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This article discusses changes in heat transfer resulting from laser pulses and magnetic fields produced in thermoelastic materials under initial stress. This paper introduces a novel approach to modeling generalized thermoelastic materials by including fractional time derivatives with Eringen's non‐local thermoelastic theory. This model incorporates both the Caputo–Fabrizio and the Atangana–Baleanu derivatives, which are novel forms of fractional derivatives in the domain of fractional calculus. Analytical formulations for system variables, such as temperature and thermal stress, were derived using the Laplace transform method. This was done considering the effects of laser pulses, non‐local actuators, and fractional actuators. The findings of these investigations are showcased through numerical illustrations and visual representations. The research also included comparisons between the acquired results and those derived from earlier theories, which may be regarded as a specific instance. Validating the suggested model and showing its correctness and applicability is seen as a crucial step. [ABSTRACT FROM AUTHOR]

Background: Left-handedness is a condition that reverses the typical left cerebral dominance of motor control to an atypical right dominance. The impact of this distinct control — and its associated neuroanatomical peculiarities — on other cognitive functions such as music processing or playing a musical instrument remains unexplored. Previous studies in right-handed population have linked musicianship to a larger volume in the (right) auditory cortex and a larger volume in the (right) arcuate fasciculus. Results: In our study, we reveal that left-handed musicians (n = 55), in comparison to left-handed non-musicians (n = 75), exhibit a larger gray matter volume in both the left and right Heschl's gyrus, critical for auditory processing. They also present a higher number of streamlines across the anterior segment of the right arcuate fasciculus. Importantly, atypical hemispheric lateralization of speech (notably prevalent among left-handers) was associated to a rightward asymmetry of the AF, in contrast to the leftward asymmetry exhibited by the typically lateralized. Conclusions: These findings suggest that left-handed musicians share similar neuroanatomical characteristics with their right-handed counterparts. However, atypical lateralization of speech might potentiate the right audiomotor pathway, which has been associated with musicianship and better musical skills. This may help explain why musicians are more prevalent among left-handers and shed light on their cognitive advantages. [ABSTRACT FROM AUTHOR]

Analyzing the viscoelastic characteristics of materials, especially polymers, is essential for understanding their mechanical properties and their capacity to function in different conditions. This paper presents a novel viscoelastic heat transfer model that integrates a memory-based derivative with the Moore–Gibson–Thomson (MGT) equation. The purpose is to examine the viscoelastic characteristics of materials and assess their response to external stresses and deformations over a certain period of time. In addition to incorporating the third-type thermoelastic model that Green and Naghdi provided, the derivation of this thermo-viscoelastic model included the integration of heat flow and its time derivative into Fourier's equation. To verify and understand the proposed model, it was applied to consider an unbounded viscoelastic semi-space immersed in a uniform magnetic field and exposed to non-Gaussian laser radiation as a heat source. An analysis of computational results was conducted to evaluate how the behavior of the field variables under consideration is affected by viscoelastic coefficients and memory-based derived factors. [ABSTRACT FROM AUTHOR]

In this paper we approach the linear mixed problem with initial and boundary values for a Cosserat body which is elastic and has pores. We coupled the equations characterizing the pores evolution with basic equations that describing the elastic deformations of the Cosserat body. The coupling is done by means of predetermined coefficients. To prove the continuous dependence of the solutions, we introduce an adequate measure which is useful in obtaining of some estimations with respect to the gradient of elastic deformations and regarding the gradient of a specific the application, introduced to characterize the behavior of the pores. [ABSTRACT FROM AUTHOR]

