Geometry and Topology of Escape II: Homotopic Lobe Dynamics

We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge geometrically upon each endpoint of every escape segment. In the present paper, we use topological techniques to: (1) show that there exists a minimal required set of escape segments within the escape-time plot; (2) develop an algorithm which computes this minimal set; (3) show that the minimal set eventually displays a recursive structure governed by an ``Epistrophe Start Rule'': a new epistrophe is spawned Delta = D+1 iterates after the segment to which it converges, where D is the minimum delay time of the complex.Comment: 13 pages, 8 figures, to appear in Chaos, second of two paper

Geometry and Topology of Escape I: Epistrophes

We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape from a bounded region of the plane as a function along the line of initial conditions, forming an ``escape-time plot''. For a chaotic system, this plot is in general not a smooth function, but rather has many singularities at which the escape time is infinite; these singularities form a complicated fractal set. In this article we prove the existence of regular repeated sequences, called ``epistrophes'', which occur at all levels of resolution within the escape-time plot. (The word ``epistrophe'' comes from rhetoric and means ``a repeated ending following a variable beginning''.) The epistrophes give the escape-time plot a certain self-similarity, called ``epistrophic'' self-similarity, which need not imply either strict or asymptotic self-similarity.Comment: 15 pages, 9 figures, to appear in Chaos, first of two paper

Analytically Derived Switching-Functions For Exact H-2(+) Eigenstates

Electron translation factors (ETF\u27s) appropriate for slow atomic collisions may be constructed using switching functions. In this paper we derive a set of switching functions for the H2+ system by an analytical two-center decomposition of the exact molecular eigenstates. These switching functions are closely approximated by the simple form f=bη, where η is the angle variable of prolate spheroidal coordinates. For given united atom angular momentum quantum numbers (l,m), the characteristic parameter blm depends only on the quantity c2=-∊R22, where ∊ is the electronic binding energy and R the internuclear distance in a.u. The resulting parameters are in excellent agreement with those found in our earlier work by a heuristic optimization scheme based on a study of coupling matrix-element behavior for a number of H2+ states. An approximate extension to asymmetric cases (HeH2+) has also been made. Nonadiabatic couplings based on these switching functions have been used in recent close-coupling calculations for H+-H(1s) collisions and He2+-H(1s) collisions at energies 1.0-20 keV

Accumulation of driver and passenger mutations during tumor progression

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the current study, we provide a novel mathematical model that begins to address this challenge. We model tumors as a discrete time branching process that starts with a single driver mutation and proceeds as each new driver mutation leads to a slightly increased rate of clonal expansion. Using the model, we observe tremendous variation in the rate of tumor development - providing an understanding of the heterogeneity in tumor sizes and development times that have been observed by epidemiologists and clinicians. Furthermore, the model provides a simple formula for the number of driver mutations as a function of the total number of mutations in the tumor. Finally, when applied to recent experimental data, the model allows us to calculate, for the first time, the actual selective advantage provided by typical somatic mutations in human tumors in situ. This selective advantage is surprisingly small, 0.005 +- 0.0005, and has major implications for experimental cancer research

Long Duration Performance of High Temperature Irradiation Resistant Thermocouples

Many advanced nuclear reactor designs require new fuel, cladding, and structural materials. Data are needed to characterize the performance of these new materials in high temperature, radiation conditions. However, traditional methods for measuring temperature inpile degrade at temperatures above 1100 ºC. To address this instrumentation need, the Idaho National Laboratory (INL) developed and evaluated the performance of a high temperature irradiation-resistant thermocouple that contains alloys of molybdenum and niobium. To verify the performance of INL’s recommended thermocouple design, a series of high temperature (from 1200 to 1800 ºC) long duration (up to six months) tests has been initiated. This paper summarizes results from the tests that have been completed. Data are presented from 4000 hour tests conducted at 1200 and 1400 ºC that demonstrate the stability of this thermocouple (less than 2% drift). In addition, post test metallographic examinations are discussed which confirm the compatibility of thermocouple materials throughout these long duration, high temperature tests

