Growth and physical properties of a new chiral open-framework crystal for NLO applications: Cesium hydrogen l-malate monohydrate

Cesium hydrogen l-malate monohydrate, CsH(C4H4O5)·H2O, is a new chiral open-framework semi-organic crystalline material with a second-harmonic generation efficiency one order of magnitude greater than KDP. Single crystals of this new material have been grown by the conventional slow cooling technique from aqueous solution. Grown crystals display both platy and prismatic morphologies depending on the imposed supersaturation. Hardness values measured using Vickers hardness indenter show considerable anisotropy. The resistivity behavior at room temperature and above, places the crystal between an ionic conductor and a dielectric. The single-crystal SHG efficiency estimated through Maker fringes experiment gives deff which is 4.24 times that of KDP. Single and multiple shot experiments performed on the grown crystals for the fundamental and second harmonic of pulsed Nd:YAG laser (1064 and 532 nm) show that it exhibits a high laser damage threshold which is a favorable property for nonlinear optical applications.

Rail power conditioner technology in Australian Heavy Haul Railway: A case study

Aurizon, Australia's largest freight railway operator, is investigating the use of Rail Power Conditioner (RPC) technology for load balancing, reactive power compensation and harmonic filtering. The new technology has the capability of replacing Static VAr Compensators (SVC) and Harmonic Filters, and is expected to have a significant impact on the overall costs of railway electrification. This paper presents the theoretical analysis of the real and reactive power flows in an RPC used to balance active powers in an existing V/V feeder station. This informed an RPC feasibility study undertaken at four existing Aurizon's feeder stations with V/V connected transformers.

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Nonlinear mode coupling of surface acoustic waves on an isotropic solid

The nonlinear mode coupling between two co-directional quasi-harmonic Rayleigh surface waves on an isotropic solid is analysed using the method of multiple scales. This procedure yields a system of six semi-linear hyperbolic partial differential equations with the same principal part governing the slow variations in the (complex) amplitudes of the two fundamental, the two second harmonic and the two combination frequency waves at the second stage of the perturbation expansion. A numerical solution of these equations for excitation by monochromatic signals at two arbitrary frequencies, indicates that there is a continuous transfer of energy back and forth among the fundamental, second harmonic and combination frequency waves due to mode coupling. The mode coupling tends to be more pronounced as the frequencies of the interacting waves approach each other.

Nonlinear surface acoustic waves on an isotropic solid

A systematic derivation of the approximate coupled amplitude equations governing the propagation of a quasi-monochromatic Rayleigh surface wave on an isotropic solid is presented, starting from the non-linear governing differential equations and the non-linear free-surface boundary conditions, using the method of mulitple scales. An explicit solution of these equations for a signalling problem is obtained in terms of hyperbolic functions. In the case of monochromatic excitation, it is shown that the second harmonic amplitude grows initially at the expense of the fundamental and that the amplitudes of the fundamental and second harmonic remain bounded for all time.

Rotational cut-off and anharmonicity effects on thermodynamic properties of gases at high temperatures

The exact expressions for the partition function (Q) and the coefficient of specific heat at constant volume (Cv) for a rotating-anharmonic oscillator molecule, including coupling and rotational cut-off, have been formulated and values of Q and Cv have been computed in the temperature range of 100 to 100,000 K for O2, N2 and H2 gases. The exact Q and Cv values are also compared with the corresponding rigid-rotator harmonic-oscillator (infinite rotational and vibrational levels) and rigid-rotator anharmonic-oscillator (infinite rotational levels) values. The rigid-rotator harmonic-oscillator approximation can be accepted for temperatures up to about 5000 K for O2 and N2. Beyond these temperatures the error in Cv will be significant, because of anharmonicity and rotational cut-off effects. For H2, the rigid-rotator harmonic-oscillator approximation becomes unacceptable even for temperatures as low as 2000 K.

Optimum design of Lanchester damper for a viscously damped single degree of freedom system by using minimum force transmissibility criterion

The problem of optimum design of a Lanchester damper for minimum force transmission from a viscously damped single degree of freedom system subjected to harmonic excitation is investigated. Explicit expressions are developed for determining the optimum absorber parameters. It is shown that for the particular case of the undamped single degree of freedom system the results reduce to the classical ones obtained by using the concept of a fixed point on the transmissibility curves.

A closed-form optimal tuning of mass dampers for one degree-of-freedom systems under rotating unbalance forcing

This paper is focused on the study of a vibrating system forced by a rotating unbalance and coupled to a tuned mass damper (TMD). The analysis of the dynamic response of the entire system is used to define the parameters of such device in order to achieve optimal damping properties. The inertial forcing due to the rotating unbalance depends quadratically on the forcing frequency and it leads to optimal tuning parameters that differ from classical values obtained for pure harmonic forcing. Analytical results demonstrate that frequency and damping ratios, as a function of the mass parameter, should be higher than classical optimal parameters. The analytical study is carried out for the undamped primary system, and numerically investigated for the damped primary system. We show that, for practical applications, proper TMD tuning allows to achieve a reduction in the steady-state response of about 20% with respect to the response achieved with a classically tuned damper. Copyright © 2015 by ASME.

