Phenomenological Estimate of the Binding Energy of Heavy Dimesons

 A phenomenological estimate is derived such that the binding energies of dimesons are expressed as combinations of masses of different mesons and baryons. The estimate is almost model-independent, the only major assumptions being that the wave functions of the two light quarks in Λ _c , Λ _b and in the and dimesons are very similar, and that for heavy quarks the QQ interaction is half as strong as the interaction. We get (I = 0, J = 1) bound by about 100 MeV and unbound. Received July 4, 2000; revised November 28, 2000; accepted for publication February 5, 2001     

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.      

Nonlinear diffraction of super-gaussian laser beams in an array of quantum-dot chains with coulomb interaction taken into account

We consider the propagation of super-Gaussian monochromatic laser beams in a three-dimensional array of quantum dots coupled by the tunneling effect along one axis. The electron energy spectrum of the system corresponds to the Hubbard model, where the Coulomb interaction of electrons in quantum dots is taken into account. The field of the laser beam is described by the Maxwell equations, from which a nonhomogeneous wave equation for the vector potential is obtained. In the approximation of slowly varying amplitudes and phases, the wave equation is reduced to a phenomenological equation describing the electromagnetic field in an array of chains of quantum dots. We study the influence of the system parameters and the frequency of the laser-beam field on the propagation in the medium by solving numerically the phenomenological equation. We obtain the dependence of the factor characterizing the diffraction blooming of the beam in an array of chains of quantum dots on the parameters of the system’s electron energy spectrum.     

A Fast Algorithm for Wave Propagation from a Plane or a Cylindrical Surface

The newly developed Taylor-Interpolation-FFT (TI-FFT) algorithm dramatically increases the computational speeds for millimeter wave propagation from a planar (cylindrical) surface onto a “quasi-planar” (“quasi-cylindrical”) surface. Two different scenarios are considered in this article: the planar TI-FFT is for the computation of the wave propagation from a plane onto a “quasi-planar” surface and the cylindrical TI-FFT is for the computation of wave propagation from a cylindrical surface onto a “quasi-cylindrical” surface. Due to the use of the FFT, the TI-FFT algorithm has a computational complexity of O(N ² log₂  N ²) for an N × N computational grid, instead of N ⁴ for the direct integration method. The TI-FFT algorithm has a low sampling rate according to the Nyquist sampling theorem. The algorithm has accuracy down to −80 dB and it works particularly well for narrow-band fields and “quasi-planar” (“quasi-cylindrical”) surfaces.     

Separation of different wave components in the Bethe–Salpeter wave function

The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by L–S coupling analysis. The cancelation formula is given, by which the terms with pure L = J + 1 wave components in the Salpeter wave function for the bound state with h_P=(-1)^J\eta_{\rm P}=(-1)^J can be obtained by separating the L = J − 1 wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of L = J − 1 and J + 1 wave states, and for solving the Salpeter equation exactly without approximation.     

Prediction and Measurement of Electron Density and Collision Frequency in a Weakly Ionised Pine Fire

Pine litter flame is a weakly ionised medium. Electron-neutral collisions are a dominant form of particle interaction in the flame. Assuming flame electrons to be in thermal equilibrium with neutrals and average electron-neutral collision frequency to be much higher than the plasma frequency, the propagation of microwaves through the flame is predicted to suffer signal intensity loss. A controlled fire burner was constructed where various natural vegetation species could be used as fuel. The burner was equipped with thermocouples and used as a cavity for microwaves with a laboratory quality network analyzer to measure wave attenuation. Electron density and collision frequency were then calculated from the measured attenuation. The parameters are important for numerical prediction of electromagnetic wave propagation in wildfire environments. A controlled pine litter fire with a maximum flame temperature of 1080 K was set in the burner and microwaves (8–10.5 GHz) were caused to propagate through the flame. A microwave signal loss of 1.6–5.8 dB was measured within the frequency range. Based on the measured attenuation, electron density and electron-neutral collision frequency in pine fire were calculated to range from 0.51–1.35 × 10¹⁶ m⁻³ and 3.43–5.97 × 10¹⁰ s⁻¹ respectively.     

