Generalization of the JTZ model to open plane wakes

The JTZ model [C. Jung, T. T¶el and E. Ziemniak, Chaos 3, (1993) 555], as a theoretical model of a plane wake behind a circular cylinder in a narrow channel at a moderate Reynolds number, has previously been employed to analyze phenomena of chaotic scattering. It is ex- tended here to describe an open plane wake without the con¯ned nar- row channel by incorporating a double row of shedding vortices into the intermediate and far wake. The extended JTZ model is found in qualitative agreement with both direct numerical simulations and ex- perimental results in describing streamlines and vorticity contours. To further validate its applications to particle transport processes, the in- teraction between small spherical particles and vortices in an extended JTZ model °ow is studied. It is shown that the particle size has signif- icant in°uences on the features of particle trajectories, which have two characteristic patterns: one is rotating around the vortex centers and the other accumulating in the exterior of vortices. Numerical results based on the extended JTZ model are found in qualitative agreement with experimental ones in the normal range of particle sizes.

Invariants, Lie-Bäcklund operators and Bäcklund transformations

This thesis is mainly concerned with the application of groups of transformations to differential equations and in particular with the connection between the group structure of a given equation and the existence of exact solutions and conservation laws. In this respect the Lie-Bäcklund groups of tangent transformations, particular cases of which are the Lie tangent and the Lie point groups, are extensively used.

In Chapter I we first review the classical results of Lie, Bäcklund and Bianchi as well as the more recent ones due mainly to Ovsjannikov. We then concentrate on the Lie-Bäcklund groups (or more precisely on the corresponding Lie-Bäcklund operators), as introduced by Ibragimov and Anderson, and prove some lemmas about them which are useful for the following chapters. Finally we introduce the concept of a conditionally admissible operator (as opposed to an admissible one) and show how this can be used to generate exact solutions.

In Chapter II we establish the group nature of all separable solutions and conserved quantities in classical mechanics by analyzing the group structure of the Hamilton-Jacobi equation. It is shown that consideration of only Lie point groups is insufficient. For this purpose a special type of Lie-Bäcklund groups, those equivalent to Lie tangent groups, is used. It is also shown how these generalized groups induce Lie point groups on Hamilton's equations. The generalization of the above results to any first order equation, where the dependent variable does not appear explicitly, is obvious. In the second part of this chapter we investigate admissible operators (or equivalently constants of motion) of the Hamilton-Jacobi equation with polynornial dependence on the momenta. The form of the most general constant of motion linear, quadratic and cubic in the momenta is explicitly found. Emphasis is given to the quadratic case, where the particular case of a fixed (say zero) energy state is also considered; it is shown that in the latter case additional symmetries may appear. Finally, some potentials of physical interest admitting higher symmetries are considered. These include potentials due to two centers and limiting cases thereof. The most general two-center potential admitting a quadratic constant of motion is obtained, as well as the corresponding invariant. Also some new cubic invariants are found.

In Chapter III we first establish the group nature of all separable solutions of any linear, homogeneous equation. We then concentrate on the Schrodinger equation and look for an algorithm which generates a quantum invariant from a classical one. The problem of an isomorphism between functions in classical observables and quantum observables is studied concretely and constructively. For functions at most quadratic in the momenta an isomorphism is possible which agrees with Weyl' s transform and which takes invariants into invariants. It is not possible to extend the isomorphism indefinitely. The requirement that an invariant goes into an invariant may necessitate variants of Weyl' s transform. This is illustrated for the case of cubic invariants. Finally, the case of a specific value of energy is considered; in this case Weyl's transform does not yield an isomorphism even for the quadratic case. However, for this case a correspondence mapping a classical invariant to a quantum orie is explicitly found.

Chapters IV and V are concerned with the general group structure of evolution equations. In Chapter IV we establish a one to one correspondence between admissible Lie-Bäcklund operators of evolution equations (derivable from a variational principle) and conservation laws of these equations. This correspondence takes the form of a simple algorithm.

In Chapter V we first establish the group nature of all Bäcklund transformations (BT) by proving that any solution generated by a BT is invariant under the action of some conditionally admissible operator. We then use an algorithm based on invariance criteria to rederive many known BT and to derive some new ones. Finally, we propose a generalization of BT which, among other advantages, clarifies the connection between the wave-train solution and a BT in the sense that, a BT may be thought of as a variation of parameters of some. special case of the wave-train solution (usually the solitary wave one). Some open problems are indicated.

