On the degeneracies of the mass-squared differences for three-neutrino oscillations

Using an algebraic formulation, we explore two well-known degeneracies involving the mass-squared differences for three-neutrino oscillations assuming CP symmetry is conserved. For vacuum oscillation, we derive the expression for the mixing angles that permit invariance under the interchange of two mass-squared differences. This symmetry is most easily expressed in terms of an ascending mass order. This can be used to reduce the parameter space by one half in the absence of the MSW effect. For oscillations in matter, we derive within our formalism the known approximate degeneracy between the standard and inverted mass hierarchies in the limit of vanishing $\theta_{13}$. This is done with a mass ordering that permits the map $\Delta_{31} \mapsto -\Delta_{31}$. Our techniques allow us to translate mixing angles in this mass order convention into their values for the ascending order convention. Using this dictionary, we demonstrate that the vacuum symmetry and the approximate symmetry invoked for oscillations in matter are distinctly different.Comment: 5 pages, revised manuscrip

Station coordinates in the standard earth 3 system and radiation-pressure perturbations from ISAGEX camera data

Simultaneous and individual camera observations of GEOS 1, GEOS 2, Pageos, and Midas 4 obtained during the International Satellite Geodesy Experiment are utilized to determine station coordinates. The Smithsonian Astrophysical Observatory Standard Earth III system of coordinates is used to tie the geometrical network to a geocentric system and as a reference for calculating satellite orbits. A solution for coordinates combining geometrical and dynamical methods is obtained, and a comparison between the solutions and terrestrial data is made. The radiation-pressure and earth-albedo perturbations for Pageos are very large, and Pageos' orbits are used to evaluate the analytical treatment of these perturbations. Residual effects, which are probably of interest to aeronomists, remain in the Pageos orbits

Measuring the mass of a sterile neutrino with a very short baseline reactor experiment

An analysis of the world's neutrino oscillation data, including sterile neutrinos, (M. Sorel, C. M. Conrad, and M. H. Shaevitz, Phys. Rev. D 70, 073004) found a peak in the allowed region at a mass-squared difference $\Delta m^2 \cong 0.9$ eV$^2$. We trace its origin to harmonic oscillations in the electron survival probability $P_{ee}$ as a function of L/E, the ratio of baseline to neutrino energy, as measured in the near detector of the Bugey experiment. We find a second occurrence for $\Delta m^2 \cong 1.9$ eV$^2$. We point out that the phenomenon of harmonic oscillations of $P_{ee}$ as a function of L/E, as seen in the Bugey experiment, can be used to measure the mass-squared difference associated with a sterile neutrino in the range from a fraction of an eV$^2$ to several eV$^2$ (compatible with that indicated by the LSND experiment), as well as measure the amount of electron-sterile neutrino mixing. We observe that the experiment is independent, to lowest order, of the size of the reactor and suggest the possibility of a small reactor with a detector sitting at a very short baseline.Comment: 4 pages, 2 figure

Vacuum-UV negative photoion spectroscopy of CH3F, CH3Cl and CH3Br

Using tunable vacuum-UV radiation from a synchrotron, negative ions are detected by quadrupolar mass spectrometry following photoexcitation of three gaseous halogenated methanes CH$_3$X (X = F,Cl,Br). The anions X$^-$, H$^-$, CX$^-$, CHX$^-$ and CH$_2$X$^-$ are observed, and their ion yields recorded in the range 8-35 eV. The anions show a linear dependence of signal with pressure, showing that they arise from unimolecular ion-pair dissociation, generically described as AB + h$v$ $\rightarrow$ A$^-$ + B$^+$ (+ neutrals). Absolute cross sections for ion-pair formation are obtained by calibrating the signal intensities with those of F$^-$ from both SF$_6$ and CF$_4$. The cross sections for formation of X$^-$ + CH$_3$$^+$ are much greater than for formation of CH$_2$X$^-$ + H$^+$. In common with many quadrupoles, the spectra of $m$/$z$ 1 (H$^-$) anions show contributions from all anions, and only for CH$_3$Br is it possible to perform the necessary subtraction to obtain the true H$^-$ spectrum. The anion cross sections are normalised to vacuum-UV absorption cross sections to obtain quantum yields for their production. The appearance energies of X$^-$ and CH$_2$X$^-$ are used to calculate upper limits to 298 K bond dissociation energies for D$^o$ (H$_3$C-X) and D$^o$ (XH$_2$C-H) which are consistent with literature values. The spectra suggest that most of the anions are formed indirectly by crossing of Rydberg states of the parent molecule onto an ion-pair continuum. The one exception is the lowest-energy peak of F$^-$ from CH$_3$F at 13.4 eV, where its width and lack of structure suggest it may correspond to a direct ion-pair transition

