A mathematical model for the atomic clock error in case of jumps

We extend the mathematical model based on stochastic differential equations describing the error gained by an atomic clock to the cases of anomalous behavior including jumps and an increase of instability. We prove an exact iterative solution that can be useful for clock simulation, prediction, and interpretation, as well as for the understanding of the impact of clock error in the overall system in which clocks may be inserted as, for example, the Global Satellite Navigation Systems

The lift of sharp-leading-edged delta wings with blowing

An analysis of the lift augmentation due to a thin jet of air issuing from a slot along the leading edge of a delta wing is presented. The problem is treated with an extension of the method of Brown and Michael, representing the separated flow on the lee side of the wing by a pair of concentrated vortices and corresponding feeding sheets. It is assumed that the jet is not affected by Coanda forces. The analysis produces qualitative agreement with experiments

Analytical observations on the aerodynamics of a delta wing with leading edge flaps

The effect of a leading edge flap on the aerodynamics of a low aspect ratio delta wing is studied analytically. The separated flow field about the wing is represented by a simple vortex model composed of a conical straight vortex sheet and a concentrated vortex. The analysis is carried out in the cross flow plane by mapping the wing trace, by means of the Schwarz-Christoffel transformation into the real axis of the transformed plane. Particular attention is given to the influence of the angle of attack and flap deflection angle on lift and drag forces. Both lift and drag decrease with flap deflection, while the lift-to-drag ratioe increases. A simple coordinate transformation is used to obtain a closed form expression for the lift-to-drag ratio as a function of flap deflection. The main effect of leading edge flap deflection is a partial suppression of the separated flow on the leeside of the wing. Qualitative comparison with experiments is presented, showing agreement in the general trends

Aerodynamics of an airfoil with a jet issuing from its surface

A simple, two dimensional, incompressible and inviscid model for the problem posed by a two dimensional wing with a jet issuing from its lower surface is considered and a parametric analysis is carried out to observe how the aerodynamic characteristics depend on the different parameters. The mathematical problem constitutes a boundary value problem where the position of part of the boundary is not known a priori. A nonlinear optimization approach was used to solve the problem, and the analysis reveals interesting characteristics that may help to better understand the physics involved in more complex situations in connection with high lift systems

Theoretical studies on flapped delta wings

The effects of leading edge flaps on the aerodynamic characteristics of a low aspect-ratio delta wing are studied theoretically. As an extension of the classical crossflow plane analysis and in order to include separated shear layers, an analogy between three dimensional steady conical and two dimensional unsteady self-similar flows is explored. This analogy provides a simple steady-unsteady relationship. The criteria for the validity of the steady-unsteady analogy are also examined. Two different theoretical techniques are used to represent the separated shear layers based on the steady-unsteady analogy, neglecting the trailing edge effect. In the first approach, each vortex system is represented by a pair of concentrated vortices connected to the separation points by straight feeding sheets. In the second approach, the vortex cloud method is adopted for simulating the flow field in the crossflow plane. The separated shear layers are replaced with a cloud of discrete vortices and the boundary element method is employed to represent the wing trace by a vorticity distribution. A simple merging scheme is used to model the core region of the vortical flow as a single vortex by imposing a restriction on the shear layer rotation angle. The results are compared with experiments and with results from 3-D panel calculations

Numerical study of delta wing leading edge blowing

Spanwise and tangential leading edge blowing as a means of controlling the position and strength of the leading edge vortices are studied by numerical solution of the three-dimensional Navier-Stokes equations. The leading edge jet is simulated by defining a permeable boundary, corresponding to the jet slot, where suitable boundary conditions are implemented. Numerical results are shown to compare favorably with experimental measurements. It is found that the use of spanwise leading edge blowing at moderate angle of attack magnifies the size and strength of the leading edge vortices, and moves the vortex cores outboard and upward. The increase in lift primarily comes from the greater nonlinear vortex lift. However, spanwise blowing causes earlier vortex breakdown, thus decreasing the stall angle. The effects of tangential blowing at low to moderate angles of attack tend to reduce the pressure peaks associated with leading edge vortices and to increase the suction peak around the leading edge, so that the integrated value of the surface pressure remains about the same. Tangential leading edge blowing in post-stall conditions is shown to re-establish vortical flow and delay vortex bursting, thus increasing C sub L sub max and stall angle