Most of the material of Chapters II and III is contained in [I], [II], [III] and [IV] and the first part of Chapter V in [V].

Group velocity of probe light pulse in an open lambda system

The group velocity of the probe light pulse (GVPLP) propagating through an open Lambda-type atomic system with a spontaneously generated coherence is investigated when the weak probe and strong driving light fields have different frequencies. It is found that adjusting the detuning or Rabi frequency of the probe light field can realize switching of the GVPLP from subluminal to superluminal. Changing the relative phase between the probe and driving light. elds or atomic exit and injection rates can lead to GVPLP varying in a wider range, but cannot induce transformation of the property of the GVPLP. The absolute value of the GVPLP always increases with Rabi frequency of the driving light field increasing. For subluminal and superluminal propagation, the system always exhibits the probe absorption, and GVPLP is mainly determined by the slope of the steep dispersion.

Lasing without or with inversion in an open four-level system with a phase-fluctuation driving field

The effect of exit rate and the ratio of atomic injection rate on gain behaviour has been investigated, and the effects of phase fluctuation on absorption, dispersion and population difference in an open four-level system have been analysed by using numerical simulation from the steady linear, analytical solution. The variation of the linewidth, Rabi frequency of the driving field, the exit rate or the ratio of atomic injection rate can change the lasing properties in the open system. The presence of finite linewidth due to driving-field phase fluctuation prevents the open four-level atomic system from obtaining a high refractive index along with zero absorption.

Wire array photovoltaics

Over the past five years, the cost of solar panels has dropped drastically and, in concert, the number of installed modules has risen exponentially. However, solar electricity is still more than twice as expensive as electricity from a natural gas plant. Fortunately, wire array solar cells have emerged as a promising technology for further lowering the cost of solar.

Si wire array solar cells are formed with a unique, low cost growth method and use 100 times less material than conventional Si cells. The wires can be embedded in a transparent, flexible polymer to create a free-standing array that can be rolled up for easy installation in a variety of form factors. Furthermore, by incorporating multijunctions into the wire morphology, higher efficiencies can be achieved while taking advantage of the unique defect relaxation pathways afforded by the 3D wire geometry.

The work in this thesis shepherded Si wires from undoped arrays to flexible, functional large area devices and laid the groundwork for multijunction wire array cells. Fabrication techniques were developed to turn intrinsic Si wires into full p-n junctions and the wires were passivated with a-Si:H and a-SiNx:H. Single wire devices yielded open circuit voltages of 600 mV and efficiencies of 9%. The arrays were then embedded in a polymer and contacted with a transparent, flexible, Ni nanoparticle and Ag nanowire top contact. The contact connected >99% of the wires in parallel and yielded flexible, substrate free solar cells featuring hundreds of thousands of wires.

Building on the success of the Si wire arrays, GaP was epitaxially grown on the material to create heterostructures for photoelectrochemistry. These cells were limited by low absorption in the GaP due to its indirect bandgap, and poor current collection due to a diffusion length of only 80 nm. However, GaAsP on SiGe offers a superior combination of materials, and wire architectures based on these semiconductors were investigated for multijunction arrays. These devices offer potential efficiencies of 34%, as demonstrated through an analytical model and optoelectronic simulations. SiGe and Ge wires were fabricated via chemical-vapor deposition and reactive ion etching. GaAs was then grown on these substrates at the National Renewable Energy Lab and yielded ns lifetime components, as required for achieving high efficiency devices.

Control of wettability of carbon nanotube array by reversible dry oxidation for superhydrophobic coating and supercapacitor applications

In this thesis, dry chemical modification methods involving UV/ozone, oxygen plasma, and vacuum annealing treatments are explored to precisely control the wettability of CNT arrays. By varying the exposure time of these treatments the surface concentration of oxygenated groups adsorbed on the CNT arrays can be controlled. CNT arrays with very low amount of oxygenated groups exhibit a superhydrophobic behavior. In addition to their extremely high static contact angle, they cannot be dispersed in DI water and their impedance in aqueous electrolytes is extremely high. These arrays have an extreme water repellency capability such that a water droplet will bounce off of their surface upon impact and a thin film of air is formed on their surface as they are immersed in a deep pool of water. In contrast, CNT arrays with very high surface concentration of oxygenated functional groups exhibit an extreme hydrophilic behavior. In addition to their extremely low static contact angle, they can be dispersed easily in DI water and their impedance in aqueous electrolytes is tremendously low. Since the bulk structure of the CNT arrays are preserved during the UV/ozone, oxygen plasma, and vacuum annealing treatments, all CNT arrays can be repeatedly switched between superhydrophilic and superhydrophobic, as long as their O/C ratio is kept below 18%.

