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Cutting-edge smart materials are transforming the domains of soft robotics, actuators, and sensors by harnessing diverse non-mechanical stimuli, such as electric and magnetic fields. Accurately modelling their physical behaviour necessitates an understanding of the complex interactions between the structural deformation and the fields in the surrounding medium. For thin shell structures, this challenge is addressed by developing a shell model that effectively incorporates the three-dimensional field it is embedded in by appropriately accounting for the relevant boundary conditions. This study presents a model for the nonlinear deformation of thin hyperelastic shells, incorporating Kirchhoff-Love assumptions and a rigorous variational approach. The shell theory is derived from 3D nonlinear elasticity by dimension reduction while preserving the boundary conditions at the top and bottom surfaces of the shell. Consequently, unlike classical shell theories, this approach can distinguish between pressure loads applied at the top and bottom surfaces, and delivers a platform to include multi-physics coupling. Numerical examples are presented to illustrate the theory and provide a physical interpretation of the novel mechanical variables of the model., Comment: arXiv admin note: text overlap with arXiv:2308.12300

We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p}(\mathbb{R}^{n})$, $n\geq2$, where the radii of the spheres are restricted to a compact subset of $(0,\infty)$. These bounds extend to general hypersurfaces with non-vanishing Gaussian curvature, to the complex spherical means, and to geodesic spheres on compact manifolds. We also obtain improved maximal function bounds and pointwise convergence statements for wave equations, both on $\mathbb{R}^{n}$ and on compact manifolds. The maximal function bounds are essentially sharp for all $p\in[1,2]\cup [\frac{2(n+1)}{n-1},\infty]$, for each such hypersurface, every complex spherical mean, and on every manifold., Comment: 32 pages. Revised version with additional sharpness statements

A geometrically exact dimensionally reduced order model for the nonlinear deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love assumptions for the mechanical fields are generalised to the magnetic variables to derive a consistent two-dimensional theory based on a rigorous variational approach. The general deformation map, as opposed to the mid-surface deformation, is considered as the primary variable resulting in a more accurate description of the nonlinear deformation. The commonly used plane stress assumption is discarded due to the Maxwell stress in the surrounding free-space requiring careful treatment on the upper and lower shell surfaces. The complexity arising from the boundary terms when deriving the Euler-Lagrange governing equations is addressed via a unique application of Green's theorem.The governing equations are solved analytically for the problem of an infinite cylindrical magnetoelastic shell. This clearly demonstrates the model's capabilities and provides a physical interpretation of the new variables in the modified variational approach. This novel formulation for magnetoelastic shells serves as a valuable tool for the accurate design of thin magneto-mechanically coupled devices.

The present study demonstrates the effectiveness of incorporating oxygen atoms into the Sb2Te3 thin film, leading to an improved power factor and reduction in thermal conductivity. Based on the experimental evidence, it can be inferred that oxygen-related impurities preferentially wet the grain boundary (GB) and introduce a double Schottky barrier at the GB interface, promoting energy-dependent carrier scattering, ultimately leading to a rise in the Seebeck coefficient. Additionally, the introduction of chemisorbed oxygen creates a high mobility state within the valence band of Sb2Te3, as corroborated by theoretical calculations, resulting in a significantly increased electrical mobility. These factors collectively contribute to improved thermoelectric performance. A set of Scanning probe (SPM) techniques is used to experimentally confirm the alteration in charge transport resulting from the oxygen-passivated grain boundary. Additionally, Scanning Thermal Microscopy (SThM) is employed to observe the spatial variations of thermal conductivity at the nanoscale regime. This study presents a comprehensive microscopic investigation of the impact of oxygen on the phonon and charge carrier transport characteristics of Sb2Te3 thermoelectric materials and indicates that incorporating oxygen may represent a feasible approach to improve the thermoelectric efficiency of these materials.

For $s \in [1/2, 1)$, let $u$ solve $(\partial_t - \Delta)^s u = Vu$ in $\mathbb R^{n} \times [-T, 0]$ for some $T>0$ where $||V||_{ C^2(\mathbb R^n \times [-T, 0])} < \infty$. We show that if for some $0< c< T$ and $\epsilon>0$ $$\frac{1}{c} \int_{[-c,0]} u^2(x, t) dt \leq Ce^{-|x|^{2+\epsilon}}\ \forall x \in \mathbb R^n,$$ then $u \equiv 0$ in $\mathbb R^{n} \times [-T, 0]$., Comment: arXiv admin note: text overlap with arXiv:2306.00341

This is a continuation of our work [BBGG23, BBGG22] where we have initiated the study of sparse domination and quantitative weighted estimates for Grushin pseudo-multipliers. In this article, we further extend this analysis to study analogous estimates for a family of operator-valued Fourier pseudo-multipliers associated to Grushin operators $G = - \Delta_{x^{\prime}} - |x^{\prime}|^2 \Delta_{x^{\prime \prime}}$ on $\mathbb{R}^{n_1+n_2}.$, Comment: This work consists of results extracted from arXiv:2112.06634v1. arXiv admin note: substantial text overlap with arXiv:2112.06634

We show that if $u$ solves the fractional parabolic equation $(\partial_t - \Delta )^s u = Vu$ in $B_5 \times (-25, 0]$ ($0

