Various scattering properties of a new PT-symmetric non-Hermitian potential

We complexify a 1-d potential V(x)=V₀cosh²μ{tanh[(x−μd)/d]+tanh(μ)}²$V\left(x\right)=V_0{cosh}^2\mu {\{tanh[(x-\mu d)/d]+tanh\left(\mu \right)\}}^2$ which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (μ,d)$(\mu ,d)$ becomes imaginary. For the case of μ→iμ$\mu \to i\mu$, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from the left (or right) at certain discrete energies. The penetrating states in the other case (d→id$d\to id$) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case.     

Elastic scattering of holes by acoustic phonons in thin GaAs/GaAlAs quantum wells

The rates of scattering by acoustic phonons _γi→j${\gamma }_{i\to j}$ from subband i→j$i\to j$ are calculated for holes in a narrow GaAs quantum well using the deformation potential, the Luttinger hamiltonian and the Debye approximation. At room temperature, we find that the energy dependences for both intra- and inter-subband scattering rates follow roughly the behavior of the density of states in the subband to which the hole scatters. Moreover, we study the influence of the overlap between the initial and final states, and for elastic processes we find that, unlike for the case of wide quantum wells, for narrow ones integration over the phonon transverse wavevector _qz$q_z$ should be restricted to about 4% of the bulk Brillouin zone extent. In addition the impact of the well width on _γi→j${\gamma }_{i\to j}$ is investigated.     

Studies of intrawall porosity in the hexagonally ordered mesostructures of SBA-15 by small angle X-ray scattering and nitrogen adsorption

Ordered mesoporous silicas (OMSs) such as SBA-15 (p6mm symmetry group) synthesized in the presence of block copolymers containing poly(ethylene oxide) blocks possess irregular complementary pores in the walls of ordered mesopores. The X-ray scattering caused by this complementary porosity contributes to the background of the SAXS patterns. This work shows the possibility of using the SAXS data for the study of intrawall channels interconnecting ordered cylinders in SBA-15. The proposed SAXS analysis was tested by using a series of SBA-15 samples obtained at different temperatures of hydrothermal treatment (from 60 to 180 °C). The structural modelling of the SAXS patterns recorded for a series of SBA-15 samples was performed by using the continuous density function (CDF) technique in combination with the derivative difference minimization (DDM) method of full-profile refinement. This method is well suited for extraction of the background curves from the SAXS patterns. The resulting smooth background curves were analyzed by the well-known method in the SAXS theory used for evaluation of heterogeneity distributions, which in this case characterize the intrawall complementary porosity. A relatively good agreement has been observed between the data obtained by SAXS and nitrogen adsorption analysis. The SAXS analysis is sufficiently sensitive for examination of heterogeneous microporosity in SBA-15 materials. The average diameter of intrawall pores for the SBA-15 sample obtained at 60 °C was only about 1.4 nm. However, this diameter increased with the increasing temperature of hydrothermal treatment; namely, it was 1.5, 1.8, 2.6, 2.6, 3.5 and 5.2 nm for the SBA-15 samples hydrothermally treated at 80, 100, 120, 140, 160 and 180 °C, respectively.     

Matroidal Entropy Functions: A Quartet of Theories of Information,Matroid, Design,and Coding

In this paper, we study the entropy functions on extreme rays of the polymatroidal region which contain a matroid, i.e., matroidal entropy functions. We introduce variable strength orthogonal arrays indexed by a connected matroid M and positive integer v which can be regarded as expanding the classic combinatorial structure orthogonal arrays. It is interesting that they are equivalent to the partition-representations of the matroid M with degree v and the (M,v) almost affine codes. Thus, a synergy among four fields, i.e., information theory, matroid theory, combinatorial design, and coding theory is developed, which may lead to potential applications in information problems such as network coding and secret-sharing. Leveraging the construction of variable strength orthogonal arrays, we characterize all matroidal entropy functions of order n≤5 with the exception of log10·U2,5 and logv·U3,5 for some v.     