Visualization of focusing–refocusing cycles during filamentation in BaF<Subscript>2</Subscript>

Filamentation occurs within a 1.5 cm-long crystal of BaF₂ during the propagation of intense, ultrashort (40 fs) pulses of 800 nm light; a systematic study as a function of incident power enables us to extract quantitative information on laser intensity within the condensed medium, the electron density and the six-photon absorption cross section. At low incident power, a single filament is formed within the crystal; two or more filaments are observed along the direction transverse to laser propagation at higher incident powers. Further, due to fluorescence from six-photon absorption (6PA), we are able to map the intensity variation in the focusing–refocusing cycles along the direction of laser propagation. At still higher incident powers, we observe splitting of multiple filaments. By measuring the radius (L _min) of single filament inside BaF₂, we obtain estimates of peak intensities (I _max) and electron densities (ρ _max) to be 3.26×10¹³ W cm⁻² and 2.81×10¹⁹ cm⁻³, respectively. Use of these values enables us to deduce that the 6PA cross-section in BaF₂ is 0.33×10⁻⁷⁰ cm¹² W⁻⁶ s⁻¹.     

Persistence Properties and Unique Continuation of Solutions to a Two-component Camassa–Holm Equation

We will consider a two-component Camassa–Holm system which arises in shallow water theory. The present work is mainly concerned with persistence properties and unique continuation to this new kind of system, in view of the classical Camassa–Holm equation. Firstly, it is shown that there are three results about these properties of the strong solutions. Then we also investigate the infinite propagation speed in the sense that the corresponding solution does not have compact spatial support for t > 0 though the initial data belongs to C₀^￥(\BbbR)C_{0}^{\infty}(\Bbb{R}).     

Three-dimensional simulation of laser–plasma-based electron acceleration

A sequential three-dimensional (3D) particle-in-cell simulation code PICPSI-3D with a user friendly graphical user interface (GUI) has been developed and used to study the interaction of plasma with ultrahigh intensity laser radiation. A case study of laser–plasma-based electron acceleration has been carried out to assess the performance of this code. Simulations have been performed for a Gaussian laser beam of peak intensity 5 × 10¹⁹ W/cm² propagating through an underdense plasma of uniform density 1 × 10¹⁹ cm^− 3, and for a Gaussian laser beam of peak intensity 1.5 × 10¹⁹ W/cm² propagating through an underdense plasma of uniform density 3.5 × 10¹⁹ cm^− 3. The electron energy spectrum has been evaluated at different time-steps during the propagation of the laser beam. When the plasma density is 1 × 10¹⁹ cm^− 3, simulations show that the electron energy spectrum forms a monoenergetic peak at ~14 MeV, with an energy spread of ±7 MeV. On the other hand, when the plasma density is 3.5 × 10¹⁹ cm^− 3, simulations show that the electron energy spectrum forms a monoenergetic peak at ~23 MeV, with an energy spread of ±7.5 MeV.     

Magnetic properties of doped GdI2

Motivated by the recent experimental studies on layered ferromagnetic metallic system GdI₂  and its doped variant GdI₂H_x we develop a model to understand their ground state magnetic phase diagram. Based on first principle electronic structure calculations we write down a phenomenological model and solve it under certain approximations to obtain the ground state energy. In the process we work out the phase diagram of the correlated double exchange model on a triangular lattice for the specific band structure at hand.     

Time-resolved processes in a pulsed electrical discharge in argon bubbles in water

A phenomenological picture of a pulsed electrical discharge in gas bubbles in water is produced by combining electrical, spectroscopic, and imaging characterization methods. The discharge is generated by applying 1 m\mu s pulses of 5 to 20 kV between a needle and a disk electrode submerged in water. An Ar gas bubble surrounds the tip of the needle electrode. Imaging, electrical characteristics, and time-resolved optical emission spectroscopic data suggest a fast streamer propagation mechanism and the formation of a plasma channel in the bubble. Comparing the electrical and imaging data for consecutive pulses applied to the bubble at a frequency of 1 Hz indicates that each discharge proceeds as an entirely new process with no memory of the previous discharge aside from the presence of long-lived chemical species, such as ozone and oxygen. Imaging and electrical data show the presence of two discharge events during each applied voltage pulse, a forward discharge near the beginning of the applied pulse depositing charge on the surface of the bubble and a reverse discharge removing the accumulated charge from the water/gas interface when the applied voltage is turned off. The pd value of ~ 300–500 torr cm, the 1 μs long pulse duration, low repetition rate, and unidirectional character of the applied voltage pulses make the discharge process here unique compared to the traditional corona or dielectric barrier discharges.     

