The work is centered on the study of dimensionally reduced vector effective field theories from the point of view of soft scalar limits using the spinor-helicity formalism. The Dirac-Born-Infeld model is singled out by its enhanced soft limit at the level of four and six-point amplitudes. In the process, the spinor-helicity formalism is outlined and its use illustrated on explicit examples. The remainder of the work is focused on the corresponding questions in six dimensions. The rel- evant version of spinor-helicity formalism is presented, followed by a discussion of little group invariants and of the (im)possibility of their use on characteriza- tion of theories. Lastly, attempts at formalizing the process of taking the soft limit are made, with inspiration from the four-dimensional case. 1

This thesis presents an improved feedback system on HBT-EP and suppression of the fast rotating kink mode using this system. HBT-EP is an experimental tokamak at Columbia University designed to study the magnetohydrodynamic (MHD) instabilities in confined fusion. The most damaging instabilities are global long wavelength kink modes, which break the toroidal symmetry of the magnetic structure and lead to plasma disruption and termination. When a tokamak is surrounded by a close fitting conducting wall, then the single helicity linear dispersion relation of the kink instability has two ominating branches: one is the "slow mode", rotating at the time scale of wall time, known as resistive wall mode (RWM), the other is the fast mode, that becomes unstable near the ideal wall stability limit. Both instabilities are required to be controlled by the feedback system in HBT-EP. In this thesis, improvements have been made upon the previous GPU-based system to enhance the feedback performance and obtain clear evidence of the feedback suppression effect. Specifically, a new algorithm is implemented that maintains an accurate phase shift between the applied perturbation and the unstable mode. This prevents the excitation of the slow kink mode observed in previous studies and results in high gain suppression for fast mode control at all frequency for the first time. When the system is turned off, suppression is lost and the fast mode is observed to grow back. The feedback performance is tested with several wall configurations including the presence of ferritic material. This provides the first comparison of feedback control between the ferritic and stainless wall. The effect of plasma rotation on feedback control is tested by applying a static voltage on a bias probe. As the mode rotation being slowed by the radial current flow, a higher gain on the kink mode is required to achieve feedback suppression. The change in plasma rotation also modifies the plasma response to the external perturbation. The optimal phase shift for suppression changes with the modified response and these observations are consistent with the predictions of the single helicity model.

Intrinsically disordered proteins (IDPs) do not form stable tertiary structures like their ordered partners. They exist as heterogeneous ensembles that fluctuate over a time scale. Intrinsically disordered regions and proteins are found across different phyla and exert crucial biological functions. They exhibit transient secondary structures in their free state and become folded upon binding to their protein partners via a mechanism called coupled folding and binding. Some IDPs form alpha helices when bound to their protein partners. We observed a set of cancer associated IDPs where the helical binding segments of IDPs are flanked by prolines on both the sides. Helix-breaking prolines are frequently found in IDPs flanking the binding segment and are evolutionarily conserved across phyla. Two studies have shown that helix flanking prolines modulate the function of IDPs by regulating the levels of disorder in their free state and in turn regulating the binding affinities to their partners. We aimed to study if this is a common phenomenon in IDPs that exhibit similar pattern in the conservation of helix flanking prolines. We chose to test the hypothesis in c-Myb-KIX : IDP-target system in which the disordered protein exhibits high residual helicity levels in its free state. c-Myb is a hematopoietic regulator that plays a crucial role in cancer by binding to the KIX domain of CBP. Studying the functional regulation of c-Myb by modulating the disorder levels in c-Myb and in IDPs in general provides a better understanding of the way IDPs function and can be used in therapeutic strategies as IDPs are known to be involved in regulating various cellular processes and diseases. To study the effect of conserved helix flanking prolines on the residual helicity levels of c-Myb and its binding affinity to the KIX domain of CBP, we mutated the prolines to alanines. Mutating prolines to alanines increased the helicity levels of c-Myb in its free state. This small increase in the helicity levels of a highly helical c-Myb showed almost no effect on the binding affinity between cMyb and KIX. We hypothesized that there is a helical threshold for coupled folding and binding beyond which helicity levels of the free state IDP have no effect on its binding to their ordered protein partner. To test this hypothesis, we mutated solvent exposed amino acid residues in c-Myb that reduce its overall helicity and studied its effect on the binding affinity between c-Myb and KIX. Over a broad range of reduction in helicity levels of the free state did not show an effect on the binding affinity but beyond a certain level, decrease in helicity levels showed pronounced effects on the binding affinity between c-Myb and KIX.

