Cuspons and Smooth Solitons of the Degasperis–Procesi Equation Under Inhomogeneous Boundary Condition

This paper is contributed to explore all possible single peakon solutions for the Degasperis–Procesi (DP) equation m _t  + m _x u + 3mu _x  = 0, m = u − u _xx . Our procedure shows that the DP equation either has cusp soliton and smooth soliton solutions only under the inhomogeneous boundary condition lim_|x|→ ∞ u =A ≠0, or possesses the regular peakon solutions ce ^{− |x − ct|} ∈ H ¹ (c is the wave speed) only when lim_|x|→ ∞ u = 0 (see Theorem 4.1). In particular, we first time obtain the stationary cuspon solution of the DP equation. Moreover we present new cusp solitons (in the space of ) and smooth soliton solutions in an explicit form. Asymptotic analysis and numerical simulations are provided for smooth solitons and cusp solitons of the DP equation.      

Electrochemical cell performance studies on all-solid-state battery using nano-composite polymer electrolyte membrane

All-solid-state proton-conducting polymeric batteries have been fabricated in the cell configurations: Zn + ZnSO₄·7H₂O (anode) || polyethylene oxide (PEO):NH₄HSO₄ + SiO₂ || MnO₂ + C (cathode) and Zn + ZnSO₄·7H₂O (anode) || PEO:NH₄HSO₄ + SiO₂ || PbO₂ + V₂O₅ + C (cathode). Nano-composite proton-conducting polymeric membrane in wt.% composition, 92PEO: 8 NH₄HSO₄ + 3 SiO₂, synthesized by solution cast technique, has been used as electrolyte. Dispersal of nanosized (8 nm) fumed-SiO₂ particles resulted into an enhancement in the room temperature conductivity of polymer electrolyte host, 92PEO: 8 NH₄HSO₄ (wt.%), approximately by an order of magnitude with the substantial increase in the mechanical strength of the films. Details on the electrolyte film casting and ion transport characterization studies have been discussed elsewhere in the literature. However, a brief mention has been made for reference. An open circuit voltage in the range 1.5–1.8 V, obtained for both the batteries, is in very good agreement with the value reported. The cell performance has been studied under varying load conditions. Paper presented at the Third International Conference on Ionic Devices (ICID 2006), Chennai, Tamilnadu, India, Dec. 7–9, 2006.     

α + 8He Elastic Scattering with the Generator-Coordinate Method

 The elastic α + ⁸He phase shifts are calculated with a two-centre generator-coordinate method. The microscopic α and ⁸He internal wave functions are defined in the harmonic-oscillator model. Bound states and resonances of ¹²Be are obtained. Among them, a 4⁺ resonance with a molecular structure should be observable in elastic scattering. The parity dependence of the microscopic phase shifts is analyzed by fitting them with simple potentials. The odd-even effect is similar in the α + ⁸He and α + ⁶He phase shifts for low partial waves but decreases more rapidly with increasing orbital momentum for α + ⁸He. Received May 14, 1999; accepted for publication July 29, 1999     

A first principles study of the adsorption and dissociation of CO<Subscript>2</Subscript> on the δ-Pu (111) surface

A complete understanding of the nature of the 5f electrons has been and continues to be a major scientific problem in condensed matter physics. Bulk and surface electronic structure studies of the actinides as also atomic and molecular adsorptions on the actinide surfaces provide a path towards this understanding. In this work, ab initio calculations within the framework of density functional theory have been used to study the adsorption of molecular CO₂ and the corresponding partially dissociated (CO + O) and completely dissociated (C + O + O) products on the δ-Pu (111) surface. The completely dissociated C + O + O configurations exhibit the strongest binding with the surface (7.92 eV), followed by partially dissociated products CO + O (5.08 eV), with molecular CO₂ adsorption having the lowest binding energies (2.35 eV). For all initial vertically upright orientations, the CO₂ molecule physisorbs or do not bind to the surface and the geometry and orientation do not change. For all initial flat lying orientations chemisorption occurs, with the final state corresponding to a bent CO₂ molecule with bond angles of 117°–130° and the elongation of the CO bond. For CO + O co-adsorption, the stable configurations corresponded to CO dipole moment orientations of 100°–172° with respect to the surface normal and the elongation of the CO bond. The most stable chemisorption cases correspond to anomalously large rumpling of the top Pu layer. The interactions of the CO₂ and CO with the Pu surface have been analyzed using the energy density of states and difference charge density distributions. The nature and the behavior of the 5f electrons have also been discussed in detail in the context of this study.     

