Function Of H0 Research Articles

On Schrödinger operators modified by [formula omitted] interactions

We study the spectral properties of a Schrödinger operator H0 modified by δ interactions and show explicitly how the poles of the new Green’s function are rearranged relative to the poles of original Green’s function of H0. We prove that the new bound state energies are interlaced between the old ones, and the ground state energy is always lowered if the δ interaction is attractive. We also derive an alternative perturbative method of finding the bound state energies and wave functions under the assumption of a small coupling constant in a somewhat heuristic manner. We further show that these results can be extended to cases in which a renormalization process is required. We consider the possible extensions of our results to the multi center case, to δ interaction supported on curves, and to the case, where the particle is moving in a compact two-dimensional manifold under the influence of δ interaction. Finally, the semi-relativistic extension of the last problem has been studied explicitly.

Three-dimensional analysis of local scouring induced by a rotating ship propeller

The jet induced by a rotating ship propeller can cause scouring of the seabed and consequent deposition of the scoured material nearby. Despite these effects are extremely important for the operability of a harbour, there is currently limited work concerning a detailed investigation of the three-dimensional (3D) characteristics of the bed topography changes induced by the ship propeller. Thus, this paper presents laboratory experiments with the aim of analysing the effects induced by a propeller on a mobile bed, in different conditions of submergence depth (h0) and rotational speed (n). The equilibrium bed surface topography was acquired with the photogrammetry technique combined with a 3D Terrestrial Laser Scanner (TLS), in order to analyse, for the first time, bed elevation data obtained from high-resolution Digital Elevation Models (DEMs). As a result, it was demonstrated that the swirling jet produced by a rotating propeller causes the development of a bed topography not symmetrical with respect to the propeller longitudinal axis, with a deeper scour hole on one side and a higher deposition mound on the other side. Therefore, the scour hole induced by a propeller cannot be assimilated to that produced by a water jet and this behaviour can be noted only with a comprehensive and detailed analysis of a 3D model of the bed topography. Furthermore, it was shown that increasing n for the same h0 (or reducing h0 by keeping n constant) causes a longer, deeper and wider scour hole and a higher deposition mound, with a greater volume of sediments eroded from the bed and deposited nearby the scour hole. To be precise, this is the first study aiming at estimating the eroded and deposited sediment volumes by a propeller jet, thanks to the use of the high-resolution DEMs. The relationships between all the involved variables were analysed, providing equations, graphs and an abacus for the prediction of the effects induced by the propeller as a function of h0 and the Froude number.

Virtual Bound Levels in a Gap of the Essential Spectrum of the Weakly Perturbed Periodic Schrödinger Operator

In the space \({L_{2}(\mathbf{R}^{d}) (d \le 3)}\) we consider the Schrodinger operator \({H_{\gamma}=-{\Delta}+ V(\mathbf{x})\cdot+\gamma W(\mathbf{x})\cdot}\), where \({V(\mathbf{x})=V(x_{1}, x_{2}, \dots, x_{d})}\) is a periodic function with respect to all the variables, \({\gamma}\) is a small real coupling constant and the perturbation \({W(\mathbf{x})}\) tends to zero sufficiently fast as \({|\mathbf{x}|\rightarrow\infty}\). We study so called virtual bound levels of the operator \({H_\gamma}\), i.e., those eigenvalues of \({H_\gamma}\) which are born at the moment \({\gamma=0}\) in a gap \({(\lambda_-,\,\lambda_+)}\) of the spectrum of the unperturbed operator \({H_0=-\Delta+ V(\mathbf{x})\cdot}\) from an edge of this gap while \({\gamma}\) increases or decreases. We assume that the dispersion function of H0, branching from an edge of \({(\lambda_-,\lambda_+)}\), is non-degenerate in the Morse sense at its extremal set. For a definite perturbation \({(W(\mathbf{x})\ge 0)}\) we show that if d ≤ 2, then in the gap there exist virtual eigenvalues which are born from this edge. We investigate their number and an asymptotic behavior of them and of the corresponding eigenfunctions as \({\gamma\rightarrow 0}\). For an indefinite perturbation we estimate the multiplicity of virtual bound levels. In particular, we show that if d = 3 and both edges of the gap \({(\lambda_-,\,\lambda_+)}\) are non-degenerate, then under additional conditions there is a threshold for the birth of the impurity spectrum in the gap, i.e., \({\sigma(H_\gamma)\cap(\lambda_-,\,\lambda_+)=\emptyset}\) for a small enough \({|\gamma|}\).

