The Modulation of Multiple Phases Leading to the Modified KdV Equation

This paper seeks to derive the modified KdV (mKdV) equation using a novel approach from systems generated from abstract Lagrangians that possess a two-parameter symmetry group. The method to do uses a modified modulation approach, which results in the mKdV emerging with coefficients related to the conservation laws possessed by the original Lagrangian system. Alongside this, an adaptation of the method of Kuramoto is developed, providing a simpler mechanism to determine the coefficients of the nonlinear term. The theory is illustrated using two examples of physical interest, one in stratified hydrodynamics and another using a coupled Nonlinear Schr\"odinger model, to illustrate how the criterion for the mKdV equation to emerge may be assessed and its coefficients generated.Comment: 35 pages, 5 figure

Then and Now: An Analysis of Broad-based Merit Aid Initial Eligibility Policies after Twenty Years

Using Hall’s framework of policy changes, we sought to document and classify changes in initial eligibility and award provisions of broad-based merit aid scholarship programs at inception and present day. Our analysis revealed five first-order changes, two second-order changes, and only one third order change. Although the policy settings, instruments, and goals remained static in five states, the scholarship dollars in four of them have not kept up with increases in overall cost of attendance

Low thrust orbit determination program

Logical flow and guidelines are provided for the construction of a low thrust orbit determination computer program. The program, tentatively called FRACAS (filter response analysis for continuously accelerating spacecraft), is capable of generating a reference low thrust trajectory, performing a linear covariance analysis of guidance and navigation processes, and analyzing trajectory nonlinearities in Monte Carlo fashion. The choice of trajectory, guidance and navigation models has been made after extensive literature surveys and investigation of previous software. A key part of program design relied upon experience gained in developing and using Martin Marietta Aerospace programs: TOPSEP (Targeting/Optimization for Solar Electric Propulsion), GODSEP (Guidance and Orbit Determination for SEP) and SIMSEP (Simulation of SEP)

Krein signature and Whitham modulation theory: the sign of characteristics and the “sign characteristic”

In classical Whitham modulation theory, the transition of the dispersionless Whitham equations from hyperbolic to elliptic is associated with a pair of nonzero purely imaginary eigenvalues coalescing and becoming a complex quartet, suggesting that a Krein signature is operational. However, there is no natural symplectic structure. Instead, we find that the operational signature is the “sign characteristic” of real eigenvalues of Hermitian matrix pencils. Its role in classical Whitham single‐phase theory is elaborated for illustration. However, the main setting where the sign characteristic becomes important is in multiphase modulation. It is shown that a necessary condition for two coalescing characteristics to become unstable (the generalization of the hyperbolic to elliptic transition) is that the characteristics have opposite sign characteristic. For example the theory is applied to multiphase modulation of the two‐phase traveling wave solutions of coupled nonlinear Schrödinger equation

Resonance between Noise and Delay

We propose here a stochastic binary element whose transition rate depends on its state at a fixed interval in the past. With this delayed stochastic transition this is one of the simplest dynamical models under the influence of ``noise'' and ``delay''. We demonstrate numerically and analytically that we can observe resonant phenomena between the oscillatory behavior due to noise and that due to delay.Comment: 4 pages, 5 figures, submitted to Phys.Rev.Lett Expanded and Added Reference

The ion environment near Europa and its role in surface energetics

This paper gives the composition, energy spectra, and time variability of energetic ions measured just upstream of Europa. From 100 keV to 100 MeV, ion intensities vary by less than a factor of ∼5 among Europa passes considered between 1997 and 2000. We use the data to estimate the radiation dose rate into Europa's surface for depths 0.01 mm – 1 m. We find that in a critical fraction of the upper layer on Europa's trailing hemisphere, energetic electrons are the principal agent for radiolysis, and their bremsstrahlung photon products, not included in previous studies, dominate the dose below about 1 m. Because ion bombardment is more uniform across Europa's surface, the radiation dose on the leading hemisphere is dominated by the proton flux. Differences exist between this calculation and published doses based on the E4 wake pass. For instance, proton doses presented here are much greater below 1 mm

Identification of LIMK2 as a therapeutic target in castration resistant prostate cancer

This study identified LIMK2 kinase as a disease-specific target in castration resistant prostate cancer (CRPC) pathogenesis, which is upregulated in response to androgen deprivation therapy, the current standard of treatment for prostate cancer. Surgical castration increases LIMK2 expression in mouse prostates due to increased hypoxia. Similarly, human clinical specimens showed highest LIMK2 levels in CRPC tissues compared to other stages, while minimal LIMK2 was observed in normal prostates. Most notably, inducible knockdown of LIMK2 fully reverses CRPC tumorigenesis in castrated mice, underscoring its potential as a clinical target for CRPC. We also identified TWIST1 as a direct substrate of LIMK2, which uncovered the molecular mechanism of LIMK2-induced malignancy. TWIST1 is strongly associated with CRPC initiation, progression and poor prognosis. LIMK2 increases TWIST1 mRNA levels upon hypoxia; and stabilizes TWIST1 by direct phosphorylation. TWIST1 also stabilizes LIMK2 by inhibiting its ubiquitylation. Phosphorylation-dead TWIST1 acts as dominant negative and fully prevents EMT and tumor formation in vivo, thereby highlighting the significance of LIMK2-TWIST1 signaling axis in CRPC. As LIMK2 null mice are viable, targeting LIMK2 should have minimal collateral toxicity, thereby improving the overall survival of CRPC patients

Reprinted Article “Subintimal Angioplasty of Femoropopliteal Artery Occlusions: The Long-term Results”

AbstractThe technique of subintimal angioplasty has been attempted on 200 consecutive femoropopliteal artery occlusions of median (range) length 11 (2–37) cm. The principle of the technique is to traverse the occlusion in the subintimal plane and recanalise by inflating the angioplasty balloon within the subintimal space. The technical success rate was 159/200 (80%) and was not significantly different for occlusions <10 cm (81%, n = 73), 11–20 cm (83%, n = 63) or >20 cm (68%, n = 23), p = 0.20. There were no deaths nor limb loss resulting from the procedure. The median (range) ankle-brachial pressure index increased from 0.61 (0.21–1.0) preangioplasty to 0.90 (0.26–1.50) postangioplasty. The actuarial haemodynamic patencies of technically successful procedures at 12 and 36 months were 71% and 58% respectively, the symptomatic patencies were 73% and 61%. A multiple regression analysis showed that smoking multiplied the risk of reocclusion by 2.70 (p < 0.001), each additional run-off vessel reduced the risk by 0.54 (p < 0.001) and the risk increased by 1.73 (p = 0.020) for every 10 cm of occlusion length. In conclusion, the technical success rate (80%) of subintimal angioplasty for femoropopliteal occlusions is unrelated to occlusion length and for all procedures, including technical failures, cumulative symptomatic and haemodynamic patencies of 46 and 48% can be achieved at 3 years. The factors influencing long-term patency were smoking, the number of calf run-off vessels and occlusion length