The transition to chaos for a special solution of the area-preserving quadratic map

Following previous work on chaotic boundaries of half-plane Hamiltonian maps a special solution of the area-preserving quadratic map is introduced and investigated. The breakdown of regular bounded motion on invariant curves is found from the radius of convergence of a power series whose successive terms oscillate wildly due to the presence of small divisors. Previous techniques for taming such series are found to be insufficient and new ones are introduced.It is found that half-plane Hamiltonian maps appear to have certain universal features and that the chaotic boundary has similarities to the boundaries of Siegel domains of complex conformal maps.The chaotic boundary function α_c(ν) has some interesting new features which are not fully understood.     

Blowup and solitary wave solutions with ring profiles of two-component nonlinear Schrödinger systems

Blowup ring profiles have been investigated by finding non-vortex blowup solutions of nonlinear Schrödinger equations (NLSEs) (cf. Fibich et al. (2005) [7] and Fibich et al. (2007) [8]). However, those solutions have infinite L² norm, so one may not maintain the ring profile all the way up to the singularity. To find H¹ non-vortex blowup solutions with ring profiles, we study the blowup solutions of two-component systems of NLSEs with nonlinear coefficients β and ν_j, j=1,2. When β<0 and ν₁?ν₂>0, the two-component system can be transformed into a multi-scale system with fast and slow variables which may produce H¹ blowup solutions with non-vortex ring profiles. We use the localized energy method with symmetry reduction to construct these solutions rigorously. On the other hand, these solutions may describe steady non-vortex bright ring solitons. Various types of ring profiles including m-ring and ring-ring profiles are presented by numerical solutions.     

Nonlinear stage of the Benjamin-Feir instability: three-dimensional coherent structures and rogue waves

A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on fully nonlinear equations describing weakly three-dimensional potential flows of an ideal fluid with a free surface in terms of conformal variables. Spontaneous formation of zigzag patterns for wave amplitude is observed in a nonlinear stage of the instability. If initial wave steepness is sufficiently high (ka>0.06), these coherent structures produce rogue waves. The most tall waves appear in turns of the zigzags. For ka<0.06, the structures decay typically without formation of steep waves.     

Results from the mainz neutrino mass experiment

The presently lowest limit for the mass of the electron neutrino is m _ν<2.2 eV/c ² 95% C.L.) derived from measurements at Mainz up to 1999. The data taken in 2000 are not fully analyzed yet, but limits of possible distortions as reported by the Troitsk group can be given.     

Growth of discontinuities in chemically reacting relativistic fluids

A relativistic theory is developed to study the growth of weak discontinuities propagating in a chemically reacting fluid mixture. The velocity of propagation is determined, which fully agrees with classical results in the nonrelativistic limit. The growth equation for the wave propagation in relativistic fluid flows with nonequilibrium effects is obtained and solved. The wave amplitude is determined as a function of time. The relativistic and relaxation effects on the global behavior of the wave amplitude are studied analytically. It is concluded that if the wave is of a compressive nature and its initial amplitude is greater than a critical value, then the discontinuity grows until it develops into a shock wave after a finite critical timet _c . But on the other hand if the initial wave amplitude is less than the critical one, the wave decays and damps out ultimately. It is shown that both relativistic and relaxation effects help in stabilizing the wave propagation by increasing the critical timet _c for the breakdown of the wave due to nonlinear steepening.     

High resolution FTIR spectroscopy of pentafluoroethane: perturbations in the Coriolis doublet of ν4 and ν13

The FTIR spectrum of pentafluoroethane (R125) was measured in the mid infrared region from 900 to 4000 cm⁻¹. Vibrational assignments for R125 are revised by comparison of previous and current experimental data with ab initio calculations at both the MP2/6-311+(d,p) and B3LYP/TZV+(3df,3p) levels of theory. High resolution FTIR spectra were recorded at room temperature and in an enclosive flow cell at a rotational temperature of 140 K. The cold spectrum was sufficiently resolved to enable rovibrational analyses of the overlapping ν₄ (1200.7341 cm⁻¹) and ν₁₃ (1223.3 cm⁻¹) bands, which have a/c hybrid and b-type character, respectively. Ground state combination differences were used to confirm assignment of 2375 lines to ν₄ (J_max = 86, K_{a max} = 50) and 2921 lines to ν₁₃ (J_max = 60, K_{a max} = 54). Effective rotational and centrifugal distortion constants were determined for ν₄, and the polarization ratio was found to be . Severe Coriolis perturbations prevent any satisfactory fit to the ν₁₃ band.     