Monte Carlo study of magnetization dynamics in uniaxial ferromagnetic nanowires in the presence of oscillating and biased magnetic fields.

We examine the dynamic phase transition properties of ferromagnetic uniaxial nanowires with tunable radius r in the presence of both oscillating and biased magnetic fields. Variation of the transition temperature as a function of amplitude h0 of the oscillating field has been analyzed in the absence of magnetic bias hb and at constant oscillation period P. We find that the transition temperature as a function of h0 exhibits an exponential decay behavior. We also investigate the magnetization dynamics in terms of magnetic hysteresis loops as functions of the parameters hb, h0, and P. Our calculations are qualitatively in agreement with the recent experimental results obtained for uniaxial cobalt films in which it was concluded that the bias field hb is the conjugate field of the dynamic order parameter.

Search for a multi-Higgs-boson cascade inW+W−bb¯events with the ATLAS detector inppcollisions ats=8 TeV

A search is presented for new particles in an extension to the Standard Model that includes a heavy Higgs boson H0, an intermediate charged Higgs boson pair H+-, and a light Higgs boson h0. The analysis searches for events involving the production of a single heavy neutral Higgs boson which decays to the charged Higgs boson and a W boson, where the charged Higgs boson subsequently decays into a W boson and the lightest neutral Higgs boson decaying to a bottom--antibottom-quark pair. Such a cascade results in a W-boson pair and a bottom--antibottom-quark pair in the final state. Events with exactly one lepton, missing transverse momentum, and at least four jets are selected from a data sample corresponding to an integrated luminosity of 20.3/fb, collected by the ATLAS detector in proton--proton collisions at sort(s)=8 TeV at the LHC. The data are found to be consistent with Standard Model predictions, and 95% confidence-level upper limits are set on the product of cross section and branching ratio. These limits range from 0.065 pb to 43 pb as a function of H0 and H+- masses, with m(h0) fixed at 125 GeV.

Change in the Acid Hydrolysis Mechanism of Esters Enforced by Strongly Acid Microemulsions

A kinetic study was carried out on the acid hydrolysis of 4-nitrophenylacetate and 4-nitrophenyllaurate in water/HOT/isooctane microemulsions. The substitution of Na+ in the sodium salt of bis(2-ethylhexyl)sulfosuccinate by H+ has permitted us to obtain a functionalized surfactant (HOT) and, consequently, strongly acid microemulsions. The use of HOT-based microemulsions allows us to reach concentrations of H+ in the aqueous core corresponding to a Hammett acidity function of H0 = -2. The rate constant at the interface and the distribution constants of the carboxylic esters throughout the different microenvironments of the microemulsion have been quantified by application of the pseudophase formalism. The results obtained show that the hydrolysis rate constant at the interface increases as the water content of the system decreases. The correlation of the rate constants at the interface of the microemulsion with the Hammett acidity function, H0 (on the basis of the Bunnett-Olsen criterion), has allowed us to confirm that the hydrolysis process takes place via an A2 mechanism for high water contents and through an A1 mechanism for values of W <or= 15 (W = [H2O]/[HOT]).

Hysteretic ac loss of superconducting strips simultaneously exposed to ac transport current and phase-different ac magnetic field

A simple analytical expression is presented for hysteretic ac loss Q of a superconducting strip simultaneously exposed to an ac transport current I0cosωt and a phase-different ac magnetic field H0cos(ωt+θ0). On the basis of the critical state model, the authors calculate Q for small current amplitude I0⪡Ic, for small magnetic field amplitude H0⪡Ic∕2πa, and for arbitrary phase difference θ0, where Ic is the critical current and 2a is the width of the strip. The resulting expression for Q=Q(I0,H0,θ0) is a simple biquadratic function of both I0 and H0, and Q becomes maximum (minimum) when θ0=0 or π (θ0=π∕2).

