Modelling of kink nucleation and propagation along steps of finite length

A discrete model for kink nucleation and propagation along steps of finite length is developed. The step velocities were calculated as a function of the step length, the first order rate constants, k_s and k_K, for kink nucleation and propagation respectively, and a kink interaction parameter. The two limiting kinetic regimes of short and long steps as well as the intermediate transitional regime were considered. For very short steps, S² ? $\text{k}{}_{\mathrm{<mtext>K</mtext>}}\text{k}{}_{\mathrm{<mtext>s</mtext>}}$, the velocity varied directly with the number of sites S. Steps which met the criterion S² ? $\text{k}{}_{\mathrm{<mtext>K</mtext>}}\text{k}{}_{\mathrm{<mtext>s</mtext>}}$, were shown to have velocities on the order (2k_Kk_s)^{$\text{1}\text{2}$}, independent of step length. Step velocities were constant over large ranges of the kink interaction parameter. The steps were shown to be “sharp” for zero or attractive kink interaction, but with sufficiently large kink repulsion very diffuse steps could be formed. The density of kinks and numbers of kinks nucleated along an atom row were also calculated.     

Catalytic decomposition of DCOOD studied by reactive scattering of a modulated DCOOD nozzle beam by a polycrystalline platinum surface in ultra high vacuum

The catalytic decomposition of formic acid by a polycrystalline platinum surface was studied by use of modulated molecular beam techniques with mass spectrometric phasesensitive detection. Kinetic information about elementary surface reaction steps was obtained. The formation of CO₂ was found to be a monomolecular, whereas that of D₂ was a bimolecular process. The resulting reaction mechanism may be described as follows:

The rate constants in dependence from the surface temperature t₀ are $\text{η = 7.1 × 10}{}^3\text{exp}\text{(?}\text{9.9}\text{RT}{}_0\text{kcal/mole}\text{),}$ The sticking probability η is provided by the temperature dependence of the intensity of the nonreactive scattered formic acid molecules; the rate constants k_d1 and k_d2 are derived from the measured phase shift between reactive and nonreactive scattered particles. From the phase angle ?, the average surface residence time τ of the intermediates is computed: 3.7 ? τ_DCOO ? 0.41 msec (418 ? T₀ ? 505 K), 31.8 ? τ_D ? 11.6 msec (418 ? T₀ ? 460 K). The difference between τ_D and τ_DCOO is because of the different molecularity of desorption.     

Stochastic saturation of three-drift-wave interaction at finite parallel wavelength

The interaction of three drift waves is considered at finite parallel wavelength. The coupling to ion sound waves has a profound effect on the saturation levels. For k_|L_n～ 1. turbulent amplitudes are of the magnitude $\text{eΦ?T}{}_{\mathrm{e}}\text{～}\text{1}\text{k}{}_{\mathrm{\perp }}\text{L}{}_{\mathrm{n}}$ as predicted by usual estimates, in contrast to previous studies neglecting this effect.     

Multidimensional elastic waves excited by oscillating domain walls

Magnetoelastic excitations with a fine structure in the 50kHz range have been observed in the study of the domain wall resonance (DWR) in magnetic garnet thin films. DWR excites standing transverse elastic waves which have a resonance frequency given by $\text{f=}\text{nv}\text{2d}$, where f is the frequency, n is an integer, v=3.5×10⁵ cm/sec is the transversal velocity of the elastic wave, and d=0.05 cm is thickness of the film/substrate system. A fine structure associated with each of these modes has been identified as due to two dimensional bulk elastic waves by using a set of parallel microstrip lines. The dispersion relation of these elastic waves is ω²=v²(k²₁+k²₂), where ω is the radial frequency, k₁ and k₂ are the wave vectors in the orientation perpendicular and parallel to the sample surface respectively. In the case of k₁?k₂, $\text{f=}\text{f}{}_0\text{+v}{}^2\text{k}{}^2{}_2\text{f}{}_0$, where f₀ is the resonance when k₂=0. The experimental results are in excellent agreement with this model. A linear dispersion, observed when using a shorted slot-line structure, is understood as the excitation of three dimensional modes due to the complex structure of the slot-line and the sample geometry.     

Eigenfunction expansions of operators admitting separation of an infinite number of variables

Let A_k be a self-adjoint operator in a Hilbert space H_k (k = 1, 2, …) and let $\text{L}$ be an operator of the form $\text{L}\text{= A}{}_{\mathrm{r}}\text{? 1 ? 1 ? … + 1 ? A}{}_2\text{? 1 ? 1 ? … + …}$ acting in the infinite tensor product $\text{?}\text{k=1}\text{∞}\text{H}{}_{\mathrm{k}}$. We construct the spectral theory of these operators. In particular, the expansion is generalized eigenvectors of this operator is constructed using the eigenvectors of the operators A_k.     

