On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation

In a recent paper Goriely considers the one--dimensional scalar reaction--diffusion equation $u_t = u_{xx} + f(u)$ with a polynomial reaction term $f(u)$ and conjectures the existence of a relation between a global resonance of the hamiltonian system $u_{xx} + f(u) = 0$ and the asymptotic speed of propagation of fronts of the reaction diffusion equation. Based on this conjecture an explicit expression for the speed of the front is given. We give a counterexample to this conjecture and conclude that additional restrictions should be placed on the reaction terms for which it may hold.Comment: 9 pages Revtex plus 4 postcript figure

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

A Cone Beam CT-Based Study For Clinical Target Definition Using Pelvic Anatomy During Post-Prostatectomy Radiotherapy

Introduction: Radiation therapy (RT) is delivered after radical prostatectomy (RP) either as salvage treatment for an elevated prostate-specific antigen (PSA) level1-6 or as adjuvant therapy for patients with highrisk pathologic features7-8. Recent prospective data demonstrated a disease-free survival benefit of adjuvant RT for pathologic T3N0 prostate cancer9-10. Despite literature supporting the delivery of post-RP RT to the prostatic fossa (PF), no clear target definition guidelines exist for intensity modulated radiation therapy (IMRT) or image-guided RT (IGRT)11. Visualization of the PF is limited on standard CT images, with significant interobserver variability and uncertainty in CTV definition12. Efforts to incorporate complementary imaging modalities such as MRI for PF target volume definition have generated neither demonstrably more reliable PF delineation, nor practical contouring guidelines13. Regardless of the imaging modality, direct visualization and delineation of the PF clinical target volume (CTV) is fraught with uncertainty. On the other hand, it is possible to distinguish the borders of important nearby pelvic structures, namely the bladder and the rectum. The reliability of rectal volume definition on helical CT is supported by analysis of rectal contours defined in a prospective trial, suggesting the feasibility of rectal dose-volume data collection in a multicenter setting14. Fiorino et al have described a correlation between PF CTV shift and anterior rectal wall shift for the cranial half of the rectum in their report of rectal and bladder movement during post-RP RT using weekly CT images15. These studies support the reliability of CT-defined rectum contours and a limited correlation between PF CTV and anterior rectal wall, an important tenet in the current study. Int. J. Radiation Oncol. Biol. Physics, Volume 70, Issue 2, pages 431-436, Feb. 1, 2008

A forward-backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space

We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert space, we propose a generalization which involves the iterative solution of simpler subproblems. Descent and convergence properties of this new algorithm are studied. Furthermore, the results are applied to the minimization of Tikhonov-functionals associated with linear inverse problems and semi-norm penalization in Banach spaces. With the help of Bregman-Taylor-distance estimates, rates of convergence for the forward-backward splitting procedure are obtained. Examples which demonstrate the applicability are given, in particular, a generalization of the iterative soft-thresholding method by Daubechies, Defrise and De Mol to Banach spaces as well as total-variation based image restoration in higher dimensions are presented

Elastic breakup cross sections of well-bound nucleons

The 9Be(28Mg,27Na) one-proton removal reaction with a large proton separation energy of Sp(28Mg)=16.79 MeV is studied at intermediate beam energy. Coincidences of the bound 27Na residues with protons and other light charged particles are measured. These data are analyzed to determine the percentage contributions to the proton removal cross section from the elastic and inelastic nucleon removal mechanisms. These deduced contributions are compared with the eikonal reaction model predictions and with the previously measured data for reactions involving the re- moval of more weakly-bound protons from lighter nuclei. The role of transitions of the proton between different bound single-particle configurations upon the elastic breakup cross section is also quantified in this well-bound case. The measured and calculated elastic breakup fractions are found to be in good agreement.Comment: Phys. Rev. C 2014 (accepted

A Vision for Ice Giant Exploration

From Voyager to a Vision for 2050: NASA and ESA have just completed a study of candidate missionsto Uranus and Neptune, the so-called ice giant planets. It is a Pre-Decadal Survey Study, meant to inform the next Planetary Science Decadal Survey about opportunities for missions launching in the 2020's and early 2030's. There have been no space flight missions to the ice giants since the Voyager 2 flybys of Uranus in 1986 and Neptune in 1989. This paper presents some conclusions of that study (hereafter referred to as The Study), and how the results feed into a vision for where planetary science can be in 2050. Reaching that vision will require investments in technology andground-based science in the 2020's, flight during the 2030's along with continued technological development of both ground- and space-based capabilities, and data analysis and additional flights in the 2040's. We first discuss why exploring the ice giants is important. We then summarize the science objectives identified by The Study, and our vision of the science goals for 2050. We then review some of the technologies needed to make this vision a reality

On Determining Dead Layer and Detector Thicknesses for a Position-Sensitive Silicon Detector

In this work, two particular properties of the position-sensitive, thick silicon detectors (known as the "E" detectors) in the High Resolution Array (HiRA) are investigated: the thickness of the dead layer on the front of the detector, and the overall thickness of the detector itself. The dead layer thickness for each E detector in HiRA is extracted using a measurement of alpha particles emitted from a $^{212}$Pb pin source placed close to the detector surface. This procedure also allows for energy calibrations of the E detectors, which are otherwise inaccessible for alpha source calibration as each one is sandwiched between two other detectors. The E detector thickness is obtained from a combination of elastically scattered protons and an energy-loss calculation method. Results from these analyses agree with values provided by the manufacturer.Comment: Accepted for publication in Nuclear Instruments and Methods in Physics Researc

Costs of Early Adjuvant Radiation Therapy After Radical Prostatectomy: A Decision Analysis

Purpose/Objective(s): Prospective, randomized trials support adjuvant radiation therapy (RT) for adverse pathologic features after radical prostatectomy (RP). However, adjuvant RT is not universally delivered in this setting. Criticisms of adjuvant RT include toxicity, financial costs, potential overtreatment, and effectiveness of salvage RT. The objective of this study was to construct a decision analytic model to estimate real world cost of RT vs. no RT within the context of the effectiveness of early adjuvant RT for prostate patients based on published clinical results of the Southwest Oncology Group prospective trial of adjuvant RT (SWOG 8794). American Society for Therapeutic Radiation Oncology (ASTRO) 52nd Annual Meeting October 31 - November 4, San Diego, C