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In this paper, we employ the finite element method based on non-uniform rational B-splines function approximation to solve the nonlinear Brinkman-Forcheimer-Darcy equation in a simply connected and bounded Lipschitz domain Ω. We provide both theoretical and numerical studies of the Dirichlet boundary problem. Utilizing a stream function formulation, we demonstrate the well-posedness of the weak form. Furthermore, we approximate the velocity and pressure fields by linearizing the nonlinear terms, resulting in an algebraic system. This Non-uniform rational B-splines method is more effective in terms of the exact representation of the geometry and the good approximation of the solution compared to the virtual element method. To validate the effectiveness of the non-uniform rational B-splines Finite Element Method, we conduct numerical simulations of fluid flow in porous media.

Abstract 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.

The inclusion of memory-dependent derivatives (MDD) in constitutive models improves the ability to predict and analyze time-dependent responses of materials, providing a more detailed depiction of their mechanical properties and structural changes. In this paper, a new thermoelasticity model is created that combines the Moore-Gibson-Thompson (MGT) equation with higher-order memory-dependent derivatives (MDD), any optional kernel function, and time delay. The objective of this model is to provide a more accurate mathematical depiction of the thermal and mechanical reactions of materials, particularly those that exhibit complex behaviors over time. A theoretical study was conducted to provide additional clarification of the proposed concept. For this purpose, thermal-mechanical waves were studied in a semi-infinite region, surrounded by a magnetic field, and exposed to a direct heat source uniformly distributed on its outer surface. To solve the coupled partial differential equations governing the system, the Laplace transform methodology was used. The effects of different kernel functions, time delays, and higher-order (HO) derivatives on the behavior of thermoelastic materials are discussed and illustrated using figures and tables.

Abstract 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.

This paper presents a more general method to study the dynamic behavior of a planar mechanism with joints. To do this, Graph Theory is used. A topological description is presented based on which a corresponding graph is attached to any mechanism. This method can be used for both kinematic and dynamic study in the same model, and many of the descriptors used in kinematic analysis can also be used for dynamic analysis. As a final result, the motion equations of the studied mechanical system can be obtained. An application is made to a flap and wing control system of a light sport aircraft. The graph associated with the mechanism first used to determine the field of velocities and accelerations of the mechanism elements is then used to obtain the motion equation for the control system. In this way, Graph Theory proves useful for the parallel study of both the kinematic and dynamic study of such problems.

The current work aims to investigate the interaction between thermal, magnetic, and elastic phenomena in a homogeneous and unbounded material that includes a spherical cavity. A laser beam with a Gaussian distribution was used to expose the solid thermal medium, thereby bringing a source of heat into the system. The study is grounded in the expanded theory of thermoelasticity without energy dissipation, which considers the interconnection between thermal, elastic, and magnetic phenomena. This theoretical framework serves as a basis for understanding the interactions and behaviors of thermal and mechanical processes within an elastic material. The system was analyzed using a direct approach, employing the Laplace transformation method to provide solutions for the system's equations. This methodology enables the computation and presentation of precise equations for several domains of concern, such as displacement, temperature, and thermal stresses. The discussion and analysis focused on a copper-based material, and graphical representations were used to demonstrate the behavior of the researched physical fields. These graphical representations aid in comprehending the development of displacement, temperature, and thermal stresses within the material caused by the laser beam and the interplay between thermal, magnetic, and elastic processes. The results demonstrate that the laser pulse parameters have a significant impact on the temperature and thermal stress distribution, thereby influencing the thermo-mechanical reactions of the solid medium. Ultimately, this study enhances our comprehension of the intricate behavior and interplay of thermal, magnetic, and elastic phenomena in thermoelastic materials.

Abstract The study of multibody systems with elastic elements involves at the moment the reevaluation of the classical methods of analysis offered by analytical mechanics. Modeling this system with the finite element method requires obtaining the motion equation for an element in the circumstances imposed by a multibody system. The paper aims to present the main analysis methods used by researchers, to make a comparative analysis, and to show the advantages or disadvantages offered by different methods. For the presentation of the main methods (namely Lagrange’s equations, Gibbs–Appell’s equations, Maggi’s formalism, Kane’s equations, and Hamilton’s equations) a unified notation is used. The paper provides a critical evaluation of the studied applications that involved some of these methods, highlighting the reason why it was decided to use them. Also, the paper identifies potential research areas to explore.