Effect of different types of pseudopotentials on study of electronic dispersion for graphene and a (5,5) SWCNT

We study the electronic dispersion for a graphene sheet and also a (5,5) single wall carbon nanotube (SWCNT) by using the PWscf code from the ‘Quantum Espresso’ package. Two different types of pseudopotentials, ‘norm conserving’ and ‘ultra soft’, have been employed and the results are more or less similar up to the Fermi level. By energy relaxation, it was found that, if the inter-layer distance of graphite expands up to 4.5 times its in-layer (hexagonal) lattice constant, then each layer can be considered as an individual graphene sheet and, in a bundle of (5,5) SWCNTs, the optimum separation between the tubes’ centers is about 19 a.u. and, if it expands to 22 a.u., then a single wall tube consideration can be made. The calculated band structure and density of states (DOS) for the (5,5) SWCNT show that in the vicinity of the Fermi level there is no energy gap (so that it is metallic) and there is a general agreement between them and zone-folding studies or other ab initio methods in the literature. The effects of curvature on the band shifts and DOS have been considered, and they magnify the departure from Mintmire and White’s universal prediction. PACS  71.20.Tx; 71.15.Mb; 73.61.Wp     

Inelastic x-ray scattering measurements of dynamical cross-over in liquid As2Se3 at high temperature and high pressure

Liquid As₂Se₃ undergoes the semiconductor-metal transition with increasing temperature when pressure is applied to avoid evaporation of the liquid. To investigate the atomic dynamics of liquid As₂Se₃, we have carried out inelastic x-ray scattering experiments of this system at 1073 K and 6 MPa and obtained the dynamic structure factor S(Q,E), from approximately 1.6 nm⁻¹ to 11 nm⁻¹, where Q and E are momentum and energy transfer, respectively. The excitation energy in the semiconducting state at 1073 K disperses as fast as the ultrasonic sound velocity at Q < 2.5 nm⁻¹ but at Q > 2.9 nm⁻¹ it disperses approximately 1.8 times faster. We analyzed S(Q,E) at 1073 K using a simple viscoelastic model and discussed Q dependence of the propagation of the acoustic mode.     

Phonons and photons in crystals

The simultaneous propagation of phonons and photons in an insulator is discussed from both phenomenological and quantum mechanical points of view. A phenomenological form of the energy of an insulator is first supposed from which is obtained the equation of propagation of modes involving nuclei displacements and an electric field. This equation is then studied, mainly in the vicinity of q=0, in order to show how various limits lead to different types of propagation. The phenomenological equations are then justified from a microscopic point of view. The proof goes in two steps. A linear screened response function of the electrons in a solid is first assumed; one then proves that all the coefficients entering into the phenomenological equations may be obtained from the sole knowledge of this response function and of the charge of the nuclei. The existence of the response function is then justified from a many-body point of view. Finally, the necessary relations between the phenomenological coefficients are proved. Some other possible applications of the microscopic equations are also discussed at the end of the paper.     

Solid Substrate–Room Temperature Phosphorimetry for the Determination of Trace Terbutaline Sulfate Based on Its Inhibition Oxidation of Rhodamine 6G by Sodium Periodate

When 1.00 mol l⁻¹ I⁻ is used as ion perturber, rhodamine 6G (Rh 6G) can emit strong and stable room temperature phosphorescence (RTP) on filter paper substrate in KHC₈H₄O₄–HCl buffer solution (pH = 3.50), heated at 70 °C for 10 min. NaIO₄ can oxidize Rh 6G, which makes the RTP signal quench. Terbutaline sulfate (TBS) can inhibit NaIO₄ from oxidizing Rh 6G, which makes the RTP signal of Rh 6G enhance sharply. The content of TBS is linear correlation to ΔIp of the system. Based on the facts above, a new inhibition solid substrate-room temperature phosphorimetry (SS-RTP) for the determination of trace TBS has been established. The linear range of this method is 0.0104–2.08 pg spot⁻¹ (corresponding concentration: 0.026–5.2 ng ml⁻¹, with a sample volume of 0.4 μl) with a detection limit (L.D.) of 2.6 fg spot⁻¹ (corresponding concentration: 6.5 × 10⁻¹² g ml⁻¹), and the regression equation of working curve is ΔIp = 2.040 + 54.54 m_TBS (pg spot⁻¹), n = 6, correlation coefficient is 0.9994. For the samples containing 0.0104 pg spot⁻¹ and 2.08 pg spot⁻¹ TBS, the relative standard deviation (RSD) are 3.8% and 2.3% (n = 8), respectively, indicating good precision. This method has been applied to determination of trace TBS in the practical samples with satisfactory results. The reaction mechanism of NaIO₄ oxidizing Rh 6G to inhibit SS-RTP for the determination of trace TBS is also discussed.     