Neutrino oscillations: measuring θ13\theta_{13} including its sign

In neutrino phenomenology, terms in the oscillation probabilities linear in $\sin \theta_{13}$ lead naturally to the question ``How can one measure $\theta_{13}$ including its sign?'' Here we demonstrate analytically and with a simulation of neutrino data that ${\mathcal P}_{e\mu}$ and {\mathcal {P}_{\mu\mu} at $L/E = 2\pi/\Delta_{21}$ exhibit significant linear dependence on $\theta_{13}$ in the limit of vacuum oscillations. Measurements at this particular value of $L/E$ can thus determine not only $\theta_{13}$ but also its sign, if CP violation is small.Comment: 5 pages, 5 figure

Local forest structure variability increases resilience to wildfire in dry western U.S. coniferous forests.

A 'resilient' forest endures disturbance and is likely to persist. Resilience to wildfire may arise from feedback between fire behaviour and forest structure in dry forest systems. Frequent fire creates fine-scale variability in forest structure, which may then interrupt fuel continuity and prevent future fires from killing overstorey trees. Testing the generality and scale of this phenomenon is challenging for vast, long-lived forest ecosystems. We quantify forest structural variability and fire severity across >30 years and >1000 wildfires in California's Sierra Nevada. We find that greater variability in forest structure increases resilience by reducing rates of fire-induced tree mortality and that the scale of this effect is local, manifesting at the smallest spatial extent of forest structure tested (90 × 90 m). Resilience of these forests is likely compromised by structural homogenisation from a century of fire suppression, but could be restored with management that increases forest structural variability

Predicting the sound insulation of lightweight sandwich panels

The sound insulation of three sandwich panels was modelled using simple sound insulation prediction methods, but the agreement between theory and experiment was not very good. The effective Young's modulus was determined over a wide frequency from the resonant frequencies of three beams of different lengths. The effective Young's modulus was found to reduce with increasing frequency as has been predicted in the literature. This decrease is due to the core starting to shear rather than bend because its Young's modulus is much less than the Young's moduli of the skins. Unfortunately the agreement between theory and experiment was still not very good. This is because many of the prediction frequencies occur in the critical frequency dip because of the variation of the Young's modulus with frequency

