Self‐trapped N?H vibrational states in the polymorphs of glycine,L‐ and DL‐alanine

The polarized Raman spectra of the oriented single crystals of L ‐ and DL ‐alanine, α‐, β‐ and γ‐polymorphs of glycine have been studied at 3–300 K. Regularly spaced band packets have been observed in the spectral range of 2500–3000 cm⁻¹, with intensity decreasing noticeably on heating. These band packets were interpreted as the manifestations of the existence of N H self‐trapped states in these systems at low temperatures. The analysis of the polarized spectra has shown that the self‐trapping is observed exclusively for the NH stretching vibration of the amino groups, which is related to the NH···O hydrogen bonds along the head‐to‐tail chains of zwitterions in the crystal structures. The wavenumber of this NH stretching vibration, however, was proposed to depend not solely on the length of this NH···O hydrogen bond, but also on the lengths of all the other NH···O hydrogen bonds formed by the NH₃⁺ and the COO⁻ groups in the structure linking the head‐to‐tail chains with each other. The arguments in favor of the hypothesis that the self‐trapping in these systems can be mediated by zero‐point quantum motions, and not by lattice phonons, are considered. The unusually low wavenumber (2500 cm⁻¹) observed for the NH stretching vibration and indicating at the formation of a very strong NH···O bond is interpreted based on considering the effect of the crystalline environment on the formation and properties of the NH···O bonds in the head‐to‐tail chains of amino acid zwitterions. The results are interesting for understanding the factors determining the dynamics and structural instability of crystalline amino acids and also for biophysical chemistry, as the hydrogen bonded chains formed by amino acid zwitterions in the crystals can mimic the peptide chains. Copyright © 2009 John Wiley & Sons, Ltd.     

Silica Nanoparticles as Adhesives for Biological Tissues? Re‐Examining the Effect of Particles Size,Particle Shape,and the Unexpected Role of Base

Development of new, effective, and patient‐friendly adhesives for biological tissues is important for medical and surgical practices such as bleeding control and organ repairing. While some commercially available silica nanoparticles such as LUDOX SM‐30 have shown adhesive properties for biological tissues, the role of inorganic base present in the adhesive properties of the silica nanoparticles has not been examined. Moreover, it remained unclear how the size and the shape of silica nanoparticles affect the adhesion properties. To address these questions, synthesis and characterization of a series of uniform silica nanostructures with different sizes and shapes is carried out. Unexpectedly, none of the synthesized silica nanostructures without additional inorganic base shows adhesion properties against liver tissues. Such surprising phenomena motivate to examine other factors in the commercial silica nanoparticles as tissue adhesives, and reach a conclusion that the inorganic base plays a key role in the adhesion properties. It is believed that this study answers the important question whether silica nanoparticles can act as biological adhesives or not. The conclusion also gives a lesson to other scientists and engineers in design and exploration of new biological adhesives.     

A note on the Holst action, the time gauge, and the Barbero–Immirzi parameter

In this note, we review the canonical analysis of the Holst action in the time gauge, with a special emphasis on the Hamiltonian equations of motion and the fixation of the Lagrange multipliers. This enables us to identify at the Hamiltonian level the various components of the covariant torsion tensor, which have to be vanishing in order for the classical theory not to depend upon the Barbero–Immirzi parameter. We also introduce a formulation of three-dimensional gravity with an explicit phase space dependency on the Barbero–Immirzi parameter as a potential way to investigate its fate and relevance in the quantum theory.     

Helmholtz, Riemann, and the Sirens: Sound, Color, and the “Problem of Space”

Emerging from music and the visual arts, questions about hearing and seeing deeply affected Hermann Helmholtz’s and Bernhard Riemann’s contributions to what became called the “problem of space [Raumproblem],” which in turn influenced Albert Einstein’s approach to general relativity. Helmholtz’s physiological investigations measured the time dependence of nerve conduction and mapped the three-dimensional manifold of color sensation. His concurrent studies on hearing illuminated musical evidence through experiments with mechanical sirens that connect audible with visible phenomena, especially how the concept of frequency unifies motion, velocity, and pitch. Riemann’s critique of Helmholtz’s work on hearing led Helmholtz to respond and study Riemann’s then-unpublished lecture on the foundations of geometry. During 1862–1870, Helmholtz applied his findings on the manifolds of hearing and seeing to the Raumproblem by supporting the quadratic distance relation Riemann had assumed as his fundamental hypothesis about geometrical space. Helmholtz also drew a “close analogy … in all essential relations between the musical scale and space.” These intersecting studies of hearing and seeing thus led to reconsideration and generalization of the very concept of “space,” which Einstein shaped into the general manifold of relativistic space-time.     