In this paper, we implement the finite detail technique primarily based on T-Splines for approximating solutions to the linear elasticity equations in the connected and bounded Lipschitz domain. Both theoretical and numerical analyses of the Dirichlet and Neumann boundary problems are presented. The Reissner–Mindlin (RM) hypothesis is considered for the investigation of the mechanical performance of a 3D cylindrical shell pipe without and with preformed hole problems under concentrated and compression loading in the linear elastic behavior for trimmed and untrimmed surfaces in structural engineering problems. Bézier extraction from T-Splines is integrated for an isogeometric analysis (IGA) approach. The numerical results obtained, particularly for the displacement and von Mises stress, are compared with and validated against the literature results, particularly with those for Non-Uniform Rational B-Spline (NURBS) IGA and the finite element method (FEM) Abaqus methods. The obtained results show that the computation time of the IGA based on the T-Spline method is shorter than that of the IGA NURBS and FEM Abaqus/CAE (computer-aided engineering) methods. Furthermore, the highlighted results confirm that the IGA approach based on the T-Spline method shows more success than numerical reference methods. We observed that the NURBS IGA method is very limited for studying trimmed surfaces. The T-Spline method shows its power and capability in computing trimmed and untrimmed surfaces.

This work demonstrates deformation in hygrothermoelastic medium with an overlying non-viscous fluid of uniform thickness. A constant mechanical force is applied along the fluid-layer. The normal-mode analysis technique is applied to solve the governing equations of the medium. The analytical expressions of displacement, moisture concentration, temperature distribution, and stresses are obtained for the hygrothermoelastic medium and depicted graphically for different values of fluid-layer depth. The finding of this work is that the values of the aforementioned physical quantities decrease with an increase in the fluid-layer, which justifies the decaying nature of waves with depth. The novelty of the problem is that no research has been carried out so far for analyzing hygrothermoelastic medium subjected to thermoelastic deformation.

A low number of individuals show an atypical brain control of language functions that differs from the typical lateralization in the left cerebral hemisphere. In these cases, the neural distribution of other cognitive functions is not fully understood. Although there is a bias towards a mirrored brain organization consistent with the Causal hypothesis, some individuals are found to be exceptions to this rule. However, no study has focused on what happens to the homologous language areas in the right frontal inferior cortex. Using an fMRI-adapted stop-signal task in a healthy non right-handed sample (50 typically lateralized and 36 atypically lateralized for language production), our results show that atypical lateralization is associated with a mirrored brain organization of the inhibitory control network in the left hemisphere: inferior frontal cortex, presupplementary motor area, and subthalamic nucleus. However, the individual analyses revealed a large number of cases with a noteworthy overlap in the inferior frontal gyrus, which shared both inhibitory and language functions. Further analyses showed that atypical lateralization was associated with stronger functional interhemispheric connectivity and larger corpus callosum. Importantly, we did not find task performance differences as a function of lateralization, but there was an association between atypical dominance in the inferior frontal cortex and higher scores on schizotypy and autistic spectrum traits, as well as worse performance on a reading accuracy test. Together, these results partially support the Causal hypothesis of hemispheric specialization and provide further evidence of the link between atypical hemispheric lateralization and increased interhemispheric transfer through the corpus callosum.

In this paper, we bring into light, study the polygonal structure of Fibonacci polynomials that are placed clockwise on these by a number corresponding to each vertex. Also, we find the relation between the numbers with such vertices. We present a relation for obtained sequence in an n-gon yielding the m-th term formed at k vertices. Also, we apply these situations to Lucas polynomials and find new recurrence relations. Then, the numbers obtained by writing the coefficients of these polynomials in step form are shown in OEIS.

Abstract 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.

In this paper, the three-phase-lag model of fractional analysis on the reflection of two-dimensional problem of p-waves with initial stress, temperature-dependent, and magnetic field is investigated. The formulation of the problem for an isotropic homogeneous medium based on a three phase-lag theory. The boundary conditions applied on the surface for the stresses and thermal insulation. The numerical solution presented as well as the graphical representation of the impact of analysis considering the external parameters. Also, the modified elastic waves reflected under the action of the magnetic field, initial stress, fractional degree coefficient, and temperature to determine the more exact nature of the reflection of these waves, particularly seismic waves. A comparison has been made between the results obtained and the previous results obtained by others and already published and are in agreement with these, when external parameters considered in the present investigation neglected. The results obtained indicate that the new external parameters have new impact on the waves reflection and applicable in diverse fields as engineering, earthquakes, volcanos, geophysics, acoustics, and astronomy.

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.