Investigating the Contribution of Disordered Domains to the Biological Activity of RNA-binding Proteins

Many proteins contain disordered domains under physiological conditions. These disordered regions may be functional, although under pathological conditions they may lead to protein aggregation and degradation, as observed in proteins related to neurodegenerative diseases. In my thesis study, I aimed to understand how the primary sequence of these proteins encodes for the diverse ensemble of conformations rather than a stable folded state. I focused on the role of disordered domains in the activity of RNA-binding proteins involved in post-transcriptional regulation, but may lead to pathogenesis in many diseases. The human TIS11 proteins bind to AU-rich elements in the 30 UTR of mRNAs through a CCCH-type tandem zinc finger (TZF) domain. Mutations in these proteins have been linked to cancer. A member of this protein family, Tristetraprolin (TTP), is partially unfolded in the C-terminal zinc finger in the apo state, but folds upon RNA binding. The homolog protein TIS11d is folded in both free and bound states. Previous studies have shown that the extent of structure of the TZF domain in the apo state does not affect the affinity to target RNA in vitro, however it modulates the activity of the protein in cell. To understand which interactions determine the zinc affinity of the C-terminal zinc fingers of TTP and TIS11d, I investigated the stability of their TZF domains using homology modeling and molecular dynamics (MD) simulations. I found that, in the C-terminal zinc finger of TIS11d, a hydrogen bond is necessary to allow for [pi-[pi] stacking between the side chains of a conserved phenylalanine and the zinc-coordinating histidine. Using mutagenesis and nuclear magnetic resonance (NMR) spectroscopy, I demonstrated that the lack of this hydrogen bond is responsible for the reduced zinc affinity, and thus lack of structure, of the C-terminal zinc finger in TTP. These results suggest that the CCCH-type TZF domain in different proteins have evolved to differentiate their function through a disorder-to-order transition. In Caenorhabditis elegans several RNA-binding proteins contain a TZF domain homologous to the RNA-binding domain of TIS11 proteins, but have different RNA-binding specificity. I characterized the structure and the dynamics of the C. elegans protein MEX-5 using NMR spectroscopy and MD simulations. I found that MEX-5, like its mammalian counterpart TTP, contains a zinc finger that is partially unfolded in the free state but that folds upon RNA-binding. To assess if the disorder-to-order transition upon RNA-binding contributes to MEX-5 function, I designed a variant MEX-5 where both zinc fingers are stably folded in the absence of RNA. I characterized the RNA-binding activity of this variant MEX-5 and I found that the binding affnity and specificity are unchanged compared to the wild type protein. Together with Ryder\u27s lab, we used CRISPR-hr to introduce this variant into the endogenous C. elegans mex-5 locus. Homozygotes animals are sterile, form massive uterine tumors within a few days of reaching adulthood, and often die by bursting. These results show that the unfolded state of MEX-5 is critical to its function in vivo by a mechanism distinct from its RNA-binding activity. To further investigate how the equilibrium between structural order and disorder affects the function of a protein in the cell, I focused on the human protein TDP-43, a major component of the cellular proteinaceous aggregates found in amyotrophic lateral sclerosis and other neurodegenerative diseases. Previous studies have shown, both in vitro and in vivo, that the second RNA recognition motif (RRM2) of TDP-43 domain contains peptide regions that are particularly prone to fibril formation. In addition, RRM2 has been shown to populate, to a small degree, one or more partially folded states under native conditions. To determine if the partially folded states of TDP-43 RRM2 contribute to the formation of aggregates observed in the human diseases, I characterized the structures of these states using MD simulations including enhanced sampling methods and restraints from experimental chemical shifts. I found that in these states the protein exposes to the solvent aggregation-prone regions that are instead buried in the protein core in the native state. These results suggest a role in fibrogenesis for the transient partially folded states of TDP-43 RRM2