Accurately characterizing the thermomechanical parameters of nanoscale systems is essential for understanding their performance and building innovative nanoscale technologies due to their distinct behaviours. Fractional thermal transport models are commonly utilized to correctly depict the heat transfer that occurs in these nanoscale systems. The current study presents a novel mathematical thermoelastic model that incorporates a new fractional differential constitutive equation for heat conduction. This heat equation is useful for understanding the effects of thermal memory. An application of a fractional-time Atangana–Baleanu (AB) derivative with a local and non-singular kernel was utilized in the process of developing the mathematical model that was suggested. To deal with effects that depend on size, nonlocal constitutive relations are introduced. Furthermore, in order to take into consideration, the viscoelastic behaviour of the material at the nanoscale, the fractional Kelvin–Voigt model is utilized. The proposed model is highly effective in properly depicting the unusual thermal conductivity phenomena often found in nanoscale devices. The study also considered the mechanical deformation, temperature variations, and viscoelastic characteristics of the functionally graded (FG) nanostructured beams. The consideration was made that the material characteristics exhibit heterogeneity and continuous variation across the thickness of the beam as the nanobeam transitions from a ceramic composition in the lower region to a metallic composition in the upper region. The complicated thermomechanical features of simply supported viscoelastic nanobeams that were exposed to harmonic heat flow were determined by the application of the model that was constructed. Heterogeneity, nonlocality, and fractional operators are some of the important variables that contribute to its success, and this article provides a full study and illustration of the significance of these characteristics. The results that were obtained have the potential to play a significant role in pushing forward the design and development of tools, materials, and nanostructures that have viscoelastic mechanical characteristics and graded functions. [ABSTRACT FROM AUTHOR]

Background: Neuropsychiatric symptoms (NPS) are a common aspect of Alzheimer's disease (AD). Multiple studies have investigated its brain correlates, but it still remains unclear how they relate with brain atrophy in mild cognitive impairment (MCI). Objective: Our objective was to investigate brain volume in MCI patients as a function of NPS. Methods: We measured grey matter volume, neuropsychological status and NPS (Neuropsychiatric Inventory, NPI), in a sample of 81 MCI patients (43 females). Participants were divided in groups depending on presence (NPS+) or absence (NPS–) of NPS and on type of NPS. Results: We found lower volume of left temporal pole in patients with depression compared to NPS– (p = 0.012), and in patients with agitation compared to NPS– in the right middle occipital gyrus (p = 0.003). We also found a significant correlation between volume of left temporal pole and MMSE (r (78) = 0.232, p = 0.019). Finally, NPS+ presented lower cross-sectional cognitive level than NPS– (t (79) = 1.79, p = 0.038), and faster cognitive decline (t (48) = –1.74, p = 0.044). Conclusions: Our results support the colocalization of structural damage as a possible mechanism underlying the relationship between MCI and depression and provide novel evidence regarding agitation. Moreover, our longitudinal evidence highlights the relevance of an adequate identification of NPS in MCI patients to identify those at risk of faster cognitive decline. [ABSTRACT FROM AUTHOR]

Our study is dedicated to a mixture composed of a dipolar elastic medium and a viscous Moore–Gibson–Thompson (MGT) material. The mixed problem with initial and boundary data, considered in this context, is approached from the perspective of the existence of a solution to this problem as well as the uniqueness of the solution. Considering that the mixed problem is very complex, both from the point of view of the basic equations and that of the initial conditions and the boundary data, the classical methods become difficult. That is why we preferred to transform it into a problem of Cauchy type on a conveniently constructed Hilbert space. In this way, we immediately proved both the existence and uniqueness of the solution, with techniques from the theory of semigroups of linear operators. [ABSTRACT FROM AUTHOR]

In this paper, the authors propose the application of the Gibbs–Appell equations to obtain the equations of motion in the case of a mechanical system that has elements with a micro-polar structure, containing voids. Voids can appear as a result of the processing or manufacturing of the parts, or can be intentionally introduced. This research involves a model of the considered solid material containing voids. To determine the dynamic behavior of such a system, the Gibbs–Appell (GA) method is used to obtain the evolution equations, as an alternative to Lagrange's classical description. The proposed method can be applied to any mechanical system consisting of materials with a micro-polar structure and voids. The study of such systems is interesting because the literature shows that even a reduce number of small voids can produce significant variations in physical behavior. The proposed method requires a smaller number of mathematical operations. To apply this method, the acceleration energy is calculated, which is then used to derive the equations. The method comes with advantages in the application to multibody systems having the mentioned properties and, in particular, in the study of robots and manipulators. Using the GA method, it is necessary to do a fewer differentiation operations than applying the Lagrange's equations. This leads to a reduced amount of computation for obtaining the evolution equations. [ABSTRACT FROM AUTHOR]