Structure,thermal properties,conductivity and electrochemical stability of di-urethanesil hybrids doped with LiCF<Subscript>3</Subscript>SO<Subscript>3</Subscript>

Variable chain length di-urethane cross-linked poly(oxyethylene) (POE)/siloxane hybrid networks were prepared by application of a sol-gel strategy. These materials, designated as di-urethanesils (represented as d-Ut(Y′), where Y′ indicates the average molecular weight of the polymer segment), were doped with lithium triflate (LiCF₃SO₃). The two host hybrid matrices used, d-Ut(300) and d-Ut(600), incorporate POE chains with approximately 6 and 13 (OCH₂CH₂) repeat units, respectively. All the samples studied, with compositions ∞ > n ≥ 1 (where n is the molar ratio of (OCH₂CH₂) repeat units per Li⁺), are entirely amorphous. The di-urethanesils are thermally stable up to at least 200 °C. At room temperature the conductivity maxima of the d-Ut(300)- and d-Ut(600)-based di-urethanesil families are located at n = 1 (approximately 2.0 × 10⁻⁶ and 7.4 × 10⁻⁵ Scm⁻¹, respectively). At about 100 °C, both these samples also exhibit the highest conductivity of the two electrolyte systems (approximately 1.6 × 10⁻⁴ and 1.0 × 10⁻³ Scm⁻¹, respectively). The d-Ut(600)-based xerogel with n = 1 displays excellent redox stability.     

Five-Body Calculation of Resonance and Scattering States of the uudd\bar{s} System

The scattering problem of the system, in the standard non-relativistic quark model of Isgur-Karl, is solved for the first time, by treating the large five-body model space, including the NK scattering channel, accurately with the Gaussian expansion method and the Kohn-type coupled-channel variational method. The calculated NK scattering phase shift shows no resonance in the energy region of the reported pentaquark Θ⁺(1540) that is, at 0–500 MeV above the NK threshold (1.4–1.9 GeV in mass). The phase shift does show two resonances just above 500 MeV: a broad ⁺ resonance with a width of Γ ∼ 110 MeV located at ∼ 520 MeV (∼ 2.0 GeV in mass) and a sharp ⁻ resonance with Γ = 0.12 MeV at 540 MeV.     

Four-Nucleon States in the Continuum: A Means to Probe the Nucleon-Nucleon Interaction

 Four-nucleon states in the continuum are studied through exact microscopic calculations based on the solution of the AGS equations for four nonrelativistic quantum particles. Our studies include calculations of cross sections and analyzing powers for all two-body reactions of interest, but here we only show results for n ³He → n ³He. The NN interactions we use are Bonn-CD, Nijmegen II, and Bonn-B. Compared to existing quality data, one finds large discrepancies and some sensitivity to the choice of NN force model. The calculated n + ³He elastic phase shifts show a very strong inelastic resonance at about 0.3 MeV which is not supported by the total cross-section data. This result is due to the existence of a ³ P ₀ (0⁻) resonance in isospin I = 0 at this energy and the undesirable coincidence of n + ³He and p + ³H thresholds in our calculation due to lack of Coulomb repulsion between protons. This interpretation is supported by R-matrix analyses of the data on the basis of coincident thresholds. Calculated 0⁺ and 0⁻ states are compared with modified R-matrix analyses. Received October 30, 2001; accepted for publication November 7, 2001     

Measurement of low-mass e+e? pair production in 1 and 2?A?GeV C–C collision with HADES