Flight metabolic rate in the Glanville fritillary butterfly

Dispersal is a highly important life history trait. In fragmented landscapes the long-term persistence of populations depends on dispersal. Evolution of dispersal is affected by costs and benefits and these may differ between different landscapes. This results in differences in the strength and direction of natural selection on dispersal in fragmented landscapes. Dispersal has been shown to be a nonrandom process that is associated with traits such as flight ability in insects. This thesis examines genetic and physiological traits affecting dispersal in the Glanville fritillary butterfly (Melitaea cinxia). Flight metabolic rate is a repeatable trait representing flight ability. Unlike in many vertebrates, resting metabolic rate cannot be used as a surrogate of maximum metabolic rate as no strong correlation between the two was found in the Glanville fritillary. Resting and flight metabolic rate are affected by environmental variables, most notably temperature. However, only flight metabolic rate has a strong genetic component. Molecular variation in the much-studied candidate locus phosphoglucose isomerase (Pgi), which encodes the glycolytic enzyme PGI, has an effect on carbohydrate metabolism in flight. This effect is temperature dependent: in low to moderate temperatures individuals with the heterozygous genotype at the single nucleotide polymorphism (SNP) AA111 have higher flight metabolic rate than the common homozygous genotype. At high temperatures the situation is reversed. This finding suggests that variation in enzyme properties is indeed translated to organismal performance. High-resolution data on individual female Glanville fritillaries moving freely in the field were recorded using harmonic radar. There was a strong positive correlation between flight metabolic rate and dispersal rate. Flight metabolic rate explained one third of the observed variation in the one-hour movement distance. A fine-scaled analysis of mobility showed that mobility peaked at intermediate ambient temperatures but the two common Pgi genotypes differed in their reaction norms to temperature. As with flight metabolic rate, heterozygotes at SNP AA111 were the most active genotype in low to moderate temperatures. The results show that molecular variation is associated with variation in dispersal rate through the link of flight physiology under the influence of environmental conditions. The evolutionary pressures for dispersal differ between males and females. The effect of flight metabolic rate on dispersal was examined in both sexes in field and laboratory conditions. The relationship between flight metabolic rate and dispersal rate in the field and flight duration in the laboratory were found to differ between the two sexes. In females the relationship was positive, but in males the longest distances and flight durations were recorded for individuals with low flight metabolic rate. These findings may reflect male investment in mate locating. Instead of dispersing, males with high flight metabolic rate may establish territories and follow a perching strategy when locating females and hence move less on the landscape level. Males with low metabolic rate may be forced to disperse due to low competitive success or may show adaptations to an alternative strategy: patrolling. In the light of life history trade-offs and the rate of living theory having high metabolic rate may carry a cost in the form of shortened lifespan. Experiments relating flight metabolic rate to longevity showed a clear correlation in the opposite direction: high flight metabolic rate was associated with long lifespan. This suggests that individuals with high metabolic rate do not pay an extra physiological cost for their high flight capacity, rather there are positive correlations between different measures of fitness. These results highlight the importance of condition.

Semi-active vibration isolation using a near-zero-spring-rate device:steady state analysis of a single-degree-of-freedom model

A vibration isolator is described which incorporates a near-zero-spring-rate device within its operating range. The device is an assembly of a vertical spring in parallel with two inclined springs. A low spring rate is achieved by combining the equivalent stiffness in the vertical direction of the inclined springs with the stiffness of the vertical central spring. It is shown that there is a relation between the geometry and the stiffness of the individual springs that results in a low spring rate. Computer simulation studies of a single-degree-of-freedom model for harmonic base input show that the performance of the proposed scheme is superior to that of the passive schemes with linear springs and skyhook damping configuration. The response curves show that, for small to large amplitudes of base disturbance, the system goes into resonance at low frequencies of excitation. Thus, it is possible to achieve very good isolation over a wide low-frequency band. Also, the damper force requirements for the proposed scheme are much lower than for the damper force of a skyhook configuration or a conventional linear spring with a semi-active damper.

Complex solitons in Bose-Einstein condensates with two- and three-body interactions

For the first time, we find the complex solitons for a quasi-one-dimensional Bose-Einstein condensate with two-and three-body interactions. These localized solutions are characterized by a power law behaviour. Both dark and right solitons can be excited in the experimentally allowed parameter domain, when two-and three-body interactions are,respectively, repulsive and attractive. The dark solitons travel with a constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity, can exist for specified interaction strengths. We also study the properties of these solitons in the presence of harmonic confinement with time-dependent nonlinearity and loss. The modulational instability and the Vakhitov-Kolokolov criterion of stability are also studied.

Compact fiber Bragg grating dynamic strain sensor cum broadband thermometer for thermally unstable ambience

An instrument for simultaneous measurement of dynamic strain and temperature in a thermally unstable ambience has been proposed, based on fiber Bragg grating technology. The instrument can function as a compact and stand-alone broadband thermometer and a dynamic strain gauge. It employs a source wavelength tracking procedure for linear dependence of the output on the measurand, offering high dynamic range. Two schemes have been demonstrated with their relative merits. As a thermometer, the present instrumental configuration can offer a linear response in excess of 500 degrees C that can be easily extended by adding a suitable grating and source without any alteration in the procedure. Temperature sensitivity is about 0.06 degrees C for a bandwidth of 1 Hz. For the current grating, the upper limit of strain measurement is about 150 mu epsilon with a sensitivity of about 80 n epsilon Hz(-1/2). The major source of uncertainty associated with dynamic strain measurement is the laser source intensity noise, which is of broad spectral band. A low noise source device or the use of optical power regulators can offer improved performance. The total harmonic distortion is less than 0.5% up to about 50 mu epsilon, 1.2% at 100 mu epsilon and about 2.3% at 150 mu epsilon. Calibrated results of temperature and strain measurement with the instrument have been presented. Traces of ultrasound signals recorded by the system at 200 kHz, in an ambience of 100-200 degrees C temperature fluctuation, have been included. Also, the vibration spectrum and engine temperature of a running internal combustion engine has been recorded as a realistic application of the system.