Theoretical investigations of experimental gravitation

This thesis has two basic themes: the investigation of new experiments which can be used to test relativistic gravity, and the investigation of new technologies and new experimental techniques which can be applied to make gravitational wave astronomy a reality.

Advancing technology will soon make possible a new class of gravitation experiments: pure laboratory experiments with laboratory sources of non-Newtonian gravity and laboratory detectors. The key advance in techno1ogy is the development of resonant sensing systems with very low levels of dissipation. Chapter 1 considers three such systems (torque balances, dielectric monocrystals, and superconducting microwave resonators), and it proposes eight laboratory experiments which use these systems as detectors. For each experiment it describes the dominant sources of noise and the technology required.

The coupled electro-mechanical system consisting of a microwave cavity and its walls can serve as a gravitational radiation detector. A gravitational wave interacts with the walls, and the resulting motion induces transitions from a highly excited cavity mode to a nearly unexcited mode. Chapter 2 describes briefly a formalism for analyzing such a detector, and it proposes a particular design.

The monitoring of a quantum mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. Chapter 3 reviews the standard techniques for monitoring the oscillator; and it introduces a new technique which, in principle, can determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator.

The standard method for monitoring the oscillator is the "amplitude- and-phase" method (position or momentum transducer with output fed through a linear amplifier). The accuracy obtainable by this method is limited by the uncertainty principle. To do better requires a measurement of the type which Braginsky has called "quantum nondemolition." A well-known quantum nondemolition technique is "quantum counting," which can detect an arbitrarily weak force, but which cannot provide good accuracy in determining its precise time-dependence. Chapter 3 considers extensively a new type of quantum nondemolition measurement - a "back-action-evading" measurement of the real part X₁ (or the imaginary part X₂) of the oscillator's complex amplitude. In principle X₁ can be measured arbitrarily quickly and arbitrarily accurately, and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force.

Chapter 3 describes explicit gedanken experiments which demonstrate that X₁ can be measured arbitrarily quickly and arbitrarily accurately, it considers approximate back-action-evading measurements, and it develops a theory of quantum nondemolition measurement for arbitrary quantum mechanical systems.

In Rosen's "bimetric" theory of gravity the (local) speed of gravitational radiation v_g is determined by the combined effects of cosmological boundary values and nearby concentrations of matter. It is possible for v_g to be less than the speed of light. Chapter 4 shows that emission of gravitational radiation prevents particles of nonzero rest mass from exceeding the speed of gravitational radiation. Observations of relativistic particles place limits on v_g and the cosmological boundary values today, and observations of synchrotron radiation from compact radio sources place limits on the cosmological boundary values in the past.

Calibration of the spring constant of cantilevers of arbitrary shape using the phase signal in an atomic force microscope.

The measurement of cantilever parameters is an essential part of performing a calibrated measurement with an atomic force microscope (AFM). The thermal motion method is a widely used technique for calibrating the spring constant of an AFM cantilever, which can be applied to non-rectangular cantilevers. Given the trend towards high frequency scanning, calibration of non-rectangular cantilevers is of increasing importance. This paper presents two results relevant to cantilever calibration via the thermal motion method. We demonstrate the possibility of using the AFM's phase signal to acquire the thermal motion. This avoids the challenges associated with connecting the raw photodiode signal to a separate spectrum analyser. We also describe how numerical calculations may be used to calculate the parameters needed in a thermal motion calibration of a non-rectangular cantilever. Only accurate knowledge of the relative size of the in-plane dimensions of the cantilever is needed in this computation. We use this pair of results in the calibration of a variety of rectangular and non-rectangular cantilevers. We observe an average difference between the Sader and thermal motion values of cantilever stiffness of 10%.