Contributions of operators of twist two and higher in large n moments of structure functions

Though high twist terms are becoming important as x→1, or equivalently, in large n moments, their detection in this regime in deep inelastic lepton scattering needs special caution. The high order terms in the twist two component are strongly dependent on n; one finds that at $\text{Q}{}^2\text{?Q}{}^2{}_7\text{?Λ}{}^2\text{a}{}_{\mathrm{k}}\text{exp}\text{[α}{}_{\mathrm{k}}\text{(}\text{log}\text{n)}{}^{\mathrm{<mtext>2?1</mtext><mtext>k</mtext>}}\text{(}\text{1+b}{}_{\mathrm{k}}\text{log}\text{n}\text{)]}$ the perturbative expansion is invalid whereas higher twist terms are important at $\text{Q}{}^2\text{?Q}{}_1{}^2\text{= Λ}{}^2\text{nC}$. Since $\text{Q}{}_7{}^2$ grows very fast with n the necessary requirement for any deep inelastic phenomenological analysis, namely $\text{Q}{}_1{}^2\text{?Q}{}_7{}^2$, cannot hold for too large moments. The scheme dependence of a_k, α_k and b_k is also discussed.     

The asymptotics of the gap in the Mathieu equation

We provide a simple proof that the kth gap, Δ_k, for the Mathieu operator $\text{?d}{}^2\text{dx}{}^2\text{+ 2κ}\text{cos}\text{(2x)}$ is $\text{Δ}{}_{\mathrm{k}}\text{= 8(}\text{κ}\text{4}\text{)}{}^{\mathrm{k}}\text{[(k ? 1)!]}{}^{\mathrm{?2}}\text{(1 + o(k}{}^{\mathrm{?2}}\text{))}$, a result obtained (up to the value of an integral) by Harrell. The key observation is that what is involved is tunneling in momentum space.     

Core-level reflectance spectroscopy of germanium by means of synchrotron radiation

Reflectance spectra due to 3d core-levels of Ge have been measured in the photon-energy region from 29 to 38 eV by means of synchrotron radiation. Second-energy-derivative spectra have newly shown pairs of doublet structures with energy separation of the Ge $\text{3d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{?}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ core-level splitting. The observed doublet structures are assigned to the transitions from the $\text{3d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ and $\text{3d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ core-levels to the flat regions of the conduction band around the particular symmetry points of Δ₆^c and L(₃^c(L₆^c, L_4,5^c).     

Dependence on interatomic distance of exchange coupling in rare-earth Al2 compounds

The effect of pressure on the Curie temperature of the heavy rare-earth dialuminides has been measured up to 3.5 kbar. The derivatives dT_c/d_p are 0.00(4), 0.09, 0.21, 0.39, 0.60 and 0.71 K/kbar respectively for TmAl₂ ErAl₂, HoAl₂, DyAl₂, TbAl₂ and GdAl₂ thus indicating a clear positive correlation between dT_c/dp and the de Gennes factor G. The results are discussed in terms of the RKKY model. However, the phenomenological parameter D/d, where D is the nearest-neighbour R-R distance and d the diameter of the 4f orbital, is used to reflect the non-δ-function character of the sf-coupling parameter Г. The experimental values of Г²D² and T_p/G are found to decrease linearly with increasing D/d. This is in keeping with the RKKY proportionality of $\text{T}{}_{\mathrm{c}}\text{?T}{}_{\mathrm{p}}$ to Γ²E^?1_FG. For GdAl₂, TbAl₂ and DyAl₂ the quantity $\text{?}\text{(}\text{d}\text{T}{}_{\mathrm{c}}\text{d}\text{p}\text{)}\text{k}{}_{\mathrm{l}}\text{(}\text{D}\text{d}\text{)}\text{G}$ coincides within the error limits with the slope of the T_p/G vs D/d plot.     

A simplified Fokker-Planck operator for unlike-particle collisions

The linearized Fokker-Planck operator reads $\text{C}{}^1{}_{\mathrm{jk}}\text{= C(f}{}_{\mathrm{1j}}\text{, f}{}_{\mathrm{0k}}\text{)}$. The first term is rather simple, but the second one is very complicated. A much simpler - though exact - form of C(f_0j, f_1k) is proposed, for a special class of f_1k occuring in diffusion theory.     

Effect of constant mismatch on stimulated scattering in laser plasma interactions

The presence of a constant wave number mismatch (Δk) renders the asymptotic steady of the backward scattered wave time dependent. While the pump wave is unaffected by the mismatch, the excited waves (with group velocities v₂, v₃) are modulated at the frequency $\text{[}\text{v}{}_2\text{v}{}_3\text{(v}{}_2\text{+ v}{}_3\text{)}\text{] Δk}$.     