A numerical study of the effects of the vertical baffle on liquid sloshing in two-dimensional rectangular tank

The liquid sloshing in a moving partially filled rectangular tank with a vertical baffle is investigated. A numerical algorithm based on the volume of fluid (VOF) technique is used to study the nonlinear behavior of liquid sloshing. The numerical model solves the complete Navier–Stokes equations in primitive variables by using of finite difference approximations with the moving coordinate system. The ratio of baffle height to the initial liquid depth has been changed in the range of 0≤h_B/h≤1.2. The critical baffle height to reach the roof of the tank and the baffle height beyond the liquid does not get over the baffle anymore have been investigated. The vortex originated by the flow separation from the baffle tip became weaker with increasing the baffle height. In order to assess the accuracy of the method used, some results with baffle height are compared with the experimental results. Comparisons show good agreement for slosh loads in the cases investigated. The free surface elevation and the time variations of pressures have been also presented.     

Diamagnetic susceptibility near the surface or twinning plane at the transition to the superconducting state

Besides the well-known bulk fluctuation contribution to the diamagnetic susceptibility there is an additional surface contribution with the singularity at T_SH exceeding the superconducting bulk transition temperature T_c(H). The results obtained allow to explain the anomalous behavior of the diamagnetic susceptibility found by Khaikin and Khlyustikov.     

Higher rotational lines in the ν2 fundamental of the H3+ molecular ion

By use of a new high-pressure hollow-cathode discharge cell and a Fourier transform spectrometer, many lines of the ν₂ fundamental band of H₃⁺ are observed in emission. These lines are discriminated from those of other species by pressure labeling, in which the relative intensities are studied as functions of the H₂ gas pressure in the cell. The H₃⁺ lines are found to persist to higher pressures than those of H atoms or H₂ or H₃ molecules. Practically all of the previously known lines of H₃⁺ are observed with this cell, and the measurements are extended to higher J because of the high rotational temperature of the H₃⁺. Absorption measurements of some high-J lines were also performed in this new cell. Altogether 113 lines of the ν₂ band of H₃⁺ with J′_max = 10 have been assigned, and 111 of them are fitted to 0.0654 cm⁻¹ with a 29-parameter effective Hamiltonian that uses a Padé formulation of the centrifugal distortion effects. Many of the higher rotational levels of ν₂ are affected by a Birss resonance with levels of ν₁. The fitted values ν₁ = 3175.0 cm⁻¹ and α₁₂ = 1.377 cm⁻¹ for the vibrational frequency and perturbation parameter are in reasonable agreement with ab initio values. Alternative fits using a vibration-rotation supermatrix model with a limited number of independent matrix elements are consistent with these assignments, but the quality of these fits degrades rapidly with increasing J′_max because the model does not describe centrifugal effects accurately.     

Topology and fractional quantum Hall effect

Starting from Laughlin-type wave functions with generalized periodic boundary conditions describing the degenerate ground state of a quantum Hall system we explicitly construct r-dimensional vector bundles. It turns out that the filling factor ν is given by the topological quantity c₁/r where c₁ is the first Chem number of these vector bundles. In addition, we managed to proof that under physical natural assumptions the stable vector bundles correspond to the experimentally dominating series of measured fractional filling factors ν = n/(2pn±1). Most remarkably, due to the very special form of the Laughlin wave functions the fluctuations of the curvature of these vector bundles converge to zero in the limit of infinitely many particles which shows a new mathematical property. Physically, this means that in this limit the Hall conductivity is independent of the boundary conditions which is very important for the observability of the effect. Finally, we discuss the relation of this result to a theorem of Donaldson.     