Die Frage nach der Herkunft und der dynamischen Entwicklung langlebiger kosmischer Magnetfelder ist in vielen Details noch unbeantwortet. Es besteht zwar kein Zweifel daran, dass das Magnetfeld der Erde und anderer kosmischer Objekte durch den sogenannten Dynamoeffekt verursacht werden, der genaue Mechanismus als auch die notwendigen Voraussetzungen und Randbedingungen der zugrundeliegenden Strömungen sind aber weitgehend unbekannt. Die für einen Dynamo interessanten Strömungsmuster, die im Inneren von Himmelskörpern durch Konvektion und differentielle Rotation entstehen, sind Konvektionsrollen parallel zur Rotationsachse. Auf einer Strömung mit eben solcher Geometrie, der sogenannten Roberts-Strömung, basieren die in der vorliegenden Arbeit untersuchten Dynamomodelle. Mit Methoden der nichtlinearen Dynamik wird versucht, das Systemverhalten bei Änderung der Systemparamter genauer zu charakterisieren. Die numerischen Untersuchungen beginnen mit einer Analyse der Dynamoaktivität der Roberts-Strömung in Abhängigkeit von den zwei freien Parametern in den Modellgleichungen, der magnetischen Prandtl-Zahl und der Stärke des Energieinputs. Gefunden werden verschiedene Lösungstypen die von einem stationären Magnetfeld über periodische bis zu chaotischen Zuständen reichen. Die yugrundeliegenden Symmetrien werden beschrieben und die Bifurkationen, die zum Wechsel der Lösungstypen führen, charakterisiert. Zusätzlich gibt es Bereiche bei sehr kleinen Prandtl-Zahlen, in denen überhaupt kein Dynamo existiert. Dieses Verhalten wird in der Literatur auch für viele andere numerisch ausgewertete Modelle beschrieben. Im Übergangsbereich zwischen dynamoaktivem und dynamoinaktivem Bereich wird das Auftreten einer sogenannten Blowout-Bifurkation gefunden. Desweiteren beschäftigt sich die Arbeit mit der Frage, inwiefern Helizität, also eine schraubenförmige Bewegung, der Strömung den Dynamoeffekt beeinflusst. Dazu werden ähnliche Strömungstypen verglichen, die sich hauptsächlich in ihrem Helizitätswert unterscheiden. Es wird gefunden, dass ein bestimmter Wert der Helizität nicht unterschritten werden darf, um einen stabilen Roberts-Dynamo zu erhalten. / The question of origin and development of longlasting cosmic magnetic fields is in many details an unanswered question. There is no doubt that the magnetic fields of cosmic objects like the earth, the sun and larger structures are caused by the so called dynamo effect. The exact mechanism as well as the necassary properties and boundary conditions for the underlying flow field are mostly unknown. The flow pattern believed to act as the source of dynamo activity in the inner of cosmic bodies are convection-like rolls parallel to the rotation axis of this objects and are results of the acting body forces due to differential rotation and thermal convection. The basis of the considered dynamo model is a flow field revealing such flow structures, the so called Roberts flow. The numerical investigations start with an analysis of dynamo activity of the Roberts flow in dependence on the two free parameters magnetic Prandtl number and forcing strength. The model shows different types of solutions starting from steady magnetic states in a very small parameter region at larger magnetic Prandtl numbers, time-periodic solutions and chaotic behavior for stronger forcing. For small magnetic Prandtl numbers the system doesn't carry any magnetic field. This 'small Prandtl number problem' is in accordance with the behavior of several other numerically investigated dynamo models described in the literature. The transient region between dynamo activity and the non-magnetic states can be classified by a so-called blowout bifurcation. Furthermore the investigation deals with the question in what way the helical structure of the flow field indicated by a non-vanishing kinetic helicity influences the dynamo process. The comparison of very similar flow families, mainly distinguishable by their different helicity values, leads to the result that beneath a lower bound no stable Roberts dynamo is working.