The A-dependence of J/ψ-particle inclusive distributions

The differential cross sections $\text{d}\text{σ}\text{d}\text{x}$ and $\text{d}\text{σ}\text{d}\text{p}{}_{\mathrm{t}}{}^2$ of inclusive J/ψ production by 43 GeV/c π^? off Be, Cu and W nuclei have been measured. Fitting $\text{d}\text{σ}\text{d}\text{p}{}_{\mathrm{t}}{}^2\text{～ A}{}^{\mathrm{\alpha }}\text{(p}{}_{\mathrm{t}}{}^2\text{)}$ we observed the increase of α with p_t².     

Octet dominance in nonleptonic decays

The question of octet enhancement for the nonleptonic decays is studied within the framework of a current-algebra approach. By writing an unsubtracted dispersion relation for the matrix elements 〈B_k|H_w|B_j〉 and 〈M_k|H_w|M_j〉 (B denoting a $\text{1}\text{2}{}^{\mathrm{+}}$ baryon and M a 0^? meson) in the momentum transfer squared variable t and using the assumption of threshold dominance, namely that two pseudoscalar meson states dominate the absorptive parts of the above matrix elements and that in the chiral limit the meson-baryon and meson-meson scattering amplitudes which enter in the absorptive parts are exactly given by current algebra low energy theorems, it is shown that the above matrix elements are octet enhanced without assuming the octet transformation property for H_w. Further it is shown that the $\text{d′}\text{f′}$ ratio for the octet enhanced matrix elements 〈B_k|H_w|B_j〉 satisfies the relation , where $\text{(}\text{f}\text{d}\text{)}{}_{\mathrm{A}}$ denotes the $\text{f}\text{d}$ ratio of the axial vector current baryon couplings. The implications of this result for the s- and p-wave hyperon non-leptonic decays are discussed.     

Low wavenumber wall pressure measurements using a rectangular membrane as a spatial filter

The response of a rectangular membrane to a convecting random pressure field is interpreted to reveal the inherent wavenumber filtering characteristics of the device. After experimental determination of its resonant response characteristics, one such membrane is used to measure the low wavenumber components of the wall pressure fluctuations beneath a plane turbulent boundary layer. The measurements were made at wavenumbers far below the convective region (k₁ = ω/U_c) but above the acoustic region (k₁ ? ω/c_o). Possible contamination by acoustic and convective ridge effects is considered. The low wavenumber measurements are also compared with values of the wavenumber-frequency pressure spectral density $\text{Φ}{}_{\mathrm{p}}\text{(}\text{k}\text{,ω)}$ obtained by Fourier transforming cross-spectral density data obtained by Blake in the same wind tunnel. From this comparison it is seen that this transformation of Blake's data (based on a Corcos model) grossly overestimates the magnitude of $\text{Φ}{}_{\mathrm{p}}\text{(}\text{k}\text{,ω)}$ in the low-wavenumber region. The measured values of $\text{Φ}{}_{\mathrm{p}}\text{(}\text{k}\text{, c}{}_{\mathrm{o}}\text{)}$ are about 36 dB down from convective ridge levels at the same frequency. The data are also compared with earlier results obtained by Jameson. In a similar frequency range the current data levels are approximately 10 dB higher than those of Jameson.     

The giant Gamow-Teller resonance states

The mean energy of the giant Gamow-Teller resonance state (GTS) is studied, which is defined by the non-energy-weighted and the linearly energy-weighted sum of the strengths for Σ^A_i = 1^τi?σⁱ? Using Bohr and Mottelson's hamiltonian with the ξl· σ force, the difference between the mean energies of GTS and the isobaric analog state (IAS) is expressed as$\text{E}{}_{\mathrm{GTS}}\text{?E}{}_{\mathrm{IAS}}\text{,≈ 2〈π¦Σ}{}^{\mathrm{A}}{}_{\mathrm{i}}\text{=1ξ}{}_{\mathrm{i}}\text{l}{}_{\mathrm{i}}\text{· σ}{}_{\mathrm{i}}\text{¦π〉/ (3T}{}_0\text{-4(k}{}_{\mathrm{\tau }}\text{?k}{}_{\mathrm{\sigma \tau }}\text{) T}{}_0$. The observed energy systematics is well explained by k_τ?k_{στ≈ 4/A MeV}. The relationship between the mean energies and the excitation energies of the collective states in the random phase approximation for charge-exchange excitations is discussed in a simple model. From the excitation energy systematics of GTS, the values of k_στ and the Migdal parameter g′ are estimated to be about $\text{k}{}_{\mathrm{\sigma \tau }}\text{=}\text{(16–24)}\text{A}\text{MeV and}\text{g′ = 0.49–0.72}$, respectively.     