Influence of multiple elastic scattering on the shape of the elastically scattered electron peak

The influence of multiple elastic scattering on the shape of the energy distribution of elastically scattered electrons is investigated. The energy of the maximum intensity of the detected electrons differs from the probe electron beam energy due to the elastic energy loss. The experimentally observed spectrum is adequately described by a Gaussian distribution with a maximum at the elastic energy loss value. In this paper the peak-broadening mechanisms due to energy-analyzer spread function, probe beam energy distribution and atomic vibration-induced broadening are considered to be independent and of random nature. Analysis of multiple elastic scattering shows some mechanisms leading to the broadening and a shift of the elastic scattering electron energy spectrum from the value defined by single elastic scattering at the certain angle. It is revealed that the magnitude of this shift and the width of energy distribution is determined by ratio (_lin/_ltr)$(l_{\text{in}}/l_{\text{tr}})$, where _lin$l_{\text{in}}$ is inelastic mean free pass, _ltr$l_{\text{tr}}$ is the transport length.     

On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering

The contribution of quarks with masses m?_ΛQCD$m?{\Lambda }_{\mathrm{QCD}}$ is the only part of the structure functions in deep-inelastic scattering (DIS) which is not yet known at the next-to-next-to-leading order (NNLO) of perturbative QCD. We present improved partial NNLO results for the most important structure function _F2(x,Q²)$F_2(x,Q^2)$ near the partonic threshold, in the high-energy (small-x  ) limit and at high scales Q²?m²$Q^2?m^2$; and employ these results to construct approximations for the gluon and quark coefficient functions which cover the full kinematic plane. The approximation uncertainties are carefully investigated, and found to be large only at very small values, x?10⁻³$x?{10}^{-3}$, of the Bjorken variable.     

Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid

Partial-wave series representation of the acoustic scattering field of high-order Bessel vortex beams by rigid oblate and prolate spheroids using the modal matching method is developed. The method, which is applicable to slightly elongated objects at low-to-moderate frequencies, requires solving a system of linear equations which depends on the partial-wave index n$n$ and the order of the Bessel vortex beam m$m$ using truncated partial-wave series expansions (PWSEs), and satisfying the Neumann boundary condition for a rigid immovable surface in the least-squares sense. This original semi-analytical approach developed for Bessel vortex beams is demonstrated for finite oblate and prolate spheroids, where the mathematical functions describing the spheroidal geometry are written in a form involving single angular (polar) integrals that are numerically computed. The transverse (θ=π/2$\theta =\pi /2$) and 3D scattering directivity patterns are evaluated in the far-field for both prolate and oblate spheroids, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid) not exceeding 3:1, the half-cone angle β$\beta$ and order m$m$ of the Bessel vortex beam, as well as the dimensionless size parameter kr₀$k{r}_0$. Periodic oscillations in the magnitude plots of the far-field scattering form function are observed, which result from the interference of the reflected waves with the circumferential (Franz’) waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the far-field scattering from the spheroid, that vanishes in the forward (θ=0$\theta =0$) and backward (θ=π$\theta =\pi$) directions. Particular applications in underwater acoustics and scattering, acoustic levitation and the detection of submerged elongated objects using Bessel vortex waves to name a few, would benefit from the results of the present investigation.     

T-odd correlation in muon neutrino elastic scattering on polarized proton target

In this paper, we analyze the elastic scattering of the muon neutrino (_νμ${\nu }_{\mu }$) beam on the polarized proton target (PPT) in a presence of induced couplings, and predict how the existence of relative phases between the complex vector (weak magnetism) and axial (induced pseudoscalar) form factors of the proton with left-chirality _νμ${\nu }_{\mu }$ affects the azimuthal dependence of the differential cross section. The neutrinos are assumed to be Dirac fermions with non-zero mass and CPT symmetry is conserved. We show that the azimuthal asymmetry of recoil protons depends on the neutrino mass, but contributions are very tiny (∼10⁻⁵$\sim {10}^{-5}$). Analysis of the differential cross section in the case of pure vector and axial couplings at zero _νμ${\nu }_{\mu }$ mass limit and zero momentum transfer shows that the T-violating phase _βVA${\beta }_{\mathit{VA}}$ generates the T-odd, P-even triple correlation and it could be detected by measuring the asymmetry between the (0,π)$(0,\pi )$ and (π,2π)$(\pi ,2\pi )$ angles. It should be clearly stressed that the considered T-odd observable is not a genuine CP-violating quantity as it can also be produced by the T-invariant contributions due to the final state interactions (FSI). Their magnitude must be precisely estimated and subtracted from the measured observable to extract information on the possible time reversal violation (TRV). We also indicate the possibility of using the PPT in the neutrino telescope.     