For the particular case of an elastic multibody system (MBS) that can be modeled using one-dimensional finite elements, the main methods offered by analytical mechanics in its classical form for analysis are presented in a unitary description. The aim of the work is to present in a unitary form the main methods offered by classical mechanics for the analysis of solid systems. There is also a review of the literature that uses and highlights these methods, which need to be reconsidered considering the progress of the industry and the complexity of the studied systems. Thus, the kinematics of a finite element is described for the calculation of the main quantities used in the modeling of multibody systems and in analytical mechanics. The main methods used in the research of MBS systems are presented and analyzed. Thus, Lagrange's equations, Gibbs–Appell equations, Maggi's formalism, Kane's equations and Hamilton's equations are studied in turn. This presentation is determined by the advantages that alternatives to Lagrange's equations can offer, which currently represent the method most used by researchers. [ABSTRACT FROM AUTHOR]

In this present study, we intend to obtain a new criterion for the analyticity of a complex function. More exactly, we will deduce some concrete restrictions that must be performed by a function that is complex, is defined on the disc centred at the origin that has radius 1 (hereinafter referred to as the unit disc), which, in addition, is continuous on this disc, including its border, to be analytic on the open unit disc. After that, as applications, we will deduce the Schwartz–Villat's formula in this context, and we will obtain the known Joukowski's function. [ABSTRACT FROM AUTHOR]

This article offers the first investigation into the thermoelectric vibration of microscale Euler‐Bernoulli beams resting on an elastic Winkler base. We developed the system of equations for thermoelastic microbeams using elastic basis theory and the generalized Moore–Gibson–Thompson (MGT) thermal transport framework with a single‐phase delay. At the front of the microbeam, a graphene strip connected to an electrical power source was employed to generate heat. In addition, the influence of an ultra‐short‐pulsed laser on the vibration of a microbeam is studied, taking into account its heating effect. The microbeam system variables were analyzed after solving the mathematical equations by applying the Laplace transform technique. Graphs showing how different inputs affect different mechanical fields, such as Winkler substrate stiffness, voltage, electrical resistance, and temperature modulus pulses, are also presented. An increase in the Winkler modulus and the shear modulus of the foundation was found to decrease the amount of deflection and axial deformation in the microbeams. The increased beam stiffness has resulted in this decrease. [ABSTRACT FROM AUTHOR]

In our study we construct a boundary value problem in elasticity of porous piezoelectric bodies with a dipolar structure To construct an eigenvalue problem in this context, we consider two operators defined on adequate Hilbert spaces. We prove that the two operators are positive and self adjoint, which allowed us to show that any eigenvalue is a real number and two eigenfunctions which correspond to two distinct eigenvalues are orthogonal. With the help of a Rayleigh quotient type functional, a variational formulation for the eigenvalue problem is given. Finally, we consider a disturbation analysis in a particular case. It must be emphasized that the porous piezoelectric bodies with dipolar structure addressed in this study are considered in their general form, i.e.,inhomogeneous and anisotropic. [ABSTRACT FROM AUTHOR]

In our study we approached the mixed problem in the context of linear theory of thermoelasticity for Cosserat bodies. After we define the finite energy solution for this mixed problem, some results with respect to the existence and uniqueness are proven of this kind of solution. To this aim, we generalized some analogous results established by Dafermos, for a mixed problem from linear theory of the classical elasticity. In another important result of our study, we introduce some specific conditions which give the possibility that the evolution of the finite energy solution to be controlled. [ABSTRACT FROM AUTHOR]

Our paper deals with a mixed initial-boundary value problem in thermoelasticity of piezoelectric bodies with dipolar structure. It is considered the general case of a thermoelastic body which inhomogeneous and also anisotropic and we add the effect of piezoelectricity. We take into account the main equations and basic conditions of a temperature rate dependent theory which predict the waves propagation with a finite speed. Using some middle conditions imposed on the boundary conditions and initial data, we obtain that our mixed problem admits one solution. A generalized form of the Hamilton's principle is obtained to cover this context. [ABSTRACT FROM AUTHOR]

In our study, we adapt certain basic results from the abstract theory of differential equations of the elliptic type with the purpose to deduce some basic results in the case of a concrete type of media. Namely, after the boundary values problem is formulated in the context of elasticity of Cosserat bodies with voids, some results on existence of a generalized solution and the uniqueness of this solution are proven. [ABSTRACT FROM AUTHOR]