Ferromagnetic Resonance Effect on Resistivity in Mesoscopic Structures

Rapid advances in controlled preparation techniques have enabled us to fabricate submicron-scale magnetic structures. Considerable interest has been paid to the spin-excitation spectrum of a small magnetic structure. Several experiments using ferromagnetic resonance absorption or Brillouin light scattering have been performed to probe how the reduction of sample size affects the spin-excitation spectrum. The measurement in these experiments is carried out for arrays of small samples. Thus, strictly speaking, the results do not reveal the spectrum of individual samples. Besides the dynamical magnetic properties, electron transport properties in mesoscopic ferromagnetic metals have been the subject of intesive study. Particularly, the magnetoresistance of thin wires containing a magnetic domain wall (DW) has attracted attention with the aim of studying DW dynamics. It has been shown that we can detect DW depinning by measuring the resistance as a function of a magnetic field. Furthermore, it it shown recently that the dynamical property of a DW can be studied by measuring the magnetoresistance. These studies suggest that the magnetoresistance of various magnetic structures may provide us useful informations on their dynamical property. In this short note, we show that the ferromagnetic resonance in small structures can be detected by measuring the magnetoresistance. We consider the resistivity of disordered ferromagnetic metals in the presence of a static field H0 and a uniform rf field with frequency being perpendicular to H0. The rf field excits uniform spinprecession mode, which induces spin-flip scattering of conduction electrons. Although the momentum of conduction electrons is completely conserved in the scattering processes, the mixing of majority and minority spin channels results in an increase of the resistivity in the presence of spin asymmetry in the elastic mean free time. The resonance frequency !0 of the uniform precession mode depends on H0 as well as the demagnetizing field. We expect that the increase of the resistivity becomes large when the ferromagnetic resonance condition 1⁄4 !0 is nearly satisfied. It is shown that the correction to conductivity normalized by the Drude conductivity 0 is given by = 0 / ð hÞ=1⁄2ð!0 Þ þ 2 , where and h are the gyromagnetic ratio and the amplitude of the rf field, respectively, and is the loss parameter of the uniform precession mode. This indicates that we can observe the ferromagnetic resonance in individual ferromagnetic structures by measuring the resistivity as a function of H0. We set h 1⁄4 kB 1⁄4 1 in the following. As an example of magnetic structures in mesoscopic dimensions, we consider a thin cylindrical wire of ferromagnetic metal lying along the z direction. Its length is assumed to be much longer than its width. Although we treat only the thin wire structures, an extention to other structures is straightforward. Let MðrÞ be the magnetization vector in the wire. We consider the case where the static field is applied parallel to the wire, that is, H0 1⁄4 ð0; 0;H0Þ. Thus, the magnetization vector becomes MðrÞ 1⁄4 ð0; 0;M0Þ in the absence of an rf field (M0: saturation magnetization). We apply a uniform rf field hðr; tÞ 1⁄4 ðh cosð tÞ; h sinð tÞ; 0Þ circularly polarized in the xy plane. The magnetization vector obeys the Landau–Lifshitz equation @Mðr; tÞ=@t 1⁄4 Mðr; tÞ Hðr; tÞ, where is the gyromagnetic ratio and H is the total effective field H 1⁄4 H0 þ hþHd. Here, the demagnetizing field Hd is approximately expressed as Hd 1⁄4 ð 2 Mx; 2 My; 0Þ in our long cylindrical structure. We have neglected the skin effect for the rf field by assuming that the width of the wire is much smaller than the penetration depth. The typical penetration depth of ferromagnetic metals is longer than micrometer scale when is of the order of 10 GHz, so that the above assumption safely holds for wire structures of sub-micron scale diameter. We assume that conduction electrons are described by

Decomposition of magnetization processes in complex permeability spectra of 3% SiFe

Complex permeability spectra were measured as a function of the ac field amplitude h0 and the cut angle α with respect to the [001] direction in a rectangular 3% SiFe sample. The spectra for α=0° at a relatively low field amplitude showed Debye-type dispersion with a relaxation frequency of 26.3 kHz. However, at a relatively high field amplitude, the spectra changed to a superposition of two dispersions, one with a relaxation frequency at 3.3 kHz and the other with a relaxation frequency at 26.3 kHz. Irreversible and reversible 180° domain wall motions were considered as mechanisms responsible for the h0 dependent relaxation at 3.3 kHz and the h0 independent relaxation at 26.3 kHz, respectively. From the α dependence of the spectra, we obtained another relaxation of the magnetization rotation, with a relaxation frequency of 0.16 MHz, in the original 180° domains for α⩾70°.