The effect of oxidation using UV/ozone and oxygen plasma treatments is highly reversible as long as the O/C ratio of the CNT arrays is kept below 18%. At O/C ratios higher than 18%, the effect of oxidation is no longer reversible. This irreversible oxidation is caused by irreversible changes to the CNT atomic structure during the oxidation process. During the oxidation process, CNT arrays undergo three different processes. For CNT arrays with O/C ratios lower than 40%, the oxidation process results in the functionalization of CNT outer walls by oxygenated groups. Although this functionalization process introduces defects, vacancies and micropores opening, the graphitic structure of the CNT is still largely intact. For CNT arrays with O/C ratios between 40% and 45%, the oxidation process results in the etching of CNT outer walls. This etching process introduces large scale defects and holes that can be obviously seen under TEM at high magnification. Most of these holes are found to be several layers deep and, in some cases, a large portion of the CNT side walls are cut open. For CNT arrays with O/C ratios higher than 45%, the oxidation process results in the exfoliation of the CNT walls and amorphization of the remaining CNT structure. This amorphization process can be implied from the disappearance of C-C sp2 peak in the XPS spectra associated with the pi-bond network.

The impact behavior of water droplet impinging on superhydrophobic CNT arrays in a low viscosity regime is investigated for the first time. Here, the experimental data are presented in the form of several important impact behavior characteristics including critical Weber number, volume ratio, restitution coefficient, and maximum spreading diameter. As observed experimentally, three different impact regimes are identified while another impact regime is proposed. These regimes are partitioned by three critical Weber numbers, two of which are experimentally observed. The volume ratio between the primary and the secondary droplets is found to decrease with the increase of Weber number in all impact regimes other than the first one. In the first impact regime, this is found to be independent of Weber number since the droplet remains intact during and subsequent to the impingement. Experimental data show that the coefficient of restitution decreases with the increase of Weber number in all impact regimes. The rate of decrease of the coefficient of restitution in the high Weber number regime is found to be higher than that in the low and moderate Weber number. Experimental data also show that the maximum spreading factor increases with the increase of Weber number in all impact regimes. The rate of increase of the maximum spreading factor in the high Weber number regime is found to be higher than that in the low and moderate Weber number. Phenomenological approximations and interpretations of the experimental data, as well as brief comparisons to the previously proposed scaling laws, are shown here.

Dry oxidation methods are used for the first time to characterize the influence of oxidation on the capacitive behavior of CNT array EDLCs. The capacitive behavior of CNT array EDLCs can be tailored by varying their oxygen content, represented by their O/C ratio. The specific capacitance of these CNT arrays increases with the increase of their oxygen content in both KOH and Et4NBF4/PC electrolytes. As a result, their gravimetric energy density increases with the increase of their oxygen content. However, their gravimetric power density decreases with the increase of their oxygen content. The optimally oxidized CNT arrays are able to withstand more than 35,000 charge/discharge cycles in Et4NBF4/PC at a current density of 5 A/g while only losing 10% of their original capacitance.

A measurement of the proton elastic form factors for 1 ≤ Q^2 ≤ 3 (GeV/c)^2

We report measurements of the proton form factors, G^p_E and G^p_M, extracted from elastic electron scattering in the range 1 ≤ Q^2 ≤ 3 (GeV/c)^2 with uncertainties of <15% in G^p_E and <3% in G^p_M. The results for G^p_E are somewhat larger than indicated by most theoretical parameterizations. The ratio of Pauli and Dirac form factors, Q^2(F^p_2/F^p_1), is lower in value and demonstrates less Q^2 dependence than these parameterizations have indicated. Comparisons are made to theoretical models, including those based on perturbative QCD, vector-meson dominance, QCD sum rules, and diquark constituents to the proton. A global extraction of the form factors, including previous elastic scattering measurements, is also presented.

Phase control of gain and dispersion in an open lambda-type inversionless lasing system

The control role of the relative phase between the probe and driving fields on the gain and dispersion in an open Lambda-type inversionless lasing system with spontaneously generated coherence (SGC) is investigated. It is shown that the inversionless gain and dispersion are quite sensitive to variation in the relative phase; by adjusting the value of the relative phase, electromagnetically induced transparency (EIT), a high refractive index with zero absorption and a larger inversionless gain can be realized. It is also shown that, in the contributions to the inversionless gain ( absorption) and dispersion, the contribution from SGC is always much larger than that from the dynamically induced coherence for any value of the relative phase. Our analysis shows that variation in the SGC effect will cause the spectrum regions and values of the inversionless gain and dispersion to vary evidently. We also found that, under the same conditions, the values of the inversionless gain and dispersion in the open system are evidently larger than those in the corresponding closed system; EIT occurs in the open system but cannot occur in the closed system.

