We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems wit...
Hamiltonian variational principles have provided, since the 1960s, the means of developing very successful wave theories for nonlinear free-surface flows, under the assumption of irrotationality. This success, in conjunction with the recognition that...
This paper considers the steady-state heat transfer process in a fin with a Robin boundary condition at the base (instead of the usual Dirichlet boundary condition at the base). Robin boundary condition models the effect of the thermal resistance bet...
In this work, the earlier variational analysis of classical non-barotropic flows is extended to the special relativistic non-barotropic case. Specifically, we present a new Eulerian variational formulation for relativistic non-barotropic flows, based...
This work introduces a path-dependent energy Lagrangian for irreversible thermomechanics that embeds heat and entropy accounting directly into the action. The formulation requires neither Lagrange multipliers nor Rayleigh potentials. An explicit
The weighted finite element method makes it possible to find an approximate solution of a boundary value problem with corner singularity without loss of accuracy. The construction of this numerical method is based on the introduction of the concept o...
In the present work, we address a nonlinear boundary value problem that models frictional contact with prescribed normal stress between a deformable body and a foundation. The body is nonlinearly elastic, the constitutive law being a subdifferential...
The main purpose of this study is to develop a variational formulation for predicting structure behavior and accounting for damage mechanics in metallic materials. Mechanical and coupled thermomechanical models are used to predict failure in manufact...
The application of continuous and discontinuous approaches of the finite element method (FEM) to the neutron transport equation (NTE) has been investigated. A comparative algorithm for analyzing the capability of various types of numerical solutions...
Mindlin’s two-dimensional theory has been derived and applied to research on quartz resonators for a long time. However, most works have focused on vibrations varying only in two directions, including thickness direction, while the effect of other di...
We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that, in addition to the...
In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite-dimensional case of discrete systems, as well as for the infinite-dimensional case of continuum systems. Starting with the fund...
This contribution presents a finite element shell model capable of performing linear vibration analyses of shell-type structures made of functionally graded material (FGM). The model is based on the seven-parameter spectral/hp finite element formulat...
Variable Angle Tow (VAT) laminates offer a promising alternative to classical straight-fiber composites in terms of design and performance. However, analyzing these structures can be more complex due to the introduction of new design variables. Carre...
The monolithic Eulerian formulation has widely been employed for solving numerically fluid–structure interaction (FSI) problems of finite structural displacement using the same mathematical variational formulation for fluid and structural dynam...
In this article, we propose an expanded mixed finite element method for variable-coefficient fractional dispersion equations (FDEs). By introducing two intermediate variables,
This study focuses on investigating the modified Benjamin-Bona-Mahony equation that is used to model the long wave in nonlinear dispersive media of the optical illusion field. Two effective techniques, the variational direct method and He’s fre...
Variable-Angle Tow (VAT) laminates can improve straight fiber composites’ mechanical properties thanks to the application of curvilinear fibers. This characteristic allows one to achieve ambitious objectives for design and performance purposes....
In this paper, the interior elastic direct and inverse scattering problem of time-harmonic waves for a non-penetrable partially coated obstacle placed in a homogeneous and isotropic medium is studied. The scattering problem is formulated via the Navi...
In this paper, the behavior of a ferromagnetic material is considered in the framework of microstructural modeling. The equations describing the behavior of such material in the magnetic field, are constructed based on minimization of total magnetic...
This article develops dual variational formulations for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality principle is dev...
The following article extends a decomposition to the Navier–Stokes Equations (NSEs) demonstrated in earlier studies by corresponding author, in order to now demonstrate the existence of a vortex elliptical set inherent to the NSEs. These vortice elli...
In this article, a microstructural model of the Heusler alloy with the shape memory effect caused by the application of an external magnetic field is constructed. The dynamics of the magnetization process are described using the Landau–Lifshitz...
This paper presents the Variable Landscape Search (VLS), a novel metaheuristic designed for global optimization of complex problems by dynamically altering the objective function landscape. Unlike traditional methods that operate within a static sear...
Within the framework of multifield continua, we move from the model of elastic microcracked body introduced in (Mariano, P.M. and Stazi, F.L., Strain localization in elastic microcracked bodies, Comp. Methods Appl. Mech. Engrg. 2001, 190, 5657–5677)...