abstract: The nucleon resonance spectrum consists of many overlapping excitations. Polarization observables are an important tool for understanding and clarifying these spectra. While there is a large data base of differential cross sections for the process, very few data exist for polarization observables. A program of double polarization experiments has been conducted at Jefferson Lab using a tagged polarized photon beam and a frozen spin polarized target (FROST). The results presented here were taken during the first running period of FROST using the CLAS detector at Jefferson Lab with photon energies ranging from 329 MeV to 2.35 GeV. Data are presented for the E polarization observable for eta meson photoproduction on the proton from threshold (W=1500 MeV) to W=1900 MeV. Comparisons to the partial wave analyses of SAID and Bonn-Gatchina along with the isobar analysis of eta-MAID are made. These results will help distinguish between current theoretical predictions and refine future theories. / Dissertation/Thesis / Ph.D. Physics 2011

Pure Yang-Mills amplitudes with all external gluons carrying positive helicity, known as all-plus amplitudes, have an especially simple structure. The tree amplitudes vanish and, up to at least two loops, the loop-level amplitudes are related to those of N = 4 super-Yang-Mills (SYM) theory. This makes all-plus amplitudes a useful testing ground for new methods of simplifing more general classes of amplitudes. In this thesis we consider three new approaches, focusing on the structure before integration. We begin with the planar (leading-colour) sector. A D-dimensional local-integrand presentation, based on four-dimensional local integrands developed for N = 4 SYM, is developed. This allows us to compute the planar six-gluon, two-loop all-plus amplitude. Its soft structure is understood before integration, and we also perform checks on collinear limits. We then proceed to consider subleading-colour structures. A multi-peripheral colour decomposition is used to find colour factors based on underlying tree-level amplitudes via generalised unitarity cuts. This allows us to find the integrand of the full-colour, two-loop, five-gluon all-plus amplitude. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. Finally, we consider representations satisfying colour-kinematics duality. We discuss obstacles to finding such numerators in the context of the same five-gluon amplitude at two loops. The obstacles are overcome by adding loop momentum to our numerators to accommodate tension between the values of certain cuts and the symmetries of certain diagrams. Control over the size of our ansatz is maintained by identifying a highly constraining, but desirable, symmetry property of our master numerator.

This dissertation consists of two parts, connected by the overarching theme of the dynamics of structured waves with internal degrees of freedom. Part I concerns light, whose internal degree of freedom is polarisation. We investigate the helicity, or handedness of light, which is a good quantum number for massless fields in general and light in particular. In free space it is always possible to describe the light field in a basis left- and right handed helicity modes which are solutions of Maxwell's equations, regardless what spatial structure is chosen. This is useful for bases of highly inhomogeneous waves, such as Bessel waves, for which the spin cannot be unambiguously defined. In chapter 1 we study the conservation of helicity and the preservation of its underlying symmetry, electric-magnetic duality symmetry when light travels through inhomogeneous and/or anisotropic media. We will discuss some of the unique properties of duality symmetric media and reformulate Maxwell's equations in such a way that the decoupling of different helicities for duality symmetric media becomes apparent. The feasibility of constructing duality symmetric media is discussed at the end of the chapter. In chapter 2 we consider superpositions of plane electromagnetic waves in free space. Such superpositions typically interfere. We present superpositions of up to six plane waves which defy this expectation by having a perfectly homogeneous mean square of the electric field. Because most matter interacts much stronger with the electric than with the magnetic field, these superpositions can be considered noninterfering. Our superpositions show complex patterns in their helicity densities, of which we will show many examples. We study the effects on our helicity patterns of imperfections that may occur in a realistic experiment: deviations from the optimal amplitudes, phases and polarisations of the superposed waves, small misalignments and partially coherent light. Our superpositions can be used to write chiral patterns in light sensitive liquid crystals. Conversely, these liquid crystals can be used for an `optical helicity camera' which records spatial variations in helicity. In the final paragraph of chapter 2 we discuss some mathematical questions concerning noninterfering superpositions. Part II concerns electrons, whose internal degree of freedom is spin. In chapter 3 we will present analytical solutions of the Dirac equation for an electron vortex beam in a homogeneous magnetic field. Including spin from the beginning reveals that spin polarised electron vortex beams have a complicated azimuthal current structure, containing small rings of counterrotating current between rings of stronger corotating current. Contrary to many other problems in relativistic quantum mechanics, there exist vortex beam solutions with exactly zero spin-orbit mixing in the highly relativistic and nonparaxial regime. Chapter 4 treats the interaction between electron vortex states in a homogeneous magnetic field and light, where we expand and quantise the radiation field in a basis of Bessel modes with definite helicity. Our results apply for magnetic field strength beyond the critical field strength at which the spin contributes as much to the electron's energy as its rest mass. We are able to compute spin flip rates for low lying states, finding a much higher degree of equilibrium spin polarisation than approximations for high lying electron states suggested.