Designing conformational control of human tissue transglutaminase

Understanding the mechanisms of enzymes is crucial for our understanding of their role in biology and for designing methods to perturb or harness their activities for medical treatments, industrial processes, or biological engineering. One aspect of enzymes that makes them difficult to fully understand is that they are in constant motion, and these motions and the conformations adopted throughout these transitions often play a role in their function.

Traditionally, it has been difficult to isolate a protein in a particular conformation to determine what role each form plays in the reaction or biology of that enzyme. A new technology, computational protein design, makes the isolation of various conformations possible, and therefore is an extremely powerful tool in enabling a fuller understanding of the role a protein conformation plays in various biological processes.

One such protein that undergoes large structural shifts during different activities is human type II transglutaminase (TG2). TG2 is an enzyme that exists in two dramatically different conformational states: (1) an open, extended form, which is adopted upon the binding of calcium, and (2) a closed, compact form, which is adopted upon the binding of GTP or GDP. TG2 possess two separate active sites, each with a radically different activity. This open, calcium-bound form of TG2 is believed to act as a transglutaminse, where it catalyzes the formation of an isopeptide bond between the sidechain of a peptide-bound glutamine and a primary amine. The closed, GTP-bound conformation is believed to act as a GTPase. TG2 is also implicated in a variety of biological and pathological processes.

To better understand the effects of TG2’s conformations on its activities and pathological processes, we set out to design variants of TG2 isolated in either the closed or open conformations. We were able to design open-locked and closed-biased TG2 variants, and use these designs to unseat the current understanding of the activities and their concurrent conformations of TG2 and explore each conformation’s role in celiac disease models. This work also enabled us to help explain older confusing results in regards to this enzyme and its activities. The new model for TG2 activity has immense implications for our understanding of its functional capabilities in various environments, and for our ability to understand which conformations need to be inhibited in the design of new drugs for diseases in which TG2’s activities are believed to elicit pathological effects.

Phase control of gain and dispersion in an open V-type system

The control role of the relative phase between the probe and driving fields on gain, dispersion and populations in an open V-type three-level system with spontaneously generated coherence is studied. The result shows that by adjusting the value of the relative phase, the transformation between lasing with inversion and lasing without inversion (LWI) can be realized and high dispersion (refractive index) without absorption can be obtained. The shape and value range of the dispersion curve are similar to those of the gain curve, and this similarity is closely related to the relative phase. The effects of the atomic exit and injection rates and the incoherent pump rate on the control role of the relative phase are also analysed. It is found easier to get LWI by adjusting the value of the relative phase using the open system rather than the closed system, and using an incoherent pump rather than without using the incoherent pump. Moreover the open system can give a larger LWI gain than the closed system.

The basque ecological debt: global socioecological impacts of a small open economy

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Effects of relative phase in an open ladder system without incoherent pumping

We studied effects of the relative phase between the probe and driving fields on the absorption and dispersion properties in an open three-level ladder system with spontaneously generated coherence but without incoherent pumping. It is shown that by the phase controlling, switching from absorption to lasing without inversion (LWI) and enhancing remarkablely LWI gain can be realized; large index of refraction with zero absorption and the electromagnetically induced transparency can be obtained. We also find that varying the atomic injection and exit rates has a considerable influence on the phase dependent-absorption property of the probe field, existent of the atomic injection and exit rates gives the necessary condition of the realization of LWI, getting LWI is impossible in the corresponding closed system without incoherent pumping. We studied effects of the relative phase between the probe and driving fields on the absorption and dispersion properties in an open three-level ladder system with spontaneously generated coherence but without incoherent pumping. It is shown that by the phase controlling, switching from absorption to lasing without inversion (LWI) and enhancing remarkablely LWI gain can be realized; large index of refraction with zero absorption and the electromagnetically induced transparency can be obtained. We also find that varying the atomic injection and exit rates has a considerable influence on the phase dependent-absorption property of the probe field, existent of the atomic injection and exit rates gives the necessary condition of the realization of LWI, getting LWI is impossible in the corresponding closed system without incoherent pumping.