Related papers: Size estimates for nanoplates
Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state-variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by…
Optical entropy bounds for metal nanoparticles immersed in nonlinear optical media and for nonlinear dielectric microdroplets on metal surfaces are calculated near the frequency of the surface plasmon resonance. Similar to the…
Interwall interaction energies, as well as barriers to relative sliding of the walls along the nanotube axis, are first calculated for pairs of both armchair or both zigzag adjacent walls of carbon nanotubes with a wide range of radiuses.…
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error is bounded in terms of the…
We find the precise growth of some invariant metrics near a point on the boundary of a domain where the Levi form has at least one negative eigenvalue. We also introduce a new invariant pseudometric which is convenient in this context, and…
Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve…
We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner…
The response of a vibrating beam to a force depends on many physical parameters including those determined by material properties. Damage caused by fatigue or cracks result in local reductions in stiffness parameters and may drastically…
An inclusion is said to be neutral to uniform fields if upon insertion into a homogenous medium with a uniform field it does not perturb the uniform field at all. It is said to be weakly neutral if it perturbs the uniform field mildly. Such…
Assessing the vulnerability of atherosclerotic plaques requires an accurate knowledge of the mechanical properties of the plaque constituents. It is possible to measure displacements in vivo inside a plaque using magnetic resonance imaging.…
The classical flexure problem of non-linear incompressible elasticity is revisited for elastic materials whose mechanical response is different in tension and compression---the so-called bimodular materials. The flexure problem is chosen to…
In a data-scarce field such as healthcare, where models often deliver predictions on patients with rare conditions, the ability to measure the uncertainty of a model's prediction could potentially lead to improved effectiveness of decision…
Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order…
The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the…
We present a framework that allows an observer to determine occluded portions of a structure by finding the maximum-likelihood estimate of those occluded portions consistent with visible image evidence and a consistency model. Doing this…
The availability of high-throughput parallel methods for sequencing microbial communities is increasing our knowledge of the microbial world at an unprecedented rate. Though most attention has focused on determining lower-bounds on the…
Deep learning based methods for automatic organ segmentation have shown promise in aiding diagnosis and treatment planning. However, quantifying and understanding the uncertainty associated with model predictions is crucial in critical…
The classical models of Hertz, Sneddon and Boussinesq provide solutions for problems of indentation of a semi-infinite elastic massif by a sphere, a sphere or a cone and a flat punch. Although these models have been widely tested, it…
We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous reference can be uniquely determined by (single-)scattered…
In safety-critical applications like medical diagnosis, certainty associated with a model's prediction is just as important as its accuracy. Consequently, uncertainty estimation and reduction play a crucial role. Uncertainty in predictions…