On the Performance Bound of Sparse Estimation with Sensing Matrix Perturbation

This paper focusses on the sparse estimation in the situation where both the the sensing matrix and the measurement vector are corrupted by additive Gaussian noises. The performance bound of sparse estimation is analyzed and discussed in depth. Two types of lower bounds, the constrained Cram\'{e}r-Rao bound (CCRB) and the Hammersley-Chapman-Robbins bound (HCRB), are discussed. It is shown that the situation with sensing matrix perturbation is more complex than the one with only measurement noise. For the CCRB, its closed-form expression is deduced. It demonstrates a gap between the maximal and nonmaximal support cases. It is also revealed that a gap lies between the CCRB and the MSE of the oracle pseudoinverse estimator, but it approaches zero asymptotically when the problem dimensions tend to infinity. For a tighter bound, the HCRB, despite of the difficulty in obtaining a simple expression for general sensing matrix, a closed-form expression in the unit sensing matrix case is derived for a qualitative study of the performance bound. It is shown that the gap between the maximal and nonmaximal cases is eliminated for the HCRB. Numerical simulations are performed to verify the theoretical results in this paper.Comment: 32 pages, 8 Figures, 1 Tabl

Tailoring Accelerating Beams in Phase Space

An appropriate design of wavefront will enable light fields propagating along arbitrary trajectories thus forming accelerating beams in free space. Previous ways of designing such accelerating beams mainly rely on caustic methods, which start from diffraction integrals and only deal with two-dimensional fields. Here we introduce a new perspective to construct accelerating beams in phase space by designing the corresponding Wigner distribution function (WDF). We find such a WDF-based method is capable of providing both the initial field distribution and the angular spectrum in need by projecting the WDF into the real space and the Fourier space respectively. Moreover, this approach applies to the construction of both two- and three-dimensional fields, greatly generalizing previous caustic methods. It may therefore open up a new route to construct highly-tailored accelerating beams and facilitate applications ranging from particle manipulation and trapping to optical routing as well as material processing.Comment: 8 pages, 6 figure

In situ deformation transmission electron microscopy investigation of the mechanical behaviours of nanomaterials

Due to their superior properties, nanomaterials (NMs) have many significant applications. The mechanical properties of NMs including nanowires (NWs) and nanofilms are a crucial factor in designing devices where predictable and reproducible operation is important. However, due to the difficulty of mechanical testing at nanoscale, mechanical properties of NMs have not been as extensively investigated. This thesis aims to apply an in situ deformation transmission electron microscopy (TEM) technique combined with finite element analysis (FEA) to investigate the mechanical behaviours of NMs. The first chapter of this thesis presents a summary of the applications, synthesis methods, nanomechanical characterisation techniques, and mechanical behaviours of nanomaterials. The second chapter provides a general description of the methods used in this thesis. Details of the experimental and modelling procedures are also described. In the third chapter, quantitative investigation of the effects of loading misalignment and tapering of NWs on the measured compression and tensile mechanical properties is presented. In the fourth chapter, the Young’s moduli of GaAs NWs with two distinct structures – defect-free single crystalline wurtzite and wurtzite containing a high density of stacking faults (SFs) – are measured. The presence of a high density of SFs was found to increase the Young’s modulus by 12%. Determination of the elastic modulus of NMs with sizes of a few nanometres is a significant challenge. In the fifth chapter, a method combining in situ compression TEM and FEA is developed to measure the Young’s modulus of nanoscale films with thicknesses down to ~ 2 nm by using a core–shell NW structure. Major conclusions are drawn from this PhD research in the last chapter. Some possible future work is proposed as extension of what has been achieved