Spin dynamics of layered triangular antiferromagnets with uniaxial anisotropy

The spin dynamics of the semiclassical Heisenberg model with uniaxial anisotropy, on the layered triangular lattice with antiferromagnetic coupling for both intralayer nearest neighbor interaction and interlayer interaction is studied both in the ordered phase and in the paramagnetic phase, using the Monte Carlo-molecular dynamics technique. The important quantities calculated are the full dynamic structure function S(q,ω)$S(\mathbf{q},\omega )$, the chiral dynamic structure function _Schi(ω)$S_{\mathrm{chi}}(\omega )$, the static order parameter and some thermodynamic quantities. Our results show the existence of propagating modes corresponding to both S(q,ω)$S(\mathbf{q},\omega )$ and _Schi(ω)$S_{\mathrm{chi}}(\omega )$ in the ordered phase, supporting the recent conjectures. Our results for the static properties show the magnetic ordering in each layer to be of coplanar 3-sublattice type deviating from 120^°${120}^{°}$ structure. In the presence of magnetic trimerization, however, we find the 3-sublattice structure to be weakened along with the tendency towards non-coplanarity of the spins, supporting the experimental conjecture. Our results for the spin dynamics are in qualitative agreement with those from the inelastic neutron scattering experiments performed recently.     

Characterization of individual ferromagnetic nanowires by in-plane magnetic measurements of arrays

We present a phenomenological model for the interaction field in ferromagnetic nanowire arrays and use it to obtain the effective anisotropy field of individual nanowires, from the in-plane saturation field of the array. In contrast to other methods which may be used to estimate this parameter, the proposed strategy requires no knowledge of the saturation magnetization nor of the nanowire radius. Applied to three arrays of different compositions, this approach yields an equivalent anisotropy field of the individual nanowires approximately equal to _Ms/2$M_{\mathrm{s}}/2$, indicating that its origin is the demagnetizing field of the wire.     

An evaluation of NMR cryoporometry, density measurement and neutron scattering methods of pore characterisation.

Sol-gel silicas with nominal pore diameters ranging from 25A to 500A were studied by NMR cryoporometry, and by neutron diffraction and small angle scattering from dry silicas over the Q range 8. 10(-4)A(-1) < or = Q < or = 17A(-1). Density and imbibation experiments were also performed. Geometric models of porous systems were constructed and were studied by both analytic techniques and Monte-Carlo integration. These models, combined with the information from the above measurements, enabled the calculation of the fully density corrected solid-solid density correlation functions G(r) for the sol-gel silicas, deduction of the (voidless) silica matrix density, measurement of the silica fraction in the grain and of the packing fraction of the silica grains and an estimation of the water equivalent residual hydrogen on the dried silica surface. In addition, the pore diameter D, pore diameter to lattice spacing ratio D/a, and pore and lattice variance sigma could also be measured. While the NMR cryoporometry pore diameter measurements for the sol-gel silicas show excellent co-linearity with the nominal pore diameters as measured by gas adsorption, and the calculated pore diameters from the measured neutron scattering show surprisingly good agreement with these measurements at large pore diameters, there is a divergence between the calibrations for pore diameters below about 100A.     

Pre-edge features in X-ray absorption structure of Mn in GaMnN,GaMnAs and GeMn

_Ga1-xMnxN${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$ samples with a wide range of concentrations, from x=0.003$x=0.003$ to 0.057, were grown by molecular beam epitaxy. X-ray diffraction and the simulation of the extended X-ray absorption fine structure (EXAFS) confirmed the wurtzite structure of the samples, without any secondary phase, and the location of Mn in the gallium sublattice of GaN. The valence state of Mn was studied using the X-ray absorption near-edge structure (XANES) at the K-edge of Mn. The shape of the measured XANES spectra does not depend on the Mn concentration: that implies the same valence state and local atomic structure around the Mn atom in all samples. A calculation of the electronic band structure of GaMnN, GaMnAs, GeMn and the XANES spectra of Mn in GaMnN was performed using the linearized augmented plane wave (LAPW) method. The calculated spectra fit well our experimental data. In particular, the comparison demonstrates that a peak in the pre-edge structure is directly related to the 3+$3+$ valence state of Mn. This was confirmed experimentally by measurements of the Mn K-edge in GaMn²⁺As${\mathrm{GaMn}}^{2+}\mathrm{As}$ and ZnMn²⁺Te${\mathrm{ZnMn}}^{2+}\mathrm{Te}$. An application of proposed interpretation for GeMn is discussed.