Shock propagation and MPT noise from a transonic rotor in non-uniform flow

One of the major challenges in hig4h-speed fan stages used in compact, embedded propulsion systems is inlet distortion noise. A body-force-based approach for the prediction of multiple-pure-tone (MPT) noise was previously introduced and validated. In this paper, it is employed with the objective of quantifying the effects of non-uniform flow on the generation and propagation of MPT noise. First-of-their-kind back-to-back coupled aero-acoustic computations were carried out using the new approach for conventional and serpentine inlets. Both inlets delivered flow to the same NASA/GE R4 fan rotor at equal corrected mass flow rates. Although the source strength at the fan is increased by 45 dB in sound power level due to the non-uniform inflow, farfield noise for the serpentine inlet duct is increased on average by only 3.1 dBA overall sound pressure level in the forward arc. This is due to the redistribution of acoustic energy to frequencies below 11 times the shaft frequency and the apparent cut-off of tones at higher frequencies including blade-passing tones. The circumferential extent of the inlet swirl distortion at the fan was found to be 2 blade pitches, or 1/11th of the circumference, suggesting a relationship between the circumferential extent of the inlet distortion and the apparent cut-off frequency perceived in the far field. A first-principles-based model of the generation of shock waves from a transonic rotor in non-uniform flow showed that the effects of non-uniform flow on acoustic wave propagation, which cannot be captured by the simplified model, are more dominant than those of inlet flow distortion on source noise. It demonstrated that non-linear, coupled aerodynamic and aeroacoustic computations, such as those presented in this paper, are necessary to assess the propagation through non-uniform mean flow. A parametric study of serpentine inlet designs is underway to quantify these propagation effects. Copyright © 2011 by ASME.

A body force-based method for prediction of multiple-pure-tone noise: Validation

Emissions, fuel burn, and noise are the main drivers for innovative aircraft design. Embedded propulsion systems, such as for example used in hybrid-wing body aircraft, can offer fuel burn and noise reduction benefits but the impact of inlet flow distortion on the generation and propagation of turbomachinery noise has yet to be assessed. A novel approach is used to quantify the effects of non-uniform flow on the creation and propagation of multiple pure tone (MPT) noise. The ultimate goal is to conduct a parametric study of S-duct inlets to quantify the effects of inlet design parameters on the acoustic signature. The key challenge is that the effects of distortion transfer, noise source generation and propagation through the non-uniform flow field are inherently coupled such that a simultaneous computation of the aerodynamics and acoustics is required to capture the mechanisms at play. The technical approach is based on a body force description of the fan blade row that is able to capture the distortion transfer and the blade-to-blade flow variations that cause the MPT noise while reducing computational cost. A single, 3-D full-wheel CFD simulation, in which the Euler equations are solved to second-order spatial and temporal accuracy, simultaneously computes the MPT noise generation and its propagation in distorted inlet flow. A new method of producing the blade-to-blade variations in the body force field for MPT noise generation has been developed and validated. The numerical dissipation inherent to the solver is quantified and used to correct for non-physical attenuation in the far-field noise spectra. Source generation, acoustic propagation and acoustic energy transfer between modes is examined in detail. The new method is validated on NASA's Source Diagnostic Test fan and inlet, showing good agreement with experimental data for aerodynamic performance, acoustic source generation, and far-field noise spectra. The next steps involve the assessment of MPT noise in serpentine inlet ducts and the development of a reduced order formulation suitable for incorporation into NASA's ANOPP framework. © 2010 by Jeff Defoe, Alex Narkaj & Zoltan Spakovszky.

Structural analysis of plate-type fuel assemblies and development of a non-destructive method to assess their integrity

This work is concerned with the structural behaviour and the integrity of parallel plate-type nuclear fuel assemblies. A plate-type assembly consists of several thin plates mounted in a box-like structure and is subjected to a coolant flow that can result in a considerable drag force. A finite element model of an assembly is presented to study the sensitivity of the natural frequencies to the stiffness of the plates' junctions. It is shown that the shift in the natural frequencies of the torsional modes can be used to check the global integrity of the fuel assembly while the local natural frequencies of the inner plates can be used to estimate the maximum drag force they can resist. Finally a non-destructive method is developed to assess the resistance of the inner plates to bear an applied load. Extensive computational and experimental results are presented to prove the applicability of the method presented. © 2013 Elsevier B.V. All rights reserved.