MIDI,the 10 μm interferometer of the VLT

We report in this paper on the current status of the mid-infrared beam combiner of the VLTI: MIDI. We explain the interest of VLTI for this range of wavelentghs and give an overview of the main characteristics of MIDI and present its scientific targets.     

The Schrödinger Equation,the Zero-Point Electromagnetic Radiation,and the Photoelectric Effect

A Schrödinger type equation for a mathematical probability amplitude Ψ(x,t) is derived from the generalized phase space Liouville equation valid for the motion of a microscopic particle, with mass M and charge e, moving in a potential V(x). The particle phase space probability density is denoted Q(x,p,t), and the entire system is immersed in the “vacuum” zero-point electromagnetic radiation. We show, in the first part of the paper, that the generalized Liouville equation is reduced to a simpler Liouville equation in the equilibrium limit where the small radiative corrections cancel each other approximately. This leads us to a simpler Liouville equation that will facilitate the calculations in the second part of the paper. Within this second part, we address ourselves to the following task: Since the Schrödinger equation depends on \(\hbar \), and the zero-point electromagnetic spectral distribution, given by \(\rho _{0}{(\omega )} = \hbar \omega ^{3}/2 \pi ^{2} c^{3}\), also depends on \(\hbar \), it is interesting to verify the possible dynamical connection between ρ₀(ω) and the Schrödinger equation. We shall prove that the Planck’s constant, present in the momentum operator of the Schrödinger equation, is deeply related with the ubiquitous zero-point electromagnetic radiation with spectral distribution ρ₀(ω). For simplicity, we do not use the hypothesis of the existence of the L. de Broglie matter-waves. The implications of our study for the standard interpretation of the photoelectric effect are discussed by considering the main characteristics of the phenomenon. We also mention, briefly, the effects of the zero-point radiation in the tunneling phenomenon and the Compton’s effect.     

Aleksandr Ivanovich Potapov September 27, 1949–February 9, 2010

Chronicle

Aleksandr Ivanovich Potapov September 27, 1949–February 9, 2010     

On the Convergence Rate of the Euler-α, an Inviscid Second-Grade Complex Fluid, Model to the Euler Equations

We study the convergence rate of the solutions of the incompressible Euler-α, an inviscid second-grade complex fluid, equations to the corresponding solutions of the Euler equations, as the regularization parameter α approaches zero. First we show the convergence in H ^s , s>n/2+1, in the whole space, and that the smooth Euler-α solutions exist at least as long as the corresponding solution of the Euler equations. Next we estimate the convergence rate for two-dimensional vortex patch with smooth boundaries.     

Acoustics of the Great Hall of the Moscow State Conservatory after reconstruction in 2010–2011

The Great Hall of the Moscow State Conservatory was built in the early 20th century. For more than 100 years of service, it had a high acoustic reputation both among musicians and audience. By the beginning of the 21st century, the hall was in nearly critical condition. Thus, major renovation was needed. In terms of architectural acoustics, the main task was to keep the good acoustics of the hall. This paper presents the results of acoustic parameter measurements of the hall after Reconstruction in 2010–2011. The parameters of the hall measured before and after reconstruction are also compared. The comparative acoustic characteristics between the Great Hall and world leading concert halls are given.     

Analysis of the common characteristics of the Hartmann,Ronchi, and Shack–Hartmann tests

An overview of the settings of the planes for the filters and observed patterns in the Hartmann and Ronchi tests is presented. Also a new set of filters for both test were developed. In a similar way, it is easy to extend this analysis to the Shack–Hartmann test, and to propose a new Null Shack–Hartmann filter.     

The Repulsive Lattice Gas, the Independent-Set Polynomial, and the Lovász Local Lemma

We elucidate the close connection between the repulsive lattice gas in equilibrium statistical mechanics and the Lovász local lemma in probabilistic combinatorics. We show that the conclusion of the Lovász local lemma holds for dependency graph G and probabilities {p_x} if and only if the independent-set polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore, we show that the usual proof of the Lovász local lemma – which provides a sufficient condition for this to occur – corresponds to a simple inductive argument for the nonvanishing of the independent-set polynomial in a polydisc, which was discovered implicitly by Shearer⁽⁹⁸⁾ and explicitly