HADES is a secondary generation experiment operated at GSI Darmstadt with the main goal to study dielectron production in proton, pion and heavy ion induced reactions. The first part of the HADES mission is to reinvestigate the puzzling pair excess measured by the DLS collaboration in C + C and Ca + Ca collisions at 1 A GeV. For this purpose dedicated measurements with the C + C system at 1 and 2 A GeV were performed. The pair excess above a cocktail of free hadronic decays has been extracted and compared to the one measured by DLS. Furthermore, the excess is confronted with predictions of various model calculations. Also at Panstwowa Wyzsza Szkola Zawodowa, 33-300 Nowy Sacz, Poland Also at Dipartimento di Fisica e Astronomia, Università di Catania, 95125 Catania, Italy Also at Universidade de Coimbra, Coimbra, Portugal Also at ISEC Coimbra, Coimbra, Portugal Also at Dipartimento di Fisica, Università di Milano, 20133 Milano, Italy     

Model for Topological Fermions

 We introduce a model designed to describe charged particles as stable topological solitons of a field with values on the internal space S ³. These solitons behave like particles with relativistic properties like Lorentz contraction and velocity dependence of mass. This mass is defined by the energy of the soliton. In this sense this model is a generalization of the Sine-Gordon model¹(We do not chase the aim to give a four-dimensional generalization of Coleman’s isomorphism between the Sine-Gordon model and the Thirring model which was shown in 2-dimensional space-time) from 1 + 1-dimensions to 3 + 1-dimensions, from S ¹ to S ³. For large distances from the centre of solitons this model tends to a dual U(1)-theory with freely propagating electromagnetic waves. Already at the classical level it describes important effects, which usually have to be explained by quantum field theory, like particle-antiparticle annihilation and the running of the coupling. Received November 30, 1999; revised June 20, 2000; accepted for publication October 2, 2000     

Theoretical study of the electronic structure of LiNa and LiNa<Superscript>+</Superscript> molecules

Adiabatic potential energy, spectroscopic constants, dipole moments, and vibrational levels of the lowest electronic states of the alkali dimer LiNa molecule dissociating into Na (3s, 3p, 4s, 3d, and 4p) + Li (2s, 2p, 3s, and 3p) in ^1,3Σ, ^1,3Π, and ^1,3Δ symmetries are presented. Adiabatic results are also reported for ²Σ, ²Π, and ²Δ electronic states of the molecular ion LiNa⁺ dissociating into Li (2s, 2p, 3s, and 3p) + Na⁺ and Li⁺  + Na(3s, 3p, 4s, 3d, and 4p). We use an ab initio approach involving a non-empirical pseudopotential for the Li (1s²) and Na (1s²2s²2p⁶) cores and core valence correlation correction. A very good agreement is obtained for some lowest states of the LiNa and LiNa⁺ molecules for spectroscopic constants with the available theoretical works. The existence of numerous avoided crossings between electronic states of ²Σ and ²Π symmetries is related to the charge transfer process between the two ionic systems Li⁺Na and LiNa⁺.     

Luminescent silicon nanoparticles with magnetic properties – production and investigation

Silicon nanoparticles (nSi) with unusual properties were studied. After suggested treatment they became luminescent and also acquired a magnetic moment. Nanoparticles were prepared by laser pyrolysis of silane in a gas flow reactor followed by chemical treatment in methanol (MeOH) + HF + FeCl₃ solution. After the treatment. nanoparticles gained stable luminescence with the peak position dependence on the excitation wavelength. With increasing of the excitation wavelength from 365 to 456 nm, the photoluminescent peak shifted from 632 to 665 nm. Luminescence of such nanoparticles had blue shift in comparison with the nanoparticles etched in widely-used solution for the silicon—MeOH + HF + HNO₃. Moreover, after such treatment the magnetic moment of nanoparticles appeared, which is not inherent for the as-prepared nSi. Multifunctional silicon nanoparticles with both stable luminescence and magnetic moment at the same time are perspective for biology and medicine use as the optical and magnetic markers.     

