Representing Reflective Logic in Modal Logic

The nonmonotonic logic called Reflective Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Reflective Logic with an initial set of axioms and defaults if and only if the meaning of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Reflective Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since all the laws of First Order Logic hold and since both the Barcan Formula and its converse hold.

Representing Default Logic in Modal Logic

The nonmonotonic logic called Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan Formula and its converse hold.

Representing Autoepistemic Logic in Modal Logic

The nonmonotonic logic called Autoepistemic Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Autoepistemic Logic with an initial set of axioms if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meaning of that initial set of sentences. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and unlike the original Autoepistemic Logic, it is easily generalized to the case where quantified variables may be shared across the scope of modal expressions thus allowing the derivation of quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan formula and its converse hold.

Volume strain sensor based on spectra analysis of in-fiber modal interferometer

An optical in-fiber modal interferometer-based volume strain sensor for earthquake prediction is proposed and experimentally demonstrated. The sensing element is formed by wrapping a multimode-singlemode-multimode fiber structure onto a polyurethane hollow column. Due to the modal interference between the excited guided modes in the fiber, strong interference pattern could be observed in the transmission spectrum. Theoretical analysis verifies that the resonant wavelength shifts as a result of the volume strain variation caused by the column deformation with square root relationship. Sensitivity > 3.93 pm/με within the volume strain ranging from 0 to 1300 με is also experimentally demonstrated. By taking the response of bidirectional change of volume strain and the sluggish character of the employed sensing material into consideration, the sensing system presents good repeatability and stability. © 2001-2012 IEEE.

Impact of inter-modal four-wave mixing on the performance of mode- and wavelength-division-multiplexing systems

In this paper, we investigate the impact of inter-modal four-wave mixing on mode- and wavelength-division-multiplexing systems. A set of coupled nonlinear Schrödinger equations, including linear mode coupling, is derived allowing to isolate the inter-modal four-wave mixing terms. The efficiency of inter-modal four-wave mixing between degenerate LP modes is found to be significantly higher than the intra-modal four-wave mixing efficiency. However, it is shown that the inter-modal four-wave mixing efficiency between degenerate modes is significantly reduced by the linear mode coupling.

Simultaneous measurement for liquid level and refractive index based on all-fiber modal interferometer

A simple fiber sensor capable of simultaneous measurement of liquid level and refractive index (RI) is proposed and experimentally demonstrated. The sensing head is an all-fiber modal interferometer manufactured by splicing an uncoated single-mode fiber with two short sections of multimode fiber. The interference pattern experiences blue shift along with an increase of axial strain and surrounding RI. Owing to the participation of multiple cladding modes with different sensitivities, the height and RI of the liquid could be simultaneously measured by monitoring two dips of the transmission spectrum. Experimental results show that the liquid level and RI sensitivities of the two dips are 245.7 pm/mm, -38 nm/RI unit (RIU), and 223.7 pm/mm, -62 nm/RIU, respectively. The approach has distinctive advantages of easy fabrication, low cost, and high sensitivity for liquid level detection with the capability of distinguishing the RI variation simultaneously. © 2013 Copyright Taylor and Francis Group, LLC.

Pd/C catalysts based on synthetic carbons with bi- and tri-modal pore-size distribution:applications in flow chemistry

Two new types of phenolic resin-derived synthetic carbons with bi-modal and tri-modal pore-size distributions were used as supports for Pd catalysts. The catalysts were tested in chemoselective hydrogenation and hydrodehalogenation reactions in a compact multichannel flow reactor. Bi-modal and tri-modal micro-mesoporous structures of the synthetic carbons were characterised by N2 adsorption. HR-TEM, PXRD and XPS analyses were performed for characterising the synthesised catalysts. N2 adsorption revealed that tri-modal synthetic carbon possesses a well-developed hierarchical mesoporous structure (with 6.5 nm and 42 nm pores), contributing to a larger mesopore volume than the bi-modal carbon (1.57 cm3 g-1versus 1.23 cm3 g-1). It was found that the tri-modal carbon promotes a better size distribution of Pd nanoparticles than the bi-modal carbon due to presence of hierarchical mesopore limitting the growth of Pd nanoparticles. For all the model reactions investigated, the Pd catalyst based on tri-modal synthetic carbon (Pd/triC) show high activity as well as high stability and reproducibility. The trend in reactivities of different functional groups over the Pd/triC catalyst follows a general order alkyne ≫ nitro > bromo ≫ aldehyde.

Experimental investigation into amplitude-dependent modal properties of an eleven-span motorway bridge

The authors would like to thank their supporters. New Zealand Earthquake Commission (EQC) Research Foundation provided financial support for experimental work (Grant No. UNI/578). New Zealand Transport Agency (NZTA) provided access to the bridge. Piotr Omenzetter’s work within the LRF Centre for Safety and Reliability Engineering at the University of Aberdeen is supported by Lloyd’s Register Foundation. The Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research. Ge-Wei Chen’s doctoral study is supported by China Scholarship Council (CSC) (Grant No. 2011637065).

Modal identification of a twelve span viaduct in two different construction stages via ambient dynamic testing

Peer reviewed

Comparison of output-only methods for modal identification of a twelve-span viaduct

Peer reviewed

Development of Multi-modal and Super-resolved Retinal Imaging Systems

Advancements in retinal imaging technologies have drastically improved the quality of eye care in the past couple decades. Scanning laser ophthalmoscopy (SLO) and optical coherence tomography (OCT) are two examples of critical imaging modalities for the diagnosis of retinal pathologies. However current-generation SLO and OCT systems have limitations in diagnostic capability due to the following factors: the use of bulky tabletop systems, monochromatic imaging, and resolution degradation due to ocular aberrations and diffraction.

Bulky tabletop SLO and OCT systems are incapable of imaging patients that are supine, under anesthesia, or otherwise unable to maintain the required posture and fixation. Monochromatic SLO and OCT imaging prevents the identification of various color-specific diagnostic markers visible with color fundus photography like those of neovascular age-related macular degeneration. Resolution degradation due to ocular aberrations and diffraction has prevented the imaging of photoreceptors close to the fovea without the use of adaptive optics (AO), which require bulky and expensive components that limit the potential for widespread clinical use.

In this dissertation, techniques for extending the diagnostic capability of SLO and OCT systems are developed. These techniques include design strategies for miniaturizing and combining SLO and OCT to permit multi-modal, lightweight handheld probes to extend high quality retinal imaging to pediatric eye care. In addition, a method for extending true color retinal imaging to SLO to enable high-contrast, depth-resolved, high-fidelity color fundus imaging is demonstrated using a supercontinuum light source. Finally, the development and combination of SLO with a super-resolution confocal microscopy technique known as optical photon reassignment (OPRA) is demonstrated to enable high-resolution imaging of retinal photoreceptors without the use of adaptive optics.

Simulation of Distributed Contact in String Instruments: a Modal Expansion Approach

Impactive contact between a vibrating string and a barrier is a strongly nonlinear phenomenon that presents several challenges in the design of numerical models for simulation and sound synthesis of musical string instruments. These are addressed here by applying Hamiltonian methods to incorporate distributed contact forces into a modal framework for discrete-time simulation of the dynamics of a stiff, damped string. The resulting algorithms have spectral accuracy, are unconditionally stable, and require solving a multivariate nonlinear equation that is guaranteed to have a unique solution. Exemplifying results are presented and discussed in terms of accuracy, convergence, and spurious high-frequency oscillations.