Sulfonated poly(ether ether ketone)/aminopropyltriethoxysilane/phosphotungstic acid hybrid membranes with non-covalent bond: Characterization, thermal stability, and proton conductivity

Sulfonated poly(ether ether ketone) (SPEEK) and aminopropyltriethoxysilane (KH550) hybrid membranes doped with different weight ratio of phosphotungstic acid (PWA) were prepared by the casting procedure, as well as PWA as a catalyst for sol-gel process of KH550. The chemical structures of hybrid membranes were characterized by energy dispersive X-ray spectrometry (EDX) and Fourier transform infrared spectroscopy (FTIR). The morphology of hybrid membranes was investigated by scanning electron microscopy (SEM) and atomic force microscopy (AFM). The results had proved the uniform and homogeneous distribution of KH550 and PWA in these hybrid membranes.

Length dependence of electron conduction for oligo(1,4-phenylene ethynylene)s: A conductive probe-atomic force microscopy investigation

The dependence of electron conduction of oligo(1,4-phenylene ethynylene)s (OPEs) on length, terminal group, and main chain structure was examined by conductive probe-atomic force microscopy (CP-AFM) via a metal substrate-molecular wire monolayer-conductive probe junction. The electron transport in the molecular junction was a highest occupied molecule orbital (HOMO)-mediated process following a coherent, non-resonant tunneling mechanism represented by the Simmons equation.

Atomic force microscopy imaging of molybdenum oxide film electrodeposited on a carbon electrode

Non-stoichiometric mixed-valent molybdenum(VI, V) oxide film was grown on carbon substrates by the electrodeposition method. Responses of the prepared molybdenum oxide thin films to potential and to different solution acidities were studied by cyclic voltammetry, and the corresponding morphological changes of the film were monitored by atomic force microscopy (AFM). AFM images of the molybdenum oxide film show that the characteristic domed structure on the film surface increased during the transition from the oxidized state to the reduced state without signification change in the KMS surface roughness value. Furthermore, AFM studies show that the solution acidity has great effect on the morphology of the films, and the films undergo a homogenizing process with increasing pH of the solutions. (C) 1999 Elsevier Science S.A. All rights reserved.

Is inorganic nutrient enrichment a driving force for the formation of red tides? A case study of the dinoflagellate Scrippsiella trochoidea in an embayment

Red tides (high biomass phytoplankton blooms) have frequently occurred in Hong Kong waters, but most red tides occurred in waters which are not very eutrophic. For example, Port Shelter, a semi-enclosed bay in the northeast of Hong Kong, is one of hot spots for red tides. Concentrations of ambient inorganic nutrients (e.g. N, P), are not high enough to form the high biomass of chlorophyll a (chl a) in a red tide when chl a is converted to its particulate organic nutrient (N) (which should equal the inorganic nutrient, N). When a red tide of the dinoflagellate Scrippsiella trochoidea occurred in the bay, we found that the red tide patch along the shore had a high cell density of 15,000 cells ml(-1), and high chl a (56 mu g l(-1)), and pH reached 8.6 at the surface (8.2 at the bottom), indicating active photosynthesis in situ. Ambient inorganic nutrients (NO3, PO4, SiO4, and NH4) were all low in the waters and deep waters surrounding the red tide patch, suggesting that the nutrients were not high enough to support the high chl a >50 mu g l(-1) in the red tide. Nutrient addition experiments showed that the addition of all of the inorganic nutrients to a non-red-tide water sample containing low concentrations of Scrippsiella trochoidea did not produce cell density of Scrippsiella trochoidea as high as in the red tide patch, suggesting that nutrients were not an initializing factor for this red tide. During the incubation of the red tide water sample without any nutrient addition, the phytoplankton biomass decreased gradually over 9 days. However, with a N addition, the phytoplankton biomass increased steadily until day 7, which suggested that nitrogen addition was able to sustain the high biomass of the red tide for a week with and without nutrients. In contrast, the red tide in the bay disappeared on the sampling day when the wind direction changed. These results indicated that initiation, maintenance and disappearance of the dinoflagellate Scrippsiella trochoidea red tide in the bay were not directly driven by changes in nutrients. Therefore, how nutrients are linked to the formation of red tides in coastal waters need to be further examined, particularly in relation to dissolved organic nutrients. (C) 2008 Elsevier B.V. All rights reserved.

