully discrete (with time discretization) is discussed in detail, and the unique solvability of the resulted schemes is discussed. A priori error estimates for the proposed schemes (semidiscrete and fully discrete) in H1‐ and L2‐norms are derived under the assumption that the source term f is Lipschitz continuous. Some numerical experiments are conducted to illustrate the performance of the proposed scheme and to confirm the theoretical convergence rates. [ABSTRACT FROM AUTHOR]

The fly ash based geopolymer concrete generally requires heat activation of different temperatures, which has been considered as an important limitation for its practical application. Such limitation can be overcome by the addition of appropriate amount of nano-silica in the mixture. Therefore, a fly ash based geopolymer concrete can be developed using 6% nano silica replacing fly ash. The structural performance of such geopolymer concrete in terms of bond strength, flexural strength and micro structural behaviour has been explored. Such nano silica modified fly ash based geopolymer concrete shows appreciable improvement in structural behaviour at different ages without any heat activation. The bond strength between reinforcement bars (deformed or mild steel) and surrounding geopolymer concrete materials (with/without nano silica) has been also compared to the conventional cement concrete. The nano silica modified geopolymer concrete exhibits better structural performance than heat cured geopolymer concrete (without nano silica) and conventional cement concrete samples. The microstructural properties of such geopolymer concrete (with/without nano silica) and cement concrete have been analyzed through Field Emission Scanning Electron Microscope (FESEM) with Energy Dispersive X-ray Spectroscopy (EDS), Fourier Transform Infrared Spectroscopy (FTIR) analysis and X-ray Diffraction (XRD) techniques. The enhancement of structural performance is mainly due to the transformation of amorphous phase to crystalline phase in the geopolymer concrete matrices in the presence of nano-silica. [ABSTRACT FROM AUTHOR]

In this work, we study the C 0 -nonconforming VEM for the fourth-order eigenvalue problems modeling the vibration and buckling problems of thin plates with clamped boundary conditions on general shaped polygonal domain, possibly even nonconvex domain. By employing the enriching operator, we have derived the convergence analysis in discrete H 2 seminorm, and H 1 , L 2 norms for both problems. We use the Babuška–Osborn spectral theory (Babuška and Osborn, 1991), to show that the introduced schemes provide well approximation of the spectrum and prove optimal order of rate of convergence for eigenfunctions and double order of rate of convergence for eigenvalues. Finally, numerical results are presented to show the good performance of the method on different polygonal meshes. [ABSTRACT FROM AUTHOR]

The cement industry plays a significant role in global carbon emissions, underscoring the urgent need for measures to transition it toward a net-zero carbon footprint. This paper presents a detailed plan to this end, examining the current state of the cement sector, its carbon output, and the imperative for emission reduction. It delves into various low-CO 2 technologies and emerging innovations such as alkali-activated cements, calcium looping, electrification, and bio-inspired materials. Economic and policy factors, including cost assessments and governmental regulations, are considered alongside challenges and potential solutions. Concluding with future prospects, the paper offers recommendations for policymakers, industry players, and researchers, highlighting the roadmap's critical role in achieving a carbon-neutral cement sector. • Cement industry faces urgent need for net-zero transition due to high carbon emissions. • Roadmap spans phases: foundation, acceleration, net-zero, targeting emissions by 2050. • Innovations like alkali-activated cements offer promise for emission reduction. • Collective action and policy crucial for sustainable transformation of cement sector. [ABSTRACT FROM AUTHOR]

This review paper provides a comprehensive analysis of cement-based solidification and immobilisation of nuclear waste. It covers various aspects including mechanisms, formulations, testing and regulatory considerations. The paper begins by emphasizing the importance of nuclear waste management and the associated challenges. It explores the mechanisms and principles in cement-based solidification, with a particular focus on the interaction between cement and nuclear waste components. Different formulation considerations are discussed, encompassing factors such as cement types, the role of additives and modifiers. The review paper also examines testing and characterisation methods used to assess the physical, chemical and mechanical properties of solidified waste forms. Then the paper addresses the regulatory considerations and compliance requirements for cement-based solidification. The paper concludes by critically elaborating on the current challenges, emerging trends and future research needs in the field. Overall, this review paper offers a comprehensive overview of cement-based solidification, providing valuable insights for researchers, practitioners and regulatory bodies involved in nuclear waste management. • Thoroughly explores cement-based nuclear waste solidification, covering mechanisms, formulations, testing, and regulations. • Highlights the critical role of nuclear waste management, acknowledging associated challenges. • Delves into intricate mechanisms governing cement-solidified waste, offering a detailed understanding. • Examines additives, modifiers, and cement types, providing nuanced insights into solidification processes. [ABSTRACT FROM AUTHOR]

Geopolymer concrete is an inorganic polymer composite which has the potential to build an eco‐friendly and sustainable construction by replacing the existing conventional concrete. Herein, cement is totally replaced by mineral admixtures rich in aluminosilicates such as fly ash and is formed by the alkali activation using alkaline activator solutions, such as sodium hydroxide (NaOH) and sodium silicate (Na2SiO3). Fly ash, a waste material from industry, can be incorporated in the manufacture of geopolymer concrete. The replacement of cement by fly ash in geopolymer concrete reduces the huge energy consumption and restricts carbon dioxide emission to the atmosphere during its production. In this paper, experimental investigations have been carried out involving the variation of total aggregate content (viz., 74, 76, 78, 80, and 82%), NaOH concentration (8, 10, 12, and 14 M), and curing temperature (60, 70, 80, 90, and 100°C) on the strength of geopolymer concrete by keeping a constant alkaline liquid to fly ash ratio of 0.45 and a 24‐hour rest period. It is concluded that 76% of total aggregate content is suitable for producing geopolymer concrete without hindering the workability. Further, strength of geopolymer concrete has been found to be increased at 90°C having 12 M NaOH concentration. [ABSTRACT FROM AUTHOR]