Search for neutrino radiative decay with a prototype Borexino detector

Results of background measurements with a prototype of the Borexino detector were used to obtain bounds on the lifetime of radiative neutrino decay ν_H→ν_L+γ. The new lower limit for the lifetime of pp and ⁷Be neutrinos is τ_c.m.(ν_H→ν_L+γ) /mν≥4.2×10³ s eV^?1(α)= 0). It is more than an order of magnitude stronger than the value obtained in previous experiments using nuclear reactors and accelerators.     

Upper critical fields of layered superconducting NbSe2 at low temperature

The upper critical field versus temperature H_c2 (T) is presented for several NbSe₂ samples. H_c2 (T) is above the dirty or clean limit, and at low T is greater than the paramagnetic limiting field. No simple T-dependence is observed. The anisotropy is 3.23 ± 0.03 for 0 ? H_o ? 150 kG and for 1.2 K ? T ? 4.2 K.     

On the tremendous effect of an electric field on the crystal lattice of quasi-one-dimensional conductors with a charge density wave

The deformation of the lattice of quasi-one-dimensional conductors with a charge density wave deformed by an electric field has been considered. In the case of the “strong” interaction between the charge density wave and lattice, the effect of the field can be compared to the usual piezoelectric effect with a tremendous piezoelectric modulus that is larger than the value in ionic crystals by a factor of L _c/λ (λ is the period of the charge density wave and L _c is the coherence length reaching several millimeters upon the sliding of the charge density wave). The interaction between the charge density wave and lattice is likely attributed to the possibility of the interband redistribution of charges (rearrangement of covalent bonds) in the process of the deformation of certain compounds with the charge density wave. The observed and expected effects provide a way of the creation of fundamentally new actuators including those of nanometer sizes.     

Eigenvalues, eigenfunctions, and surface states in finite periodic systems

Using a simple approach that requires neither the Bloch functions nor the reciprocal lattice, new, compact, and rigorous analytical formulas are derived for an accurate evaluation of resonant energies, resonant states, energy eigenvalues and eigenfunctions of open and bounded n-cell periodic systems with arbitrary 1D potential shapes, provided the single cell transfer matrix is given. These formulas are applied to obtain the energy spectra and wave functions of a number of simple but representative open and bounded superlattices. We solve the fine structure in bands and exhibit unambiguously that the true eigenfunctions do no not fulfill the periodicity property |Ψ_μ,ν (z + l_c)|² = |Ψ_μ,ν (z)|², with l_c the single cell length. We show that the well known surface states and surface energy levels come out naturally. We analyze the surface repulsion effect and calculate exactly the surface energy levels for different potential discontinuities an the ends.     

Water Spectra in the Region 4200-6250 cm, Extended Analysis of ν1+ν2, ν2+ν3, and 3ν2 Bands and Confirmation of Highly Excited States from Flame Spectra and from Atmospheric Long-Path Observations

Water vapor infrared spectra have been recorded at room temperature in the range 4200-6250 cm⁻¹ at resolutions (FWHM) between 0.0053 and 0.0080 cm⁻¹. The use of a White-type multireflection cell made large pressure × pathlength products possible up to 31.27 mbar×288.5 m. The high signal-to-noise ratio allowed us to observe lines with intensities as small as 10⁻²⁶ cm⁻¹/molecule cm⁻² at T=296 K. Among about 5100 recorded water lines, about half of which are reported for the first time, 2351 lines have been assigned to the second triad of H₂¹⁶O (bands ν₁+ν₂, ν₂+ν₃, and 3ν₂). This has allowed the determination of line positions and corresponding upper rovibrational states with considerably improved accuracy. The assignments of certain highly excited states have been confirmed by the analysis of flame spectra and hot emission spectra. New values of effective Hamiltonian parameters for the upper states {(110), (030), (011)} have been determined. The generating function model was used in the data reduction to account for the anomalously strong centrifugal distortion of the rovibrational levels and resonance interactions. The RMS standard deviation of the least-squares fit of the assigned H₂O data was 5×10⁻³ cm⁻¹ for line positions and 7×10⁻³ cm⁻¹ for energy levels up to J_max=20 and K_a(max)=13. Particular attention was paid to water lines in the transparency window 4200-5000 cm⁻¹, in which existing databases are not sufficient. In this region, 1395 lines of four isotopic species of water have been recorded and over 900 accurate line positions of nine bands of H₂¹⁶O (ν₁, ν₃, 2ν₂, ν₁+ν₂, ν₂+ν₃, 3ν₂, 4ν₂−ν₂, 2ν₂+ν₃−ν₂, ν₁+2ν₂−ν₂) are reported in this range. A comparison of laboratory spectra with long path atmospheric spectra (20 km slant path in the mountains) in this region shows that many lines missing from available spectroscopic compilations (or considerably shifted compared to observations) are important for a proper interpretation of atmospheric observations. A comparison of the observed data with the best available predictions from the molecular electronic potential energy surface is discussed.     