In this study, the effects of laser light on the heat transfer of a thin beam heated by an applied current and voltage are investigated. Laser heating pulses are simulated as endogenous heat sources with discrete temporal properties. The heat conduction equation is developed using the energy conservation equation and the modified Moore–Gibson–Thompson (MGT) heat flow vector. Thermal and structural analysis of Euler–Bernoulli microbeams is provided with the support of visco-Pasternak's base with three parameters. Using the Laplace transform method, an approximation of an analytical solution is found for the field variables being examined. A comparison was made of the impacts of laser pulse length, the three foundation coefficients, and the thermal parameters on the responses to changes in measured thermophysical fields, such as deflection and temperature. [ABSTRACT FROM AUTHOR]

By laminating piezoelectric and flexible materials, we can increase their performance. Therefore, the electrical and mechanical properties of layered piezoelectric materials subjected to electromechanical loads and heat sources must be analyzed theoretically and mechanically. Since the problem of infinite wave propagation cannot be addressed using classical thermoelasticity, extended thermoelasticity models have been derived. The thermo-mechanical response of a piezoelectric functionally graded (FG) rod due to a moveable axial heat source is considered in this paper, utilizing the dual-phase-lag (DPL) heat transfer model. It was supposed that the physical characteristics of the FG rod varied exponentially along the axis of the body. Both ends hold the rod, and there is no voltage across them. The Laplace transform and decoupling techniques were used to obtain the physical fields that have been analyzed. A range of heterogeneity, rotation, and heat source velocity measures were used to compare the results presented here and those in the previous literature. [ABSTRACT FROM AUTHOR]

This paper introduces size-dependent modeling and investigation of the transverse vibrational behavior of rotating thermoelastic nanobeams by means of nonlocal elasticity theory. In the formulation, a model of thermal conductivity with two-phase delays (DPL) was utilized. By incorporating the interactions between phonons and electrons, this model took into account microstructural influences. Also, we have employed the state-space approach and Laplace transform approach to solve the governing equations, which were developed in the context of the nonlocal Eringen model. The nanobeam material is subjected to a changeable temperature field produced by the graphene tape attached to the nanobeam and connected to an electrical source. In addition, the nanobeam material is fully encompassed by an axially applied magnetic field. It has been revealed how coefficients such as the rotational angular velocity of the nanobeam, nonlocal coefficient, voltage, electrical resistance, and applied magnetic field influence its behavior. [ABSTRACT FROM AUTHOR]

First we construct the boundary value problem in the context of the elastostatics of elastic orthotropic beams, which are loaded on the ends and on the lateral surface. Then we determine the solution of this problem with the help of some functions of stress. In this way we find an extension of Prandtl's method and, in the same time, an natural extension of the known Almansi's problem from the classical plane problem of torsion. [ABSTRACT FROM AUTHOR]

In this article, a modified Moore–Gibson–Thompson heat transfer equation with a memory-dependent derivative is utilized to investigate the thermoelastic interaction induced by non-Gaussian lasers in an infinitely elastic nonlocal medium. A memory-based derivative is also examined, and it was discovered to be superior at predicting the pattern of real-life challenges. This finding is part of the conviction that is currently analyzed. The idea of a memory-dependent derivative is attractive since it has some peculiarities. These characteristics include remarkable components as the kernel function and time lag, both of which can be freely selected according to the specifications of the problem. In addition, the non-local concept of Eringen was utilized in the research project so that the small-scale influence could be understood. Using the Laplace transform as a method, analytical–numerical solutions to problems involving thermo-physical fields, such as dimensionless temperature and deformation, as well as nonlocal physical stress, can be analyzed and compared. Numerical solutions have been used to explore the influence of memory-dependent derivative components such as the kernel function and the time delay coefficient on the studied domain variables of the medium. The computational outcomes of the studied fields are also used to find out the role of the non-local index. [ABSTRACT FROM AUTHOR]

We consider a thermoelastic Cosserat body with dual-phase lag. In order to formulate a dual-phase-lag model, an equation is introduced, of the time differential type, to characterize the thermal effects and the coupling with the deformation from an elastic point of view. We associate with this model a mixed problem with initial data and conditions to the limit. We then obtain some qualitative estimates on the solutions of this mixed problem, without resorting to restrictive conditions on the thermoelastic coefficients. In order to obtain the uniqueness of the solution, we appeal to a Lagrange-type identity, easily obtained in the given context, and to a law of conservation, previously demonstrated. Then, we establish an inequality which is of the Gronwall's type, that is useful for proving the continuous dependence of the solutions in relation to initial values and loads, which is another important result of our study. [ABSTRACT FROM AUTHOR]