The present study demonstrates a large enhancement in the Seebeck coefficient and ultralow thermal conductivity (TE) in Sb$_2$Te$_3$-AgSbTe$_2$ nanocomposite thin film. The addition of Ag leads to the in-situ formation of AgSbTe$_2$ secondary phase nanoaggregates in the Sb$_2$Te$_3$ matrix during the growth resulting in a large Seebeck coefficient and reduction of the thermal conductivity. A series of samples with different amounts of minor AgSbTe$_2$ phases are prepared to optimize the TE performance of Sb$_2$Te$_3$ thin films. Based on the experimental and theoretical evidence, it is concluded that a small concentration of Ag promotes the band flattening and induces a sharp resonate-like state deep inside the valence band of Sb$_2$Te$_3$, concurrently modifying the density of states (DOS) of the composite sample. In addition, the electrical potential barrier introduced by the band offset between the host TE matrix and the secondary phases promotes strong energy-dependent carrier scattering in the composite sample, which is also responsible for enhanced TE performance. A contemporary approach based on scanning thermal microscopy is performed to experimentally obtain thermal conductivity values of both the in-plane and cross-plane directions, showing a reduced in-plane thermal conductivity value by ~ 58% upon incorporating the AgSbTe$_2$ phase in the Sb$_2$Te$_3$ matrix. Benefitting from the synergistic manipulation of electrical and thermal transport, a large ZT value of 2.2 is achieved at 375 K. The present study indicates the importance of a combined effect of band structure modification and energy-dependent charge carrier scattering along with reduced thermal conductivity for enhancing TE properties.

In this article, we address sparse bounds for a class of spectral multipliers that include oscillating multipliers on stratified Lie groups. Our results can be applied to obtain weighted bounds for general Riesz means and for solutions of dispersive equations.

The inflation of hyperelastic thin shells is an important and highly nonlinear problem that arises in multiple engineering applications involving severe kinematic and constitutive nonlinearities in addition to various instabilities. We present an isogeometric approach to compute the inflation of hyperelastic thin shells, following the Kirchhoff-Love hypothesis and associated large deformation. Both the geometry and the deformation field are discretized using Catmull-Clark subdivision bases which provide the C1-continuous finite element framework required for the Kirchhoff-Love shell formulation. To follow the complex nonlinear response of hyperelastic thin shells, the inflation is simulated incrementally, and each incremental step is solved via the Newton-Raphson method enriched with arc-length control. Eigenvalue analysis of the linear system after each incremental step allows for inducing bifurcation to a lower energy mode in case stability of the equilibrium is lost. The proposed method is first validated using benchmarks, and then applied to engineering applications, where we demonstrate the ability to simulate large deformation and associated complex instabilities., Comment: 25 pages, 12 figures

In this paper, we prove the strong unique continuation property at the origin for solutions of the following scaling critical parabolic differential inequality \[ |\operatorname{div} (A(x,t) \nabla u) - u_t| \leq \frac{M}{|x|^{2}} |u|,\ \ \ \ \] where the coefficient matrix $A$ is Lipschitz continuous in $x$ and $t$. Our main result sharpens a previous one of Vessella concerned with the subcritical case as well as extends a recent result of one of us with Garofalo and Manna for the heat operator.

In this article, we obtain hessian estimates for Kolmogorov-Fokker-Planck operators in non-divergence form in several Banach function spaces. Our approach relies on a representation formula and newly developed sparse domination techniques in Harmonic Analysis. Our result when restricted to weighted Lebesgue spaces yields sharp quantitative hessian estimates for the Kolmogorov-Fokker-Planck operators.

In this article, we establish pointwise sparse domination results for Grushin pseudo-multipliers corresponding to various symbol classes, as a continuation of our investigation initiated in [BBGG21]. As a consequence, we deduce quantitative weighted estimates for these pseudo-multipliers., Comment: 39 pages

In this article, we introduce an analogue of Kenig and Stein's bilinear fractional integral operator on the Heisenberg group $\mathbb{H}^n$. We completely characterize exponents $\alpha, \beta$ and $\gamma$ such that the operator is bounded from $L^{p}(\mathbb{H}^n, |x|^{\alpha p})\times L^{q}(\mathbb{H}^n, |x|^{\beta q})$ to $L^{r}(\mathbb{H}^n, |x|^{-\gamma r})$.

In this article, we prove sharp quantitative weighted $L^p$-estimates for Grushin pseudo-multipliers satisfying H\"ormander's condition as an application of pointwise domination of Grushin pseudo-multipliers by appropriate sparse operators., Comment: Following valuable comments and suggestions of a journal reviewer, we have revised the presentation of the article. Results are same as in the previous version (v2)

In this article we introduce the fractional Hardy-Littlewood maximal function on the infinite rooted $k$-ary tree and study its weighted boundedness. We also provide examples of weights for which the fractional Hardy-Littlewood maximal function satisfies strong type $(p, q)$ estimates on the infinite rooted $k$-ary tree.

Compression-induced buckling instability of metal thin films on a compliant base result in surface wrinkles. A stiff thin film, perfectly bonded to an infinitely deep pre-stretched dielectric elastomer (DE) substrate, is considered. Linear perturbation analysis reveals the critical strain in the layer at the onset of wrinkling. A fully coupled Finite-Element (FE) scheme, based on large deformation electroelasticity, where domains of the mechanical and electrical problems coincide, is developed to model the elastomer. The procedure can handle nearly incompressible materials, which require careful considerations. The thin film is modeled as a beam. The numerical technique is used to study the post-buckling behavior upon relaxation of the pre-strained substrate. The FE domain is a unit cell of twice the characteristic wavelength. Assuming that there is no wrinkling-induced delamination at the film/substrate interface, the numerical analyses overview various tunable surface configurations distinctly different from the sinusoidal shape. The several topographic options broaden the functional horizon of surface instability patterns. Again, corrugation is essential to provide a degree of electrode compliance when the elastomer elongates in the lateral direction due to an applied electric potential. Simulations show the response of DE for the different surface profiles and also demonstrate the failure mechanisms that limit the actuation., Comment: Certain modifications are required which will take considerable time to simulate and organize and the also the title may be modified