Super‐Resolution Nonlinear Photothermal Microscopy

Super‐resolution fluorescence microscopy enables imaging of fluorescent structures beyond the diffraction limit. However, this technique cannot be applied to weakly fluorescent cellular components or labels. As an alternative, photothermal microscopy based on nonradiative transformation of absorbed energy into heat has demonstrated imaging of nonfluorescent structures including single molecules and ~1‐nm gold nanoparticles. However, previously photothermal imaging has been performed with a diffraction‐limited resolution only. Herein, super‐resolution, far‐field photothermal microscopy based on nonlinear signal dependence on the laser energy is introduced. Among various nonlinear phenomena, including absorption saturation, multiphoton absorption, and signal temperature dependence, signal amplification by laser‐induced nanobubbles around overheated nano‐objects is explored. A Gaussian laser beam profile is used to demonstrate the image spatial sharpening for calibrated 260‐nm metal strips, resolving of a plasmonic nanoassembly, visualization of 10‐nm gold nanoparticles in graphene, and hemoglobin nanoclusters in live erythrocytes with resolution down to 50 nm. These nonlinear phenomena can be used for 3D imaging with improved lateral and axial resolution in most photothermal methods, including photoacoustic microscopy.     

Nonlinear rotation‐free three‐node shell finite element formulation

A new triangular thin‐shell finite element formulation is presented, which employs only translational degrees of freedom. The formulation allows for large deformations, and it is based on the nonlinear Kirchhoff thin‐shell theory. A number of static and dynamic test problems are considered for which analytical or benchmark solutions exist. Comparisons between the predictions of the new model and these solutions show that the new model accurately reproduces complex nonlinear analytical solutions as well as solutions obtained using existing, more complex finite element formulations. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonlinear modal analysis via non‐parametric machine learning tools

Modal analysis is an important tool in the structural dynamics community; it is widely utilised to understand and investigate the dynamical characteristics of linear structures. Many methods have been proposed in recent years regarding the extension to nonlinear analysis, such as nonlinear normal modes or the method of normal forms, with the main objective being to formulate a mathematical model of a nonlinear dynamical structure based on observations of input/output data from the dynamical system. In fact, for the majority of structures where the effect of nonlinearity becomes significant, nonlinear modal analysis is a necessity. The objective of the current paper is to demonstrate a machine learning approach to output‐only nonlinear modal decomposition using kernel independent component analysis and locally linear‐embedding analysis. The key element is to demonstrate a pattern recognition approach which exploits the idea of independence of principal components from the linear theory by learning the nonlinear manifold between the variables. In this work, the importance of output‐only modal analysis via “blind source” separation tools is highlighted as the excitation input/force is not needed and the method can be implemented directly via experimental data signals without worrying about the presence or not of specific nonlinearities in the structure.     

Sequence‐Specific HCV RNA Quantification Using the Size‐Dependent Nonlinear Optical Properties of Gold Nanoparticles

The hepatitis C virus (HCV) is a single‐stranded (ss) RNA virus that is responsible for chronic liver diseases, such as cirrhosis, end‐stage liver disease, and hepatocellular carcinoma. Driven by the need to detect the presence of the HCV viral sequence, herein it is demonstrated for the first time that the nonlinear optical (NLO) properties of gold nanoparticles can be used for screening and quantifying HCV RNA without any modification, with excellent detection limit (80 pM ) and selectivity (single base‐pair mismatch). The hyper‐Rayleigh scattering (HRS) intensity increases 25 times when label‐free, 145‐mer, HCV ss‐RNA is hybridized with 400 pM target RNA. The mechanism of HRS intensity change is discussed with experimental evidence for a higher multipolar contribution to the NLO response of gold nanoparticles.     

Nonlinear model order reduction based on local reduced‐order bases

A new approach for the dimensional reduction via projection of nonlinear computational models based on the concept of local reduced‐order bases is presented. It is particularly suited for problems characterized by different physical regimes, parameter variations, or moving features such as discontinuities and fronts. Instead of approximating the solution of interest in a fixed lower‐dimensional subspace of global basis vectors, the proposed model order reduction method approximates this solution in a lower‐dimensional subspace generated by most appropriate local basis vectors. To this effect, the solution space is partitioned into subregions, and a local reduced‐order basis is constructed and assigned to each subregion offline. During the incremental solution online of the reduced problem, a local basis is chosen according to the subregion of the solution space where the current high‐dimensional solution lies. This is achievable in real time because the computational complexity of the selection algorithm scales with the dimension of the lower‐dimensional solution space. Because it is also applicable to the process of hyper reduction, the proposed method for nonlinear model order reduction is computationally efficient. Its potential for achieving large speedups while maintaining good accuracy is demonstrated for two nonlinear computational fluid and fluid‐structure‐electric interaction problems. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonlinear manifold learning for meshfree finite deformation thin‐shell analysis

Calculations on general point‐set surfaces are attractive because of their flexibility and simplicity in the preprocessing but present important challenges. The absence of a mesh makes it nontrivial to decide if two neighboring points in the three‐dimensional embedding are nearby or rather far apart on the manifold. Furthermore, the topology of surfaces is generally not that of an open two‐dimensional set, ruling out global parametrizations. We propose a general and simple numerical method analogous to the mathematical theory of manifolds, in which the point‐set surface is described by a set of overlapping charts forming a complete atlas. We proceed in four steps: (1) partitioning of the node set into subregions of trivial topology; (2) automatic detection of the geometric structure of the surface patches by nonlinear dimensionality reduction methods; (3) parametrization of the surface using smooth meshfree (here maximum‐entropy) approximants; and (4) gluing together the patch representations by means of a partition of unity. Each patch may be viewed as a meshfree macro‐element. We exemplify the generality, flexibility, and accuracy of the proposed approach by numerically approximating the geometrically nonlinear Kirchhoff–Love theory of thin‐shells. We analyze standard benchmark tests as well as point‐set surfaces of complex geometry and topology. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonlinear Saturable Absorption of Liquid‐Exfoliated Molybdenum/Tungsten Ditelluride Nanosheets

Molybdenum disulfide (MoS₂) and tungsten disulfide (WS₂), two representative transition metal dichalcogenide materials, have captured tremendous interest for their unique electronic, optical, and chemical properties. Compared with MoS₂ and WS₂, molybdenum ditelluride (MoTe₂) and tungsten ditelluride (WTe₂) possess similar lattice structures while having smaller bandgaps (less than 1 eV), which is particularly interesting for applications in the near‐infrared wavelength regime. Here, few‐layer MoTe₂/WTe₂ nanosheets are fabricated by a liquid exfoliation method using sodium deoxycholate bile salt as surfactant, and the nonlinear optical properties of the nanosheets are investigated. The results demonstrate that MoTe₂/WTe₂ nanosheets exhibit nonlinear saturable absorption property at 1.55 μm. Soliton mode‐locking operations are realized separately in erbium‐doped fiber lasers utilizing two types of MoTe₂/WTe₂‐based saturable absorbers, one of which is prepared by depositing the nanosheets on side polished fibers, while the other is fabricated by mixing the nanosheets with polyvinyl alcohol and then evaporating them on substrates. Numerous applications may benefit from the nonlinear saturable absorption features of MoTe₂/WTe₂ nanosheets, such as visible/near‐infrared pulsed laser, materials processing, optical sensors, and modulators.