Vacuum-UV negative photoion spectroscopy of CF3Cl, CF3Br and CF3I

Using synchrotron radiation negative ions have been detected by mass spectrometry following vacuum-UV photoexcitation of trifluorochloromethane (CF$_3$Cl), trifluorobromomethane (CF$_3$Br) and trifluoroiodomethane (CF$_3$I). The anions F$^-$, X$^-$, F$_2^-$, FX$^-$, CF$^-$, CF$_2^-$ and CF$_3^-$ were observed from all three molecules, where X = Cl, Br or I, and their ion yields recorded in the range 8-35 eV. With the exception of Br$^-$ and I$^-$, the anions observed show a linear dependence of signal with pressure, showing that they arise from unimolecular ion-pair dissociation. Dissociative electron attachment, following photoionization of CF$_3$Br and CF$_3$I as the source of low-energy electrons, is shown to dominate the observed Br$^-$ and I$^-$ signals, respectively. Cross sections for ion-pair formation are put on to an absolute scale by calibrating the signal strengths with those of F$^-$ from both SF$_6$ and CF$_4$. These anion cross sections are normalized to vacuum-UV absorption cross sections, where available, and the resulting quantum yields are reported. Anion appearance energies are used to calculate upper limits to 298 K bond dissociation energies for $D^0$(CF$_3$-X) which are consistent with literature values. We report new data for $D^0$(CF$_2$I$^-$-F) ≤ 2.7 ± 0.2 eV and $\Delta_fH^0_{298}$ (CF$_2$I$^+$) ≤ (598 ± 22) kJ mol$^{-1}$. No ion-pair formation is observed below the ionization energy of the parent molecule for CF$_3$Cl and CF$_3$Br, and only weak signals (in both I$^-$ and F$^-$) are detected for CF$_3$I. These observations suggest neutral photodissociation is the dominant exit channel to Rydberg state photoexcitation at these lower energies

Spatial adaptivity of the SAAF and Weighted Least Squares (WLS) forms of the neutron transport equation using constraint based, locally refined, isogeometric analysis (IGA) with dual weighted residual (DWR) error measures

This paper describes a methodology that enables NURBS (Non-Uniform Rational B-spline) based Isogeometric Analysis (IGA) to be locally refined. The methodology is applied to continuous Bubnov-Galerkin IGA spatial discretisations of second-order forms of the neutron transport equation. In particular this paper focuses on the self-adjoint angular flux (SAAF) and weighted least squares (WLS) equations. Local refinement is achieved by constraining degrees of freedom on interfaces between NURBS patches that have different levels of spatial refinement. In order to effectively utilise constraint based local refinement, adaptive mesh refinement (AMR) algorithms driven by a heuristic error measure or forward error indicator (FEI) and a dual weighted residual (DWR) or goal-based error measure (WEI) are derived. These utilise projection operators between different NURBS meshes to reduce the amount of computational effort required to calculate the error indicators. In order to apply the WEI to the SAAF and WLS second-order forms of the neutron transport equation the adjoint of these equations are required. The physical adjoint formulations are derived and the process of selecting source terms for the adjoint neutron transport equation in order to calculate the error in a given quantity of interest (QoI) is discussed. Several numerical verification benchmark test cases are utilised to investigate how the constraint based local refinement affects the numerical accuracy and the rate of convergence of the NURBS based IGA spatial discretisation. The nuclear reactor physics verification benchmark test cases show that both AMR algorithms are superior to uniform refinement with respect to accuracy per degree of freedom. Furthermore, it is demonstrated that for global QoI the FEI driven AMR and WEI driven AMR produce similar results. However, if local QoI are desired then WEI driven AMR algorithm is more computationally efficient and accurate per degree of freedom

A New Approach for Sampling Ordered Parameters in Probabilistic Sensitivity Analysis

Background Probabilistic sensitivity analysis (PSA) in cost-effectiveness analysis involves sampling a large number of realisations of an economic model. For some parameters, we may be uncertain around the true mean values of the variables, but the ordering of the values is known. Typical sampling approaches lack either statistical or clinical validity. For example, sampling using a common number generator results in extreme dependence and independent sampling can lead to realisations with incorrect ordering. Methods We propose a new sampling approach for ordered parameters, the Difference Method approach, which samples the parameters of interest via a difference parameter. If the parameters of interest are bounded, it involves transforming the variables so that they are unbounded and then sampling via the difference parameter. We have provided an Excel workbook to implement the method. The proposed approach is illustrated with an example sampling ordered parameters for utility and cost. Results The DM approach has a number of advantages when comparing with the typical approaches used in practice. The DM approach generates PSA samples which have similar summary statistics as the given values in our examples whilst maintaining the constraint that one value was greater than another. The method also implies plausible positive correlation between the two ordered variables. Conclusions Both clinical and statistical validity should be checked when producing PSA samples. The DM approach should be considered as a solution to potential problems in generating PSA samples for ordered parameters