In engineering practice, structures with identical components or parts are useful from several points of view: less information is needed to describe the system; designs can be conceptualized quicker and easier; components are made faster than during traditional complex assembly; and finally, the time needed to achieve the structure and the cost involved in manufacturing decrease. Additionally, the subsequent maintenance of this system then becomes easier and cheaper. The aim of this Special Issue is to provide an opportunity for international researchers to share and review recent advances in the finite element modeling of computational friction contact mechanics. Numerical modeling in mathematics, mechanical engineering, computer science, computers, etc. presents many challenges. The finite element method applied in solid mechanics was designed by engineers to simulate numerical models in order to reduce the design costs of prototypes, tests and measurements. This method was initially validated only by measurements but gave encouraging results. After the discovery of Sobolev spaces, the abovementioned results were obtained, and today, numerous researchers are working on improving this method. Some of applications of this method in solid mechanics include mechanical engineering, machine and device design, civil engineering, aerospace and automotive engineering, robotics, etc. Frictional contact is a complex phenomenon that has led to research in mechanical engineering, computational contact mechanics, composite material design, rigid body dynamics, robotics, etc. A good simulation requires that the dynamics of contact with friction be included in the formulation of the dynamic system so that an approximation of the complex phenomena can be made. To solve these linear or nonlinear dynamic systems, which often have non-differentiable terms, or discontinuities, software that considers these high-performance numerical methods and computers with high computing power are needed. This Special Issue is dedicated to this kind of mechanical structure and to describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are also considered. Additionally, theoretical models, mathematical methods and numerical analysis of these systems, such as the finite element method and experimental methods, are used in these studies. Machine building, automotive, aerospace and civil engineering are the main areas in which such applications appear, but they can also be found in most other engineering fields. With this Special Issue, we want to disseminate knowledge among researchers, designers, manufacturers and users in this exciting field. [ABSTRACT FROM AUTHOR]

In our article, we deduce a reciprocal relation in the context of dipolar porous materials. As an application, we analyze the effect of the dipolar structure on bodies charges which are similar to a dislocation of seismic type. Our results appear as generalizations of equivalent statements from the simpler theory of classical elastic bodies and they cover the more complicated theory of thermoelastic bodies with a dipolar structure. [ABSTRACT FROM AUTHOR]

An interesting feature that appears in the thermoelastic interaction in an orthotropic material containing cylindrical cavities is addressed in this study. For this purpose, the Finite Element Method is applied to analyze a generalized thermoelasticity theory with a relaxation time. For the development of the model, a thermal conductivity that is dependent on the temperature of the orthotropic medium was considered. The boundary condition for the internal surface of a cylindrical hollow is defined by the thermal shocks and the traction on the free surface. The nonlinear formulations of thermoelastic based on thermal relaxation time in orthotropic mediums are abbreviated using the Finite Element Method. The nonlinear equations without Kirchhoff's transformations are presented. The results are graphically represented to demonstrate how changing thermal conductivity affects all physical values. [ABSTRACT FROM AUTHOR]

The paper aims to identify the situations in which a complex elastic system, which is subject to mechanical vibrations, can act as a dynamic absorber of vibrations for certain frequencies. The conditions that the system must fulfill in order to achieve this goal are determined and then a calculation example is presented. The method is interesting because it allows to avoid attaching an absorber specially built for this, a situation that complicates the project and increases manufacturing costs. [ABSTRACT FROM AUTHOR]

This paper deals with the linear theory of thermoelastic Cosserat bodies. At the beginning, we formulate the mixed initial-boundary value problem in this context and obtain new theorems of reciprocity in the thermodynamics theory of these media. Then we prove that these new reciprocity relations imply the uniqueness of solution of the mixed problem. Based on the same reciprocal relations, we establish a minimum variational principle, which generalizes those from the theory of classical thermoelasticity. [ABSTRACT FROM AUTHOR]

In this paper, we extend some results involving the energy release rate in the case of the propagation of a straight crack in an elastic solid. These results, approached by Gurtin and Yatomi in classical elasticity, are generalized in order to cover a Cosserat-type elastic body. We also investigate the effects of the microinertia and the couple stresses on the energy release rate. [ABSTRACT FROM AUTHOR]