Protonation constants of hydroxybenzenes in hydrochloric acid

The absorption spectra of monohydroxybenzene (Fen), 1,3-dihydroxybenzene (Rez), 1,4-dihydroxybenzene (Hi), 1,2,3-trihydroxybenzene (Pg) and 1,3,5-trihydroxy-benzene (Fg) in aqueous solutions of hydrochloric acid with different values of the Hammett acidity function(H0) have two absorption bands in the region between 190-220 nm and 260-290 nm. This behavior is similar in another mineral acids (H2SO4, H3PO4, HClO4). The absorbance decreases with increasing of acidity (with decreasing of H0 values) because of O-protonation. The absorption maxima shift to longer wave-lengths, and the graphic dependence of the absorption of the second band as a function of H0 gives characteristic S-curves. These curves show the different effect of the acid on the form the protonation of the investigated hydroxybenzenes. The potonation constants of the hydroxybenzenes were calculated: pKFen=-1.95; pKRez=-2.40; pKHi= -1.93; pKPg=-2.95; pKFg=-1.83.

Hysteretic internal fields and critical currents in polycrystalline superconductors

The transport critical current Jc in a polycrystalline superconductor is a hysteretic function of applied magnetic field H0 due to flux trapping by grains. This effect has been observed by several groups and attempts have been made to calculate the intergranular field Hi as a function of the applied H0 in terms of an effective geometrical demagnetization factor D. In general a first-principles calculation of D is very difficult, and furthermore, D is not constant but is itself a hysteretic function of H0. We develop a self-consistent scheme to extract the D and Hi directly from the Jc(H0) data itself. Our model exploits the fact that there are two field ranges for which the demagnetizing field is a simple function of H0. At low virgin fields, in the Meissner state, the susceptibility χv≈−1/4π is well defined, leading to a multiplicative correction: Hi=H0/(1+D4πχv). For fields that have returned from high values, a complete critical state is established and M is well defined—although χv is unknown. This leads to an additive correction: Hi=H0−D4πM for the total field. By matching Jc data in increasing and decreasing fields that satisfy these special cases, it is possible to extract the relevant parameters of the problem without detailed knowledge of the demagnetization geometry. We use this model to analyze data measured on sintered YBa2Cu3O7 superconductive rods.

Stability of an unneutralized rigidly rotating electron beam

An unneutralized rigidly rotating electron beam is absolutely stable if the distribution function is a monotonically decreasing function of H0 −ωLLz and if (ρBωl/c) &amp;lt; 1, where HO and Lz are the single-particle energy and canonical angular momentum, ωL is the angular velocity, and ρB is the radius of an enclosing infinitely conducting cylindrical wall.

The relationship between HR and H0 in moderately concentrated aqueous perchloric and hydrochloric acids

HR is a non-linear function of H0 in 0·1–1·5 M aqueous perchloric and hydrochloric acids; this complicates data extrapolation through these regions but is of use in connection with mechanistic details of acid catalysis.

Protonierungs‐ und Deprotonierungskinetik des Systems Azulen‐Azuleniumkation, ein Beitrag zur Kenntnis der Hammett'schen Ho‐Aciditätsfunktion

AbstractUsing a flashphotolysis‐method to evaluate the rates of the protonation of azulene and the deprotonation of azuleniumcation as a function of H0 the validity of the Hammett H0‐function was examined. Using this technique it was possible to obtain information on the behaviour of the activity coefficients and to show that the Hc‐acidityfunction of Reagan [1] is a better measure of the hydrogen activity than the H0‐function. The dependence of the deprotonation rate on H0 is explained as a consequence of the different behaviour of the activity coefficients of Hammett‐indicators and azulene/azuleniumcation, respectively.