Evaluation of Specialized Thermocouples for High-Temperature In-Pile Testing

Many advanced nuclear reactor designs require new fuel, cladding, and structural materials. Data are needed to characterize the performance of these new materials in high temperature, oxidizing, and radiation conditions. To obtain this data, robust instrumentation is needed that can survive proposed test conditions. Standard thermocuoples for measuring temperature in-pile degrade at temperatures above 1100 ºC. Hence, INL initiated a project to develop specialized thermocouples for high temperature in-pile applications. Results from efforts to develop, fabricate, and evaluate specialized high-temperature thermocouples for in-pile applications suggest that several material combinations are viable. Tests show that several low neutron cross-section candidate materials are resistant to material interactions and remain ductile at high temperatures. In addition, results indicate that the thermoelectric response is singlevalued and repeatable with acceptable resolution for the candidate thermoelements considered. The final selection of the thermocouple materials will depend on the desired peak temperature and accuracy requirements. If thermocouples are needed that measure temperatures at 1600 ºC or higher, the doped Mo / Nb-1%Zr and Mo-1.6% Nb / Nb-1%Zr thermoelement wire combinations are recommended with HfO2 insulation, and a Nb-1%Zr sheath. Additional evaluations are underway to characterize the performance of this proposed thermocouple design. INL has worked to optimize this thermocouple’s stability. With appropriate heat treatment and fabrication approaches, results indicate that the effects of thermal cycling on the calibration of the proposed thermocouple design can be minimized. INL has initiated a series of high temperature (from 1200 to 1800 ºC) long duration (up to six months) tests. Initial results indicate the INL-developed thermocouple’s termoelectric response is stable with less than 15 ºC drift observed in over 3500 hours of the planned 4000 hours of tests at 1200 ºC. In comparison, commercially-available Type K and N thermocouples included in these 1200 ºC tests have experienced drifts up to of over100 ºC

[Arctic] Greenland ice sheet [in “State of the Climate in 2012”]

Melting at the surface of the Greenland Ice Sheet set new records for extent and melt index (i.e., the number of days on which melting occurred multiplied by the area where melting was detected) for the period 1979–2012, according to passive microwave observations (e.g., Tedesco 2007, 2009; Mote and Anderson 1995). Melt extent reached ~97% of the ice sheet surface during a rare, ice-sheet-wide event on 11–12 July (Fig. 5.13a; Nghiem et al. 2012). This was almost four times greater than the average melt extent for 1981–2010. The 2012 standardized melting index (SMI, defined as the melting index minus its average and divided by its standard deviation) was +2.4, almost twice the previous record of about +1.3 set in 2010

Differential cross sections for pion charge exchange on the proton at 27.5 MeV

We have measured pion single charge exchange differential cross sections on the proton at 27.5 MeV incident $\pi^-$ kinetic energy in the center of momentum angular range between $0^\circ$ and $55^\circ$. The extracted cross sections are compared with predictions of the standard pion-nucleon partial wave analysis and found to be in excellent agreement.Comment: ReVTeX v3.0 with aps.sty, 23 pages in e-print format, 7 PostScript Figures and 4 Tables, also available via anonymous ftp at ftp://helena.phys.virginia.edu/pub/preprints/scx.p

The Negative Feedback-Loop between the Oncomir Mir-24-1 and Menin Modulates the Men1 Tumorigenesis by Mimicking the “Knudson’s Second Hit”

Multiple endocrine neoplasia type 1 (MEN1) syndrome is a rare hereditary cancer disorder characterized by tumors of the parathyroids, of the neuroendocrine cells, of the gastro-entero-pancreatic tract, of the anterior pituitary, and by non-endocrine neoplasms and lesions. MEN1 gene, a tumor suppressor gene, encodes menin protein. Loss of heterozygosity at 11q13 is typical of MEN1 tumors, in agreement with the Knudson’s two-hit hypothesis. In silico analysis with Target Scan, Miranda and Pictar-Vert softwares for the prediction of miRNA targets indicated miR-24-1 as capable to bind to the 3′UTR of MEN1 mRNA. We investigated this possibility by analysis of miR-24-1 expression profiles in parathyroid adenomatous tissues from MEN1 gene mutation carriers, in their sporadic non-MEN1 counterparts, and in normal parathyroid tissue. Interestingly, the MEN1 tumorigenesis seems to be under the control of a “negative feedback loop” between miR-24-1 and menin protein, that mimics the second hit of Knudson’s hypothesis and that could buffer the effect of the stochastic factors that contribute to the onset and progression of this disease. Our data show an alternative way to MEN1 tumorigenesis and, probably, to the “two-hit dogma”. The functional significance of this regulatory mechanism in MEN1 tumorigenesis is also the basis for opening future developments of RNA antagomir(s)-based strategies in the in vivo control of tumorigenesis in MEN1 carriers