A planar mechanism represents a mechanism that is frequently used in engineering, and very often, the elasticity of some elements of the mechanism cannot be neglected. Consideration of all rigid elements does not allow the analysis of vibrations or situations of loss of stability of some elements. Gibbs–Appell's generalized equations are used in this paper to obtain the governing equations for a two-dimensional finite element, which is in plane motion. Using Lagrange's equations is the most widely used way for researchers to address such a problem. This is mainly due to the familiarity of researchers with this robust calculation method. There are two major advantages of applying this formalism: a smaller number of differentiation operations is needed to be performed and, by eliminating Lagrange multipliers, the number of unknowns decreases significantly. The method is applied for the plane multibody systems with elastic elements. We hope that this method, due to its simplicity, will be interesting for mechanical designers. [ABSTRACT FROM AUTHOR]

A matrix-based representation of the inertial characteristics with possible used in multibody dynamics is presented in the paper. The paper aims to develop a unitary formalism that will help to model multibody systems, for the purpose of kinematic and dynamic analysis. Properties of the inertia matrix due to the symmetry of this matrix are presented. The points with spherical and cylindrical symmetry are identified, which allow the easier writing of the equations of motion. The form of the inertia matrix from any body of a multibody system in the global reference system is shown. [ABSTRACT FROM AUTHOR]

Our study is a generalization of some results obtained by Synge in the classical theory of elasticity. By this extension, we wish to cover the theory of micropolar elastic bodies. More precisely, we approach the electroacoustic energy flux in the case of plane waves of harmonic type which propagate in piezoelectric crystals which are supposed to be prepolarized and prestressed. [ABSTRACT FROM AUTHOR]

In this study it is approached a linear model for the mixture of two Cosserat bodies having pores. It is formulated the mixed problem with initial and boundary data in this context. The main goal is to show that the coefficients that realize the coupling of the elastic effect with the one due to voids can vary, without the mixture being essentially affected. In a more precise formulation, this means that a small variation of the coefficients in the constitutive equations of the two continua causes only a small variation of the solutions of the corresponding mixed problems, that is, the continuous dependence of the solutions in relation to these coefficients is ensured. The considered mixture model is consistent because all estimates, specific to continuous dependence, are made based on rigorous mathematical relationships. [ABSTRACT FROM AUTHOR]

The paper aims to study, using the finite element method, the elastic behavior of a cylinder made by a material with micropolar structure, containing (as the results of the processing or introduced intentionally) voids. To study such a type of problem, a theoretical model of a continuous solid body with voids in the material is presented, after which, in order to determine the effect that these voids have, a model with finite elements is made, using Lagrange's equations. This model can be applied to any type of elastic solid with voids. In the paper study the elastic response of a hollow cylinder made by a material with voids. Finally, comparative results are obtained to show the influence of voids on the elastic behavior of the body in some classic cases. These results are compared with the values obtained in the literature by experimental methods. It is found that a small percentage of voids can lead to significant variations on the mechanical properties. [ABSTRACT FROM AUTHOR]

The study of the effect of the microstructure is important and is most evident in elastic vibrations of high frequency and short-wave duration. In addition to deformation caused by temperature and acting forces, the theory of micropolar thermoelasticity is applied to investigate the microstructure of materials when the vibration of their atoms or molecules is increased. This paper addresses a two-dimensional problem involving a thermoelastic micro-polar half-space with a traction-free surface and a known conductive temperature at the medium surface. The problem is treated in the framework of the concept of two-temperature thermoelasticity with a higher-order time derivative and phase delays, which takes into consideration the impact of microscopic structures in non-simple materials. The normal mode technique was applied to find the analytical formulas for thermal stresses, displacements, micro-rotation, temperature changes, and coupled stress. The numerical results are graphed, and the effect of the discrepancy indicator and higher-order temporal derivatives is examined. There are also some exceptional cases that are covered. [ABSTRACT FROM AUTHOR]