An inequality for the trace of matrix products

In this paper we consider a product of n complex m×m matrices A_k (k=1,…,n) with singular values ∝^(k)_i ordered in decreasing magnitude. Using the spectral resolution for the operators $\text{A}{}^{\mathrm{dagger;}}{}_{\mathrm{k}}\text{A}{}_{\mathrm{k}}$, it is shown that $\text{|}\text{Tr}\text{A}{}_1\text{…A}{}_{\mathrm{n}}\text{|≤}\text{∑}\text{i=1}\text{m}\text{Φ}\text{i=1}\text{n}\text{α}{}^{\mathrm{(k)}}{}_{\mathrm{i}}\text{.}$This inequality is an extension of an inequality of von Neumann in the simple case that n=2. The necessary and sufficient condition for the equality sign to hold is established. Application of Hölder's inequality leads to further inequalities which can be useful in statistical mechanics.     

On the order of levels in charmonium

We prove a theorem concerning the energies of the 2S and 3D states in a potential $\text{V(r) =}\text{?g}{}^2\text{r}\text{+ V}{}_{\mathrm{<mtext>c</mtext>}}\text{(r)}$, where V_c is a non-singular confining potential. If $\text{(}\text{d}\text{d}\text{r)}{}^3\text{(r}{}^2\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{)}$ is positive, then the 3D state lies above the 2S state, provided

$\text{d}\text{d}\text{r}\text{1}\text{r}\text{d}\text{d}\text{r}\text{2V}{}_{\mathrm{<mtext>c</mtext>}}\text{+r}\text{d}\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{d}\text{r}\text{< 0, ?}{}_{\mathrm{r}}\text{>0.}$

For V_c = r^α, this corresponds to 0 < α < 2.     

Experimental evidence of low frequency defect vibrations in the fcc metal lead observed by superconducting tunneling

Superconducting tenneling measurements of Al-Al_xO_y-Pb junctions taken after low temperature irradiation with 10 MeV oxygen ions are reported. The normalized differential conductance $\text{σ}{}_{\mathrm{norm}}\text{= (}\text{d}\text{I}\text{d}\text{U}\text{)}{}_{\mathrm{s}}\text{/ (}\text{d}\text{I}\text{d}\text{U}\text{)}{}_{\mathrm{n}}$ shows additional low frequency structures to an enhancement of the Eliashberg function α²F(ω) in the range from 1.5 to 3.2 meV. The position in energy and the annealing behaviour corroborate that vibrational modes or irradiation induced self-interstitials are observed.     

Surface temperature modulation in molecular beam relaxation spectrometry applied to catalytic decomposition of CH3OH on NiO

A new modification of molecular beam relaxation spectrometry (MBRS) of surface processes is described making use of partial modulation in order to study nonlinear processes: a constant particle beam is directed towards the catalyst surface, the surface temperature is modulated due to absorption of a modulated beam of UV light, reaction products are analyzed by use of phase sensitive mass spectrometric detection. The application of the method is shown by a study of catalytic decomposition of methanol on polycrystalline NiO. Formation of CO was found to be a monomolecular, formation of H₂ and H₂O bimolecular processes. The resulting mechanism may be described as follows:

Rate constants in dependence from surface temperature T₀ are η = 1.8 × 10³$\text{exp(?}\text{46}\text{RT}{}_{\mathrm{o}}\text{kJ}\text{mol}\text{)}$; k_d1 = 1.8 × 10¹⁰$\text{exp(?}\text{92}\text{RTl}{}_0\text{kJ}\text{mol}\text{)}$ s^?1; k_d2 = 1.2 × 10^?2$\text{exp (?}\text{88}\text{RT}{}_0\text{kJ}\text{mol}\text{)}$ cm² particles^?1 s^?1; k_d3 = 3.5 × 10^?4$\text{exp(?}\text{88}\text{RT}{}_0\text{kJ}\text{mol}\text{)}$ cm² particles^?1 s^?1. Average surface residence times of the intermediates are: $\text{27 ?}{}^{\mathrm{\tau }}\text{HCO}\text{}\text{?}\text{1 ms}$ at 550 ? T₀ ? 650 K; $\text{42 ?}{}^{\mathrm{\tau }}\text{H ? 7 ms}$ at 540 ?T₀ ? 610 K; $\text{177 ?}{}^{\mathrm{\tau }}\text{OH ? 19 ms}$ at 550 ? T₀ ? 645 K.