Nonlinear transformation of a spectrum of femtosecond laser pulses in a gas-filled microcapillary

Features of light pulse propagation and nonlinear optical transformation of the spectrum generated by titanium-sapphire laser pulses (τ_0.5 = 27 fs, λ₀ = 790 nm) have been studied experimentally in a 50-cm cylindrical hollow waveguide (microcapillary with 280-μm diameter core) filled with gaseous molecular nitrogen and helium. Stable guided propagation of light pulses with an intensity of ~1.5⋅10¹⁴ W/cm² in the fundamental EH₁₁ mode of the gas-filled capillary has been demonstrated. Exact focusing of the laser light made it possible to obtain rather high relative (≥95%) and absolute (~60%) energy transmission efficiencies for the pulses at gas pressures equal to or lower than 760 Torr. A method to determine the nonlinear phase shift of the pulses has been proposed. Values of the nonlinear refractive index n₂ ≈ 4.5⋅10^–23 cm²/(W⋅Torr) (N₂) and n₂ ≈ 2.8⋅10^–23 cm²/(W⋅Torr) (He) have been found. A short-wavelength shift in addition to the Kerr nonlinearity has been shown to be contributed by the generated electron plasma at high pulse intensities (≥10¹⁴ W/cm²).     

Estimation of applicability of perturbation theory to solution of the kinetic Boltzmann equation in calculations of charge-carrier relaxation time in isotropic polycrystalline <Emphasis Type="Italic">p-</Emphasis>silicon

A condition is formulated for application of perturbation theory to solution of the kinetic Boltzmann equation in calculations of charge-carrier relaxation time in an isotropic silicon polycrystal, where holes are scattered both by a disordered system of potential barriers formed on crystallite surfaces and by a disordered lattice of silicon atoms characterized by local ordering. The total specific resistance of p-type isotropic polycrystalline silicon is estimated for the grain size d = 230 ?, temperature T = 300 K, and hole concentration p = (5.0 – 10.0) ⋅ 10¹⁹ cm⁻³. The calculated specific resistances of p-type polycrystalline silicon are compared with the experimental data.     

Biophysical Studies on the Interactions of a Classic Mitochondrial Uncoupler with Bovine Serum Albumin by Spectroscopic,Isothermal Titration Calorimetric and Molecular Modeling Methods

The interaction between a classic uncoupler (2,4-dinitrophenol, DNP) and bovine serum albumin (BSA) was investigated by fluorescence spectroscopy under the physiological conditions. The fluorescence quenching constants were calculated by the Stern-Volmer equation, and based upon the temperature dependence of quenching constants, it was proved that DNP caused a static quenching of the intrinsic fluorescence of BSA. Owing to the static quenching mechanism, different associative binding constants at various temperatures were determined and thus the thermodynamic parameters, namely enthalpy (ΔH = −21.12 kJ mol⁻¹) and entropy changes (ΔS = 23.51 J mol⁻¹ K⁻¹) could be calculated based on the binding constants. Moreover, the enthalpy and entropy changes are consistent with the “Enthalpy-Entropy Compensation” equation obtained from our previous work. The negative enthalpy and positive entropy indicated that the electrostatic interactions played a major role in DNP-BSA binding process. Site marker competitive displacement experiments were carried out by using fluorescence and isothermal titration calorimetry (ITC) methods. These results showed that DNP bound with high affinity to Sudlow’s site I (subdomain IIA) of BSA. The distance (r = 3.78 nm) between donor (BSA) and acceptor (DNP) was obtained according to the mechanism of fluorescence resonance energy transfer (FRET). Furthermore, the results of synchronous fluorescence and circular dichroism (CD) spectroscopic studies indicated that the microenvironment and the secondary conformation of BSA were altered. The above results were supported by theoretical molecular modeling methods.     

Three-Body Dynamics in One Dimension: A Test Model for the Three-Nucleon System with Irreducible Pionic Diagrams

 We formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As an application, we develop a spinless, one-dimensional (1-D) model that mimics three-nucleon dynamics in one dimension. Using simple two-body potentials that reproduce the deuteron binding, we obtain that the three-body system binds at about 7.5 MeV. We then consider two types of residual pionic corrections in the dynamical equation; one related to the 2π-exchange three-body diagram, the other to the 1π-exchange three-body diagram. We find that the first contribution can produce an additional binding effect of about 0.9 MeV. The second term produces smaller binding effects, which are, however, dependent on the uncertainty in the off-shell extrapolation of the two-body t-matrix. This presents interesting analogies with what occurs in three dimensions. The paper also discusses the general three-particle quantum scattering problem, for motion restricted to the full line. Received March 5, 2002; accepted July 19, 2002