This study is concerned with the theory of Cosserat thermoelastic media, whose micro-particles possess microtemperatures. The mixed initial boundary value problem considered in this context is transformed in a temporally evolutionary equation on a Hilbert space. Using some results from the theory of semigroups, the existence and uniqueness of solution is proved. In the same manner, it approached the continuous dependence of the solution upon initial data and loads. From what we have studied, neither on the internet nor in the databases, we have not found qualitative issues addressed regarding the mixed problem in the context of the theory of thermoelasticity of Cosserat environments, in which the contribution of inner structure and microtemperatures are taken into account. [ABSTRACT FROM AUTHOR]

In this study, we consider the final boundary value problem for a thermoelastic Cosserat material. With the help of a simple translation, our final problem is transformed in a usual mixed problem with boundary relations and initial data. For this new problem, we obtain some theorems of uniqueness of solutions. For this, we do not use any law of conservation of energy, as is usually done to obtain a result of uniqueness. Moreover, we do not need assumptions to ensure the boundedness of the tensors which characterize thermoelastic coefficients. [ABSTRACT FROM AUTHOR]

Our study deals with a thermoelastic body with pores. We have added a new independent variable, namely the time derivative of the voidage. Within the theory of such media, we analyze the spatial and temporal evolution of solutions. For the spatial behavior, we will prove certain estimations of the Saint-Venant type, in the situation the bodies are bounded. In the case the bodies are unbounded bodies, to describe the spatial evolution we consider certain estimations of the Phragmén–Lindelöf type. [ABSTRACT FROM AUTHOR]

In our present study, we approach a linear theory for the thermoelasticity of type III for Cosserat media. At the beginning we introduce the equations and conditions, specific for a mixed problem in this context, namely the motion and energy equations, the initial condition and boundary relations. After that, we establish two results regarding the solution unique to the problem and two results on the continuous dependence of solutions, for the same mixed problem. Both problems that we address in our paper (uniqueness and continuous dependence) are not based on the material symmetries of the medium. Moreover, our results concern the theory of type III thermoelasticity for Cosserat media in their most general form, namely anisotropic. [ABSTRACT FROM AUTHOR]

We study the linear theory of thermo-electro-viscoelasticity of Green–Naghdi type for the case of a one-dimensional body. For the corresponding mathematical model, we prove a uniqueness theorem of the solution to the mixed boundary-initial-value problem by means of the Laplace transform after rewriting the constitutive equations in an appropriate form. Moreover, we derive a result of continuous dependence upon the supply terms. [ABSTRACT FROM AUTHOR]

We consider a thermoelastic theory in which the equations that govern the evolution are linear with respect to the thermal displacement and nonlinear with regards to gradients of displacements and temperature. Our results refer to the non-existence of solutions for some mixed problems, considered in this context. We also address the instability of solutions of the considered problems. We will treat separately the case where the mechanical effects are neglected, taking into account only the thermal effect. In this case our problem has a nonlinear structure. [ABSTRACT FROM AUTHOR]

In this study, we approach the strain gradient thermoelasticity of bodies with microtemperatures. We define the internal energy corresponding to an arbitrary solution of the mixed problem with boundary and initial values, considered in the context of strain gradient thermoelasticity of bodies with microtemperatures. The Cesaro means of different parts of the internal energy are considered. In our main result, we prove the asymptotic equipartition of the strain and kinetic energies, in the case t → ∞ . [ABSTRACT FROM AUTHOR]

Lagrange's equations represent the common approach in finite element analysis of an elastic multibody system. The most important step in this case is to write the governing equations. The work develops an alternative method to obtain these equations, using so-called Gibbs–Appell formalism. The advantage of this method is the decrease in the number of calculations to be made. The acceleration energy will be calculated first for a one-dimensional finite element, and then Gibbs–Appell equations are applied in the classical form. The number of differentiations required, compared to the method of Lagrange's equations, decreases significantly, with effects on the computational time required to solve such a problem. We can assume that, due to its simplicity, this method will determine the interest of researchers in the case of large industrial applications. [ABSTRACT FROM AUTHOR]

We consider the mixed initial‐boundary value problem in the context of the Moore‐Gibson‐Thompson theory of thermoelasticity for dipolar bodies. We consider the case of heat conduction with dissipation. Even if the elasticity tensors are not supposed to be positively defined, we have proven both, the uniqueness and the instability of the solution of the mixed problem. In the case that the mass density and the thermal conductivity tensor are positive, we obtain the uniqueness of the solution using some Lagrange type identities. [ABSTRACT FROM AUTHOR]

