2,214 research outputs found
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
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
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
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
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