There is wide variation in how individuals perceive the chemosensory attributes of liquid formulations of ibuprofen, encompassing both adults and children. To understand personal variation in the taste and chemesthesis properties of this medicine, an...
This study introduces a theoretical and computational framework for modeling acoustic wave propagation in defective concrete, with applications to non-destructive testing and structural health monitoring. The formulation is based on a coupled system...
Configuration entropy is believed to stabilize disordered solid solution phases in multicomponent systems at elevated temperatures over intermetallic compounds by lowering the Gibbs free energy. Traditionally, the increment of configuration entropy w...
A recently developed theory is applied to deduce the well posedness and the finite element approximability of time-harmonic electromagnetic scattering problems involving bianisotropic media in free-space or inside waveguides. In particular, three exa...
In this article, based on the theory of micromagnetism, a microstructural model of the behavior of the Heusler alloy in a magnetic field is constructed. The dynamics of the magnetic process is described by the Landau–Lifshitz–Gilbert equa...
The port-Hamiltonian system approach is intended to be an innovative and unifying way of modeling multiphysics systems, by expressing all of them as systems of conservation laws. Indeed, the increasing developments in recent years allow finding bette...
Shells are significant structural components that are extensively utilized in numerous engineering fields, including architectural and infrastructural projects. These components are employed in the construction of domes, water tanks, stadiums and aud...
Chamomile essential oils (EOs) are widely used in cosmetics for their antioxidant, anti-inflammatory, and antimicrobial properties. Bulgaria, with its long-standing tradition in EO production, provides an ideal setting to examine the influence of spe...
A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundar...
In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body that is immersed in a compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided t...
High intra-patient variability (IPV) of tacrolimus levels is associated with poor long-term outcome after transplantation. We aimed to evaluate whether the number of regularly prescribed medications is associated with the tacrolimus IPV. We have stud...
This paper presents a novel non-classical Timoshenko–Ehrenfest beam model based on a reformulated strain gradient elasticity theory. The strain gradient effect, couple stress effect, and velocity gradient effect for vibration are included in th...
In this paper, we are concerned with approach solutions for Sturm–Liouville problems (SLP) using variational problem (VP) formulation of regular SLP. The minimization problem (MP) is also set forth, and the connection between the solution of ea...
The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory....
Many isothermal dissipative continuum problems can be formulated in a variational setting using the concept of “standard dissipative continua”. A major advantage of this approach is that complex problems can be cast into a compact, thermo...
The problem of formulating variational models for irreversible processes of media deformation is considered in this paper. For reversible processes, the introduction of variational models actually comes down to defining functionals with a given list...
Zinc (Zn) is critical for the activity of many enzymes including involved photosynthetic CO2 fixation and indirectly involved in the production of growth hormones and internode elongation in crop plants. In this regard, a field experiment was conduct...
Modern agriculture uses techniques and technologies that have provided farmers with increased yield and a possible reduction in costs. Optimizing the use of inputs by applying exact and accurate doses, which match the real needs of the soil, in addit...
This Special Issue presents efficient formulations and implementations of sequential and variational data assimilation methods. The methods address three important issues in the context of operational data assimilation: efficient implementation of lo...
This paper deals with the problem of establishing a systematic theoretical formulation of variational principles for the continuum gravitational field dynamics of classical General Relativity (GR). In this reference, the existence of multiple Lagrang...
A variational formulation and variationally consistent boundary conditions were derived for a coupled system of two boron nitride nanotubes (BNNTs), with the piezoelectric and surface effects taken into account in the formulation. The coupling betwee...
The implications of the principles of general and manifest covariance, together with those of the objectivity principle, are considered for the purpose of establishing a DeDonder–Weyl-type Hamiltonian variational formulation for classical gener...
The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibri...
Concrete cores extracted from the same structural element may show variations in strength resulting from a lack of homogeneity and variations in the grade of compactness. This paper, while accounting for such variability, introduces a new formulation...
In this paper, a simple evolution formulation, based on polar coordinate, is proposed to efficiently and accurately simulate the dynamic movement of sandy shoreline in a crenulate-shaped bay. The consistent actions by seasonal waves and swell usually...
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