The Synthesis of Stable Force-Closure Grasps

This thesis addresses the problem of synthesizing grasps that are force-closure and stable. The synthesis of force-closure grasps constructs independent regions of contact for the fingertips, such that the motion of the grasped object is totally constrained. The synthesis of stable grasps constructs virtual springs at the contacts, such that the grasped object is stable, and has a desired stiffness matrix about its stable equilibrium. A grasp on an object is force-closure if and only if we can exert, through the set of contacts, arbitrary forces and moments on the object. So force-closure implies equilibrium exists because zero forces and moment is spanned. In the reverse direction, we prove that a non-marginal equilibrium grasp is also a force-closure grasp, if it has at least two point contacts with friction in 2D, or two soft-finger contacts or three hard-finger contacts in 3D. Next, we prove that all force-closure grasps can be made stable, by using either active or passive springs at the contacts. The thesis develops a simple relation between the stability and stiffness of the grasp and the spatial configuration of the virtual springs at the contacts. The stiffness of the grasp depends also on whether the points of contact stick, or slide without friction on straight or curved surfaces of the object. The thesis presents fast and simple algorithms for directly constructing stable fore-closure grasps based on the shape of the grasped object. The formal framework of force-closure and stable grasps provides a partial explanation to why we stably grasp objects to easily, and to why our fingers are better soft than hard.

Statistical Properties of Single and Competing Non-Linear Fast-Slow Oscillators in Noise

Statistical properties offast-slow Ellias-Grossberg oscillators are studied in response to deterministic and noisy inputs. Oscillatory responses remain stable in noise due to the slow inhibitory variable, which establishes an adaptation level that centers the oscillatory responses of the fast excitatory variable to deterministic and noisy inputs. Competitive interactions between oscillators improve the stability in noise. Although individual oscillation amplitudes decrease with input amplitude, the average to'tal activity increases with input amplitude, thereby suggesting that oscillator output is evaluated by a slow process at downstream network sites.

Emergence of Tri-Phasic Muscle Activation from the Non-linear Interactions of Central and Spinal Neural Network Circuits

The origin of the tri-phasic burst pattern, observed in the EMGs of opponent muscles during rapid self-terminated movements, has been controversial. Here we show by computer simulation that the pattern emerges from interactions between a central neural trajectory controller (VITE circuit) and a peripheral neuromuscularforce controller (FLETE circuit). Both neural models have been derived from simple functional constraints that have led to principled explanations of a wide variety of behavioral and neurobiological data, including, as shown here, the generation of tri-phasic bursts.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Using ground reaction force to predict knee kinetic asymmetry following anterior cruciate ligament reconstruction.

Asymmetries in sagittal plane knee kinetics have been identified as a risk factor for anterior cruciate ligament (ACL) re-injury. Clinical tools are needed to identify the asymmetries. This study examined the relationships between knee kinetic asymmetries and ground reaction force (GRF) asymmetries during athletic tasks in adolescent patients following ACL reconstruction (ACL-R). Kinematic and GRF data were collected during a stop-jump task and a side-cutting task for 23 patients. Asymmetry indices between the surgical and non-surgical limbs were calculated for GRF and knee kinetic variables. For the stop-jump task, knee kinetics asymmetry indices were correlated with all GRF asymmetry indices (P < 0.05), except for loading rate. Vertical GRF impulse asymmetry index predicted peak knee moment, average knee moment, and knee work (R(2)  ≥ 0.78, P < 0.01) asymmetry indices. For the side-cutting tasks, knee kinetic asymmetry indices were correlated with the peak propulsion vertical GRF and vertical GRF impulse asymmetry indices (P < 0.05). Vertical GRF impulse asymmetry index predicted peak knee moment, average knee moment, and knee work (R(2)  ≥ 0.55, P < 0.01) asymmetry indices. The vertical GRF asymmetries may be a viable surrogate for knee kinetic asymmetries and therefore may assist in optimizing rehabilitation outcomes and minimizing re-injury rates.