一槽式HAP-PNAプロセスに関する基礎的研究

Tohoku University博士（工学）要約のみthesi

PREDICTION OF SUBSURFACE DAMAGE DURING MACHINING NICKEL-BASED SUPERALLOYS

Nickel-based superalloys are widely utilized in hostile environments such as jet engines and gas turbines due to their high resistance to oxidation, high corrosion resistance, good thermal fatigue-resistance and fracture toughness. Subsurface damage is typically generated during the machining of these materials, and in particular, ã\u27-strengthened nickel-based superalloys. The depth of the subsurface damage is a critical requirement specified by the customer. Therefore, it is critical to predict, measure and control subsurface damage. This research specifically targets the development of a model to predict subsurface damage during the machining of ã\u27-strengthened nickel-based superalloys. To accomplish this, a modified Johnson-Cook model is developed to represent the plasticity behavior of the material using elevated temperature tests. The proposed model integrates a piece-wise method, strain hardening function, thermal sensitivity function, and flow softening function accurately model anomalous strength behavior. Material subroutines are developed for finite element analysis (FEA) simulation and applied with the ABAQUS/Explicit solver. Orthogonal cutting experiments are conducted to verify FEA results. Recrystallization techniques are utilized for estimation of the depth of subsurface damage. By comparing the subsurface damage between experimental and FEM simulation results, a threshold value is established for determining the depth of subsurface damage. A high agreement between FEA simulation and experimental results is observed. From the cutting force aspect, the agreement is more than 90% for unaggressive cutting inputs. On the other hand, the model agreement is slightly lower, 85%, for aggressive machining conditions. This is due to the fact that the severe rake face wear cannot be comprehensively represented in the FEA simulation. In addition, the depth of subsurface damage predicted from the FEA simulations reached an agreement of 95% when compared to experimental findings. Therefore, a subsurface damage model between cutting inputs and depth of subsurface damage has been established based on the results derived from FEA simulations

Kink-antikink asymmetry and impurity interactions in topological mechanical chains

We study the dynamical response of a diatomic periodic chain of rotors coupled by springs, whose unit cell breaks spatial inversion symmetry. In the continuum description, we derive a nonlinear field theory which admits topological kinks and antikinks as nonlinear excitations but where a topological boundary term breaks the symmetry between the two and energetically favors the kink configuration. Using a cobweb plot, we develop a fixed-point analysis for the kink motion and demonstrate that kinks propagate without the Peierls-Nabarro potential energy barrier typically associated with lattice models. Using continuum elasticity theory, we trace the absence of the Peierls-Nabarro barrier for the kink motion to the topological boundary term which ensures that only the kink configuration, and not the antikink, costs zero potential energy. Further, we study the eigenmodes around the kink and antikink configurations using a tangent stiffness matrix approach appropriate for pre-stressed structures to explicitly show how the usual energy degeneracy between the two no longer holds. We show how the kink-antikink asymmetry also manifests in the way these nonlinear excitations interact with impurities introduced in the chain as disorder in the spring stiffness. Finally, we discuss the effect of impurities in the (bond) spring length and build prototypes based on simple linkages that verify our predictions.Comment: 20 pages, 21 figure

Spin-orbit interaction of light induced by transverse spin angular momentum engineering

We report the first demonstration of a direct interaction between the extraordinary transverse spin angular momentum in evanescent waves and the intrinsic orbital angular momentum in optical vortex beams. By tapping the evanescent wave of whispering gallery modes in a micro-ring-based optical vortex emitter and engineering the transverse spin state carried therein, a transverse-spin-to-orbital conversion of angular momentum is predicted in the emitted vortex beams. Numerical and experimental investigations are presented for the proof-of-principle demonstration of this unconventional interplay between the spin and orbital angular momenta, which could provide new possibilities and restrictions on the optical angular momentum manipulation techniques on the sub-wavelength scale. This phenomenon further gives rise to an enhanced spin-direction coupling effect in which waveguide or surface modes are unidirectional excited by incident optical vortex, with the directionality jointly controlled by spin-orbit states. Our results enrich the spin-orbit interaction phenomena by identifying a previously unknown pathway between the polarization and spatial degrees of freedom of light, and can enable a variety of functionalities employing spin and orbital angular momenta of light in applications such as communications and quantum information processing