The influence of wetting-layer states on quantum-dot states and vice versa is analysed numerically for electrons in the conduction band in the general case with arbitrary kinetic energy in the plane of the quantum-well wetting layer. Since the analysed quantum dot is embedded in a barrier material with different properties, the effective mass approximation methodology leads to a Schrödinger model with discontinuous coefficients. This complicates the analysis and, in addition, requires a special attention to the formulation of boundary conditions for the entire structure, consisting of the quantum dot with wetting layer embedded in a barrier material. In the present paper, the complete model is formulated and solved numerically via a variational approach based on finite element approximations and Arnoldi iterations. By analysing different geometrical configurations, we demonstrate that the ground eigenstate of the entire structure can be considerably affected by the presence of the wetting layer. The dependency demonstrated between eigenstates of the 'pure' quantum dots and the quantum-well wetting layers indicates that a conventional analysis of quantum-dot structures without accounting for wetting layers may not be sufficient for an adequate characterization of quantum dots as active regions in future electronic and optical devices.

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The dynamics of phase transitions and hysteresis phenomena in materials with memory are described by a strongly nonlinear coupled system of partial differential equations which, in its generality, can be solved only numerically. Following principles of extended thermodynamics, in this paper we construct a new model for the description of this dynamics based on the CattaneoVernotte law for heat conduction. Models based on the Fourier law follow from this general consideration as special cases. We develop a general procedure for the solution of the resulting systems by their reduction to differential-algebraic systems. Finally, a computational code for the numerical implementation of this procedure is explained in detail, and representative numerical examples are given. IntroductionOne of the most difficult problems in computational mechanics is to quantify phase transformations in complex materials. For the so-called ''smart'' materials this problem is of enormous technological importance. Indeed, performance demands on materials and systems used in engineering applications and infrastructure necessitate the development of such ''smart'' materials that have the ability to change their properties in response to external and internal stimuli. In this way, new engineering components can be developed leading to improved efficiency and reliability of the whole structure. For many such materials phase transformations and accompanied hysteresis phenomena, demonstrated by the strain-temperature, stress-strain, and stress-temperature relations, are intrinsic parts of the material dynamics. From a mathematical point of view, one of the major difficulties come from the fact that these transformations cannot be characterised by a single-valued function. Indeed, in those solids that do not exhibit structure transitions or plastic deformations, the strain is a single-valued function of stress and temperature, which might not be the case for many ''smart'' materials exhibiting hysteresis loops. Typical to ferromagnetic, ferroelectric, plasticity effects, such loops arise due to the fact that the underlying process has more than one stable equilibrium. The free energy function for this thermodynamic process should be derived from statistical models, and any physically reasonable approximation of this function will result in a non-convex energy function. In this paper we focus on a specific type of phase transformations, so-called solid-solid phase transformations, in ''smart'' materials known as shape memory alloys (SMAs). In contrast to ferroelectricity, ferromagnetism, plasticity, where hysteresis phenomena relatively well investigated, this is not the case for pseudoelastic effects that are observed in SMA materials. At the same time, these materials have a huge potential in such fields as electronics, biomedical and environmental engineering, energy production systems, various consumer products, aerospace, and automotive industry, because they can provide functions of sensing, processing, actuation, and feedback [8]. In compa...

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Mapping the brain imaging data to networks, where nodes represent anatomical brain regions and edges indicate the occurrence of fiber tracts between them, has enabled an objective graph-theoretic analysis of human connectomes. However, the latent structure on higher-order interactions remains unexplored, where many brain regions act in synergy to perform complex functions. Here we use the simplicial complexes description of human connectome, where the shared simplexes encode higher-order relationships between groups of nodes. We study consensus connectome of 100 female (F-connectome) and of 100 male (M-connectome) subjects that we generated from the Budapest Reference Connectome Server v3.0 based on data from the Human Connectome Project. Our analysis reveals that the functional geometry of the common F&M-connectome coincides with the M-connectome and is characterized by a complex architecture of simplexes to the 14th order, which is built in six anatomical communities, and linked by short cycles. The F-connectome has additional edges that involve different brain regions, thereby increasing the size of simplexes and introducing new cycles. Both connectomes contain characteristic subjacent graphs that make them 3/2-hyperbolic. These results shed new light on the functional architecture of the brain, suggesting that insightful differences among connectomes are hidden in their higher-order connectivity.

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We demonstrate that the conventional application of linear models to the analysis of optoelectromechanical properties of nanostructures in bandstructure engineering could be inadequate. Such linear models are usually derived from the traditional bottom-up approach applied to the analysis of nanostructure properties. At the same time, in the hierarchy of mathematical models for semiconductor device modelling constructed on the basis of the top-down approach, we deal predominantly with models where nonlinearity is essential. In this contribution, we analyze these two fundamental approaches in bridging the scales in mathematical models for the description of optoelectromechanical properties of nanostructures. The focus of the present paper is on a model based on the coupled Schrodinger-Poisson system where we account consistently for the piezoelectric effect and analyze the influence of different nonlinear terms in strain components. The examples given in this paper show that the piezoelectric effect contributions are essential and have to be accounted for with fully coupled models. While in structural applications of piezoelectric materials at larger scales, the minimization of the full electromechanical energy is now a routine in many engineering applications, in bandstructure engineering conventional approaches are still based on linear models with minimization of uncoupled, purely elastic energy functionals with respect to displacements. Generalizations of the existing models for bandstructure calculations are presented in this paper in the context of coupled effects.