Evaluation of the rate constants of dissociative and ternary recombination reactions of argon ions on the basis of the results of ballistic experiments

AbstractExperimental data on the change in the electron density in the wake of a ballistic object traveling at velocities V _∞=3.4–4.9 km/s in argon at pressures p _∞=30–100 Torr are processed and analyzed. A reaction scheme is proposed which takes into account the recombination of charged particles, processes of ionic conversion, and the excited states of the atom. The solution of the equations of a nonequilibrium boundary layer for flow in the wake is used to formulate the inverse problem of determining the rate constants for dissociative recombination Ar ₂ ⁺ +e→Ar+Ar and ternary recombination Ar⁺+e+Ar→Ar+Ar. The “nearest-neighbor” approximation is used to obtain theoretically an expression for the ternary recombination coefficient as a function of temperature and pressure. Numerous solutions of inverse problems and a comparison with experiments demonstrates the validity of the expression obtained for the ternary recombination coefficient. It is shown that this expression is valid for moderate pressures and complements the Pitaevskii result for low pressures and the Langevin result for high pressures. Zh. Tekh. Fiz. 67, 12–18 (May 1997)     

Nonlinear fractional relaxation

We define a nonlinear model for fractional relaxation phenomena. We use ε-expansion method to analyse this model. By studying the fundamental solutions of this model we find that when t → 0 the model exhibits a fast decay rate and when t → ∞ the model exhibits a power-law decay. By analysing the frequency response we find a logarithmic enhancement for the relative ratio of susceptibility.     

Electrical conductivity response and sensitivity of ZSM-5, Y,and mordenite zeolites towards ethanol vapor

This work is an attempt to search for highly selective sensing materials for ethanol vapor. The electrical conductivity response of ZSM-5, Y, and mordenite zeolites towards ethanol vapor have been investigated for the effects of the framework, the charge balancing cation type, and the Si/Al ratio. All zeolites were characterized using XRD, FT-IR, SEM, TGA, BET, and NH₃-TPD techniques. For the effect of the zeolite framework type, H⁺Y has a higher electrical conductivity sensitivity value than that of H⁺MOR because of a greater pore volume and available surface area. For the effect of the charge balancing cation, all NH₄ ⁺ZSM-5 zeolites (Si/Al = 23, 50, 80, 280) show negative responses, whereas the H⁺Y zeolites (Si/Al = 30, 60, 80) and the H⁺MOR zeolites (Si/Al = 30, 200) show positive responses. These differing behaviors can be traced to the electrostatic field at the cation sites in zeolite micropores, and their hydrophilic–hydrophobic character, which affect the adsorption properties of the zeolites. For the effect of Si/Al ratio, the electrical conductivity sensitivity towards the ethanol decreases with increasing Si/Al ratio or decreasing Al content, and there is a lesser degree of interaction between ethanol molecules and the active sites of the zeolites due to its higher hydrophobicity and the lower amount of cations. However, the H⁺Y (Si/Al = 5.1) and the H⁺MOR (Si/Al = 19) zeolites have lower conductivity sensitivity than those of H⁺Y (Si/Al = 30) and H⁺MOR (Si/Al = 30), respectively. The interactions between the C₂H₅OH molecules and the zeolites with respect to the electrical conductivity sensitivity were investigated and verified through infrared spectroscopy.     

Search for excited leptons in e+e- collisions at \sqrt{s}=189–209 GeV

A search for excited lepton production in e⁺e^- collisions was performed using the data collected by the DELPHI detector at LEP at centre-of-mass energies ranging from 189 GeV to 209 GeV, corresponding to an integrated luminosity of approximately 600 pb^-1. No evidence for excited lepton production was found. In searches for pair-produced excited leptons, lower mass limits were established in the range 94–103 GeV/c², depending on the channel and model assumptions. In searches for singly-produced excited leptons, upper limits on the parameter f/Λ were established as a function of the mass.     