Relaxation phenomena and nuclear magnetic resonance of116In(T 1/2=14s) produced by capture of polarized neutrons in the indium III–V compounds

Polarized116In nuclei have been produced by capture of polarized thermal neutrons in several In compounds. At temperaturesT below 77 °K and magnetic field strengthsH 0 of several kOe, asymmetries of a few percent of the β− decay of the116In ground state could be observed in polycrystalline InP, InAs and InSb, thus indicating the nuclear polarization. Nuclear magnetic resonance signals have been measured with the result for the magnetic moment μ i (116In)=2.7723 (10) nm (uncorrected). β− decay asymmetry and spin lattice relaxation timeT 1 have been studied as a function ofH 0 andT. The effect ofH 0 is to decouple the hyperfine interaction caused by the capture-γ recoil process. However,H 0 has no influence uponT 1, which demonstrates the absence of nuclear relaxation due to paramagnetic impurities.T 1 is determined by quadrupolar relaxation. A quadrupole momentQ(116In)=0.09 (2) b was calculated by comparison of the116In relaxation rates with those of the stable115In isotope in the same compounds. Above 30 °K the temperature dependence of 1/T 1 agrees with a recent theoretical investigation. Below 30 °K the relaxation rate shows an anomalous behaviour, which can be explained by resonance modes due to recoil lattice defects.

Addition to unsaturated carbonyl compounds. Part I. The addition of hydrogen halides to propiolic acid

The kinetics, products, and stereochemistry of the addition of hydrogen chloride, bromide, and iodide to propiolic acid in water have been studied. The addition is predominantly trans to give the cis-3-halogenoacrylic acid. Both the rate of addition and the selectivity giving trans-addition increase with the nucleophilicity of the halide in water, i.e., I– > Br– > Cl–. The reaction is of the first order in propiolic acid and the halide anion, whilst the dependence on acidity appears to be a function of H0. Solvent isotope, salt, and solvent effects have been observed. Addition appears to involve two mechanistic pathways: a major trans-addition via a transient carbanion formed with specific geometry and a minor cis-addition process.

The kinetics of hydrogen isotope exchange reactions. Part XIV. Acid-catalysed tritium exchange and its relationship to the dehydration of t-butyl alcohol

The rate of hydrogen exchange between tritium-containing aqueous perchloric acid and the C–H bond of dissolved t-butyl alcohol has been measured at 25° as a function of acid concentration. The logarithm of the rate constant is a linear function of H0 with slope –1·35. On the assumption that exchange takes place by dehydration to isobutene followed by re-addition of labelled water, the results are used to obtain the rate constant for dehydration of t-butyl alcohol in 0·5M-perchloric acid. The value found agrees with one calculated by combining the previously determined rate constant for hydration of isobutene with the equilibrium constant for the hydration reaction evaluated from thermodynamic data. This agreement supports the view that the route via olefin is the most significant mechanism of hydrogen exchange of t-butyl alcohol in moderately dilute aqueous acid at 25°.

Mössbauer Studies of Spin Flop in Antiferromagnetic Hematite

The antiferromagnetic sublattice magnetizations below the Morin transition temperature TM≈260°K, are parallel and antiparallel to the trigonal axis of rhombohedral α-Fe2O3. Experiments at 80°K, using the Mössbauer technique together with high external magnetic fields on both polycrystalline and single-crystal samples, show that the directions of the sublattice magnetizations flop from along the trigonal axis for the applied field H0&amp;lt;Hc to perpendicular to the trigonal axis for H0&amp;gt;Hc; Hc is found to be 67.5±3 kOe. In the polycrystalline sample this behavior is exhibited through the occurrence of a maximum in the width of the outer lines of the Mössbauer spectrum plotted as a function of H0. In the single crystal, which is oriented so that the gamma rays propagate along the [111] direction, the magnetic transition is clearly observed as a sudden qualitative as well as quantitative change in the appearance of the Mössbauer hyperfine spectrum; below the critical field the Δm=0 lines are the strongest components of the six-line spectrum.