No description available.

Between 2011-2021, violent tornadoes accounted for an average of 65% of all tornado-related fatalities. The Violent Tornado Parameter (VTP), created in 2018, attempts to address this forecast problem but has issues with false alarms. Storm Relative Helicity has historically been used in tornado forecasting. Recent studies have shown the 0-500 m effective layer SRH (ESRH) has skill in discerning significantly tornadic events from those that are not. This study explored the effects of incorporating 0-500 m ESRH into the VTP and issues relating to the parameter’s false alarm rate by examining RUC/RAP forecast soundings for 302 U.S. tornadic events (83 violent, 122 strong, 97 weak) from 2011 to 2020, along with test data from 2021. Overall, the study found that 0-500 m ESRH has skill in forecasting violent tornadoes, and that both the 0-3 km MLCAPE and 0-3 km Lapse Rate terms raised the parameter’s false alarm rate.

Collagen is one of the most important and abundant proteins in mammals. It consists of three left-handed PPII helixes coiled along a common axis to form a very compact right-handed super helix. The primary structure is shown to be (Gly-Xaa-Yaa)n repeats with high content of prolyl residues at both Xaa and Yaa positions. <i>Cis-trans</i> isomerization of the prolyl amide bonds is one of the rate-limiting steps during collagen triple helix folding. The conformationally locked alkene isosteres Fmoc-Gly-Ψ[(E)CH=C]-Pro-Hyp(tBu)-OH and Fmoc-Pro-Ψ[(E)CH=C]-Pro-OH were designed and synthesized. The synthesis of the Gly-Pro isostere had no stereo-control, and the two diastereomers of the tripeptide isostere Fmoc-Gly-Ψ[(E)CH=C]-Pro-Hyp(tBu)-OBn were separated by normal phase HPLC. Although the stereoselectivity of the asymmetric reduction was not good for the Pro-Pro isostere, the resulting diastereomers was separable by flash chromatography, and the absolute stereochemistry of the two diastereomers was determined by Mosher's method. The Gly-Pro alkenyl peptides, and their control peptide Ac-(Gly-Pro-Hyp)8-Gly-Gly-Tyr-NH2 were synthesized and purified. All three peptides showed a maximum around 225 nm and a minimum close to 200 nm in the CD spectra, which indicated the formation of PPII helixes. The Tm value of the control peptide was determined to be 50.0 °C. The peptide with Gly-Ψ[(E)CH=C]-L-Pro-Hyp as the guest triplet formed a stable triple helix with a Tm value of 28.3 °C. The peptide with Gly-Ψ[(E)CH=C]-D-Pro-Hyp as the guest triplet showed a linear decrease in the ellipticity with increasing temperature, which indicated that no triple helix was formed. The Pro-Pro alkenyl peptide and its control peptide H-(Pro-Pro-Gly)₁₀-OH were synthesized and purified. The T_m value of control peptide was determined to be 31.6 °C by extrapolation to 0 M TMAO in PBS buffer, which was very close to the measured value of 31.5 °C. The Pro-Pro alkenyl peptide began to show a maximum around 225 nm in the CD spectra when the concentration of TMAO was higher than 2.5 M. After extrapolation to 0 M TMAO, the T_m value was determined to be –22.0 °C. These results indicate that the backbone inter-chain hydrogen bond is one of the major forces in stabilizing the collagen triple helix, while <i>cis-trans</i> isomerization has limited contribution. The intrinsic properties of the amide bond may have huge influence on the stability of the collagen triple helix. The helix-turn-helix motif is an important tertiary structure in DNA-binding proteins. Stepwise modifications of the Antennapedia HTH peptide (27-55) were performed to improve the helicity and stability. The peptide with more side-chain ion-pairs was over 4 times more helical than the native Antp peptide, while the Ala-based peptide was over 9 times more helical than the native peptide. A 12-membered ring, Fmoc-protected HTH-turn mimic was designed and synthesized, and was ready for solid phase peptide synthesis. The solubility of the cyclic peptide was very poor, and the purification of the final product was very difficult. The solubility problem might also affect solid phase peptide synthesis in the future. / Ph. D.