Modified grating-based external cavity diode laser for simultaneous dual-wavelengths operation

We have reported a modified V-shaped external cavity, which is constructed around a commercial diode laser operating at a center wavelength of λ=785 nm by adding a new coated glass plate with about 50% reflectivity to the cavity. This allows simultaneous dual-wavelengths operation in the vicinity of Δν_min=0.18 THz to Δν_max=0.22 THz, which can be used as laser source for terahertz generation either for semiconductor devices or nonlinear schemes.     

The overtone spectrum of C2D2 and C2H2 by ICLAS-VECSEL near 1 μm

The intracavity laser absorption spectra (ICLAS) of dideuteroacetylene, C₂D₂, and acetylene, C₂H₂, have been recorded between 1.03 and 0.99 μm with a vertical external cavity surface emitting laser (VECSEL) leading to the observation of seven and six bands, for C₂D₂ and C₂H₂ respectively, most of them newly reported. The strong ν₁+3ν₃ band of C₂D₂ at is found accompanied by the two Π-Π hot bands with v₄=1 and v₅=1 lower state and by the ν₂+3ν₃+2ν₄ band near . This last band results from an intensity transfer from the ν₁+3ν₃ band induced by the 1/244 anharmonic interaction. The ν₁+3ν₃ band of , present in natural abundance in the sample, could also be detected at in full agreement with local mode model predictions. The different bands of both C₂H₂ and C₂D₂ were found mostly unperturbed and the spectroscopic parameters retrieved from the rovibrational analyses agree satisfactorily with the predictions of the respective effective Hamiltonian models.     

Paramagnetic limiting in superconducting LiTiO ternary system

Measurements of upper critical fields H_c2 vs temperature are presented for several LiTiO compounds which have a nearly constant T_c = 11.2 ± 0.3 K and widely varying values of H_c2. Stable compounds have small spin-orbit scattering and show paramagnetic limiting effects, with the highest H_c2(4.2K) = 162 kG. Several compounds with large scattering showed a decrease in H_c2 over a period of about one year.     

Zero Tension Kardar-Parisi-Zhang Equation in (d + 1)–Dimensions

The joint probability distribution function (PDF) of the height and its gradients is derived for a zero tension d + 1-dimensional Kardar-Parisi-Zhang (KPZ) equation. It is proved that the height's PDF of zero tension KPZ equation shows lack of positivity after a finite time t _c . The properties of zero tension KPZ equation and its differences with the case that it possess an infinitesimal surface tension is discussed. Also potential relation between the time scale t _c and the singularity time scale t _c.v→0 of the KPZ equation with an infinitesimal surface tension is investigated.     

The fourth-order nonlinear Schrödinger equation for the envelope of Stokes waves on the surface of a finite-depth fluid

The method of multiple scales is used to derive the fourth-order nonlinear Schrödinger equation (NSEIV) that describes the amplitude modulations of the fundamental harmonic of Stokes waves on the surface of a medium-and large-depth (compared to the wavelength) fluid layer. The new terms of this equation describe the third-order linear dispersion effect and the nonlinearity dispersion effects. As the nonlinearity and the dispersion decrease, the equation uniformly transforms into the nonlinear Schrödinger equation for Stokes waves on the surface of a finite-depth fluid that was first derived by Hasimoto and Ono. The coefficients of the derived equation are given in an explicit form as functions of kh (h is the fluid depth, and k is the wave number). As kh tends to infinity, these coefficients transform into the coefficients of the NSEIV that was first derived by Dysthe for an infinite depth.