Role of composite MnO2 cathode on electrochemical cells based on polymer electrolyte (PEO/NaClO3)

Thin-film sodium-ion-conducting polymer electrolyte based on polyethylene oxide (PEO) system was prepared by solvent casting method. The thin-film electrolytes were characterized by X-ray diffraction (XRD), infrared (IR), cyclic voltammetry (CV) and alternating current conductivity, and Wagner’s polarization method. The complexation of salt with PEO was confirmed by XRD and IR studies. The charge transport of these electrolytes is mainly due to ions, which was confirmed by the transference number experiment. The conductivity studies show that the conductivity value of PEO/NaClO₃ complex increases with the increase of temperature as well as the addition of low molecular weight polyethylene glycol, dimethyl formamide, and propylene carbonate. The electrolyte stability and cell reversibility were analyzed by CV studies. Electrochemical cells have been fabricated with a common cell configuration Na|electrolyte|(MnO₂ + I₂ + C + electrolyte), and their discharge characteristic studies were made through a load 100 kΩ at room temperature. The measured open circuit voltage ranges from 2.80 to 2.54 V with short circuit current ranges from 667 to 1,000 μA and several other cell parameters were evaluated. Finally, the merit of the composite cathode is found with the comparison of the MnO₂ cathode.     

Studying the energy dependence of elliptic and directed flow within a relativistic transport approach

The energy excitation functions of directed flow (v₁) and elliptic flow (v₂) from E_beam=90 A MeV to E_cm=200 A GeV are explored within the UrQMD framework and discussed in the context of the available data. The radial and the elliptic flow of the particles produced in a relativistic heavy-ion collision are intimately connected to the pressure and its gradients in the early stage of the reaction. Therefore, these observables should also be sensitive to changes in the equation of state. To prove this connection, the temporal evolution of the pressure, pressure gradients and elliptic flow are shown. For the flow excitation functions it is found that, in the energy regime below E_beam≤10 A GeV, the inclusion of nuclear potentials is necessary to describe the data. Above 40 A GeV beam energy, the UrQMD model starts to underestimate the elliptic flow. Around the same energy the slope of the rapidity spectra of the proton directed flow develops negative values. This effect is known as the third flow component (“antiflow”) and cannot be reproduced by the transport model. The difference between the data and the UrQMD model can possibly be explained by assuming a phase transition from hadron gas to quark–gluon plasma around E_lab=40 A GeV. This would be consistent with the model calculations, indicating a transition from hadronic matter to “string matter” in this energy range. Thus, we speculate that the missing pressure might be generated by strong interactions in the early pre-hadronic/partonic phase of central Au + Au (Pb + Pb) collisions already at lower SPS energies. PACS 25.75.-q; 25.75.Ld; 25.75.Dw; 25.75.Gz; 24.10.Lx     

New result on the measurement of the direct photon emission in K+→π+π0γ decay

We present a new result on the K⁺→π⁺π⁰γ decay measurement using stopped kaons. The best fit to the decay spectrum comprised of 10 k events gives a branching ratio for the direct photon emission of [3.8±0.8 (stat)±0.7 (syst)]×10^-6 in the π⁺ kinetic energy region of 55 to 90 MeV. This result has been obtained with the assumption that there is no component due to interference with the inner bremsstrahlung. PACS 13.20.Eb, 14.40.Aq     

Absolute frequency and isotope shift measurements of the cooling transition in singly ionized indium

We report greater than two orders of magnitude improvements in the absolute frequency and isotope shift measurements of the In⁺ 5s^{2 1}S₀ (F = 9/2)–5s5p ³P₁ (F = 11/2) transition near 230.6 nm. The laser-induced fluorescence from a single In⁺ in a radio-frequency trap is detected. The fourth-harmonic of a semiconductor laser is used as the light source. The absolute frequency is measured with the help of a frequency comb referenced to a Cs atomic clock. The resulting transition frequencies for isotopes ¹¹⁵In⁺ and ¹¹³In⁺ are measured to be 1 299 648 954.54(10) MHz and 1 299 649 585.36(16) MHz, respectively. The deduced cooling transition frequency difference is 630.82(19) MHz. By taking into account of the hyperfine interaction, the isotope shift is calculated to be 695.76(1.68) MHz.