In our present paper, we approach the mixed problem with initial and boundary conditions, in the context of thermoelasticity without energy dissipation of bodies with a dipolar structure. Our first result is a reciprocal relation for the mixed problem which is reformulated by including the initial data into the field equations. Then, we deduce a generalization of Gurtin's variational principle, which covers our generalized theory for bodies with a dipolar structure. It is important to emphasize that both results are obtained in a very general context, namely that of anisotropic and inhomogeneous environments, having a center of symmetry at each point. [ABSTRACT FROM AUTHOR]

Our study is dedicated to a composite, which, in fact, is a mixture of two thermoelastic micropolar bodies. We formulate the mixed initial boundary value problem in this context and define the domain of influence for given data. For any solution of the mixed problem we associate a measure and prove a second-order differential inequality for it. Based on the maximum principle for the heat equation and on the second-order differential inequality, we establish an estimate which proves that the thermal and the mechanical effects, at large distance from the domain of influence, are dominated by an exponential decay. [ABSTRACT FROM AUTHOR]

In our study, we formulate the boundary value problem in the context of the nonlinear theory of dipolar, porous, and elastic materials. For this problem, some existence and uniqueness results are proven. The results are natural generalizations of the results obtained by Langenbach for the classical elastic bodies. [ABSTRACT FROM AUTHOR]

In our paper we formulate a theory for thermoelastic porous dipolar bodies in which we consider a new independent variable, namely the heat-flux vector. Furthermore, we add, to the differential equations that describe the behavior of the body, a new differential equation which is an equation of evolution which is satisfied by the components of the heat-flux vector. The basic system of the mixed initial-boundary value problem in this context consists of equations of the hyperbolic type. In order to ensure the consistency of the constructed theory, we formulate and prove an uniqueness result, with regards to the solution of the mixed problem. [ABSTRACT FROM AUTHOR]

Multiphase phase flows include the flow of matter in two or more than two thermodynamic phases and involve solid-gas flows, bubbly flows, and sprays. According to the results, it is found that heat transfer is maximum for the lamina shape nanoparticles and the sphere shape nanoparticles show a considerable behavior in temperature profile as compared to other types of nanoparticles. Rashid et al. [[2]] studied gold nanoparticles suspended in the water-based nanofluid under heat transfer effects. [Extracted from the article]

• Displacements, microdeformations, temperature and microtemperatures are coupled in a multiphysics process. • Existence, uniqueness and continuous dependence results are shown for the mathematical model. • The plane strain problem is studied by the finite element method. In this study we formulate the mixed initial boundary value problem for a dipolar thermoelastic material whose micro-particles possess microtemperatures. Then this mixed problem is transformed in a Cauchy problem attached to a temporally equation of evolution on a specific Hilbert space, which will be suitably chosen. As such, we will be able to use certain results specific to the theory of the semigroups of contractions in order to obtain the existence and uniqueness of the solution for our problem. The theory of semigroups also facilitates our approach regarding the continuous dependence of the solution upon initial data and loads. Finally, we reduce our model to the isotropic case and perform numerical simulations for the corresponding system of partial differential equations by means of the finite element method. [ABSTRACT FROM AUTHOR]

Background and purpose: Previous investigations show that bilinguals exhibit the first symptoms of dementia 4–5 years later than monolinguals. Therefore, bilingualism has been proposed as a cognitive reserve mechanism. Recent studies have advanced towards an understanding of the brain mechanisms underlying bilingualism's protection against dementia, but none of them deals with white matter (WM) diffusion. Methods: In this study, the topic was investigated by measuring WM integrity in a sample of 35 bilinguals and 53 passive bilinguals with mild cognitive impairment. Results: No significant differences were found between the groups in cognitive level, education, age or sex. However, bilinguals showed higher mean diffusivity in the fornix, but higher fractional anisotropy, lower mean diffusivity, axial diffusivity and radial diffusivity in the parahippocampal cingulum, and lower radial diffusivity in the right uncinate fasciculus. Significant correlations were also found between WM integrity in the left parahippocampal cingulum and the Boston Naming Test in passive bilinguals. Conclusions: These results suggest that bilingualism contributes to a differential pattern of WM disintegration due to mild cognitive impairment in fibers related to bilingualism and memory. [ABSTRACT FROM AUTHOR]