Oscillator strengths and line widths of dipole-allowed transitions in ¹⁴N₂ between 89.7 and 93.5 nm

Line oscillator strengths in the 20 electric dipole-allowed bands of ¹⁴N₂ in the 89.7–93.5nm (111480–106950cm⁻¹) region are reported from photoabsorptionmeasurements at an instrumental resolution of ∼6mÅ (0.7cm⁻¹) full width at half maximum. The absorptionspectrum comprises transitions to vibrational levels of the 3pσᵤc′₄¹Σᵤ⁺, 3pπᵤc³Πᵤ, and 3sσgo₃¹ΠᵤRydberg states and of the b′¹Σᵤ⁺ and b¹Πᵤ valence states. The J dependences of band f values derived from the experimental line f values are reported as polynomials in J′(J′+1) and are extrapolated to J′=0 in order to facilitate comparisons with results of coupled Schrödinger-equation calculations. Most bands in this study are characterized by a strong J dependence of the band f values and display anomalous P-, Q-, and R-branch intensity patterns. Predissociation line widths, which are reported for 11 bands, also exhibit strong J dependences. The f value and line width patterns can inform current efforts to develop comprehensive spectroscopic models that incorporate rotational effects and predissociation mechanisms, and they are critical for the construction of realistic atmospheric radiative-transfer models.This work was supported in part by NASA Grant No. NNG05GA03G to Wellesley College and Australian Research Council Discovery Program Grant No. DP0558962

A family of tridiagonal pairs and related symmetric functions

A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect the dual eigenbasis are described. The overlap functions between the two dual basis are shown to satisfy a coupled system of recurrence relations and a set of discrete second-order $q-$difference equations which generalize the ones associated with the Askey-Wilson orthogonal polynomials with a discrete argument. Normalizing the fundamental solution to unity, the hierarchy of solutions are rational functions of one discrete argument, explicitly derived in some simplest examples. The weight function which ensures the orthogonality of the system of rational functions defined on a discrete real support is given.Comment: 17 pages; LaTeX file with amssymb. v2: few minor changes, to appear in J.Phys.A; v3: Minor misprints, eq. (48) and orthogonality condition corrected compared to published versio

Memory and chaos in an Ising spin glass

The non-equilibrium dynamics of the model 3d-Ising spin glass - Fe$_{0.55}$Mn$_{0.45}$TiO$_3$ - has been investigated from the temperature and time dependence of the zero field cooled magnetization recorded under certain thermal protocols. The results manifest chaos, rejuvenation and memory features of the equilibrating spin configuration that are very similar to those observed in corresponding studies of the archetypal RKKY spin glass Ag(Mn). The sample is rapidly cooled in zero magnetic field, and the magnetization recorded on re-heating. When a stop at constant temperature $T_s$ is made during the cooling, the system evolves toward its equilibrium state at this temperature. The equilibrated state established during the stop becomes frozen in on further cooling and is retrieved on re-heating. The memory of the aging at $T_s$ is not affected by a second stop at a lower temperature $T'_s$. Reciprocally, the first equilibration at $T_s$ has no influence on the relaxation at $T'_s$, as expected within the droplet model for domain growth in a chaotic landscape.Comment: REVTeX style; 4 pages, 4 figure

Oscillator strengths and line widths of dipole-allowed transitions in ¹⁴N₂ between 86.0 and 89.7 nm

Oscillator strengths of 23 electric-dipole-allowed bands of ¹⁴N₂ in the 86.0–89.7 nm (111 480–116 280 cm⁻¹) region are reported from synchrotron-based photoabsorptionmeasurements at an instrumental resolution of 6.5×10⁻⁴ nm (0.7 cm⁻¹) full width at half maximum.Partial support for this research was provided by the Australian Research Council Discovery Program through Grant No. DP0558962 and by NASA Grant No. NNX08AE786 to Wellesley College

Effects of hydrogen bonding on supercooled liquid dynamics and the implications for supercooled water

The supercooled state of bulk water is largely hidden by unavoidable crystallization, which creates an experimentally inaccessible temperature regime - a 'no man's land'. We address this and circumvent the crystallization problem by systematically studying the supercooled dynamics of hydrogen bonded oligomeric liquids (glycols), where water corresponds to the chain-ends alone. This novel approach permits a 'dilution of water' by altering the hydrogen bond concentration via variations in chain length. We observe a dynamic crossover in the temperature dependence of the structural relaxation time for all glycols, consistent with the common behavior of most supercooled liquids. We find that the crossover becomes more pronounced for increasing hydrogen bond concentrations, which leads to the prediction of a marked dynamic transition for water within 'no man's land' at T~220 K. Interestingly, the predicted transition thus takes place at a temperature where a so called 'strong-fragile' transition has previously been suggested. Our results, however, imply that the dynamic transition of supercooled water is analogous to that commonly observed in supercooled liquids. Moreover, we find support also for the existence of a secondary relaxation of water with behavior analogous to that of the secondary relaxation observed for the glycols.Comment: 20 pages, 5 figures; corrected typos, title changed, small clarifying text changes, two labels removed from Fig. 2

Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

On the high energy proton spectrum measurements

The steepening of the proton spectrum beyond 1000 GeV and the rise in inelastic cross sections between 20 and 600 GeV observed by the PROTON-1-2-3 satellite experiments were explained by systematic effects of energy dependent albedo (backscatter) from the calorimeter

Elastic precursor of the transformation from glycolipid-nanotube to -vesicle

By the combination of optical tweezer manipulation and digital video microscopy, the flexural rigidity of single glycolipid "nano" tubes has been measured below the transition temperature at which the lipid tubules are transformed into vesicles. Consequently, we have found a clear reduction of the rigidity obviously before the transition as temperature increasing. Further experiments of infrared spectroscopy (FT-IR) and differential scanning calorimetry (DSC) have suggested a microscopic change of the tube walls, synchronizing with the precursory softening of the nanotubes.Comment: 9 pages, 6 figure

Electronic correlation in the infrared optical properties of the quasi two dimensional κ\kappa-type BEDT-TTF dimer system

The polarized optical reflectance spectra of the quasi two dimensional organic correlated electron system $\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]$Y$, $Y =$ Br and Cl are measured in the infrared region. The former shows the superconductivity at $T_{\rm c} \simeq$ 11.6 K and the latter does the antiferromagnetic insulator transition at $T_{\rm N} \simeq$ 28 K. Both the specific molecular vibration mode $\nu_{3}(a_{g})$ of the BEDT-TTF molecule and the optical conductivity hump in the mid-infrared region change correlatively at $T^{*} \simeq$ 38 K of $\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br, although no indication of $T^{*}$ but the insulating behaviour below $T_{\rm ins} \simeq$ 50-60 K are found in $\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Cl. The results suggest that the electron-molecular vibration coupling on the $\nu_{3}(a_{g})$ mode becomes weak due to the enhancement of the itinerant nature of the carriers on the dimer of the BEDT-TTF molecules below $T^{*}$, while it does strong below $T_{\rm ins}$ because of the localized carriers on the dimer. These changes are in agreement with the reduction and the enhancement of the mid-infrared conductivity hump below $T^{*}$ and $T_{\rm ins}$, respectively, which originates from the transitions between the upper and lower Mott-Hubbard bands. The present observations demonstrate that two different metallic states of $\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br are regarded as {\it a correlated good metal} below $T^{*}$ including the superconducting state and {\it a half filling bad metal} above $T^{*}$. In contrast the insulating state of $\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Cl below $T_{\rm ins}$ is the Mott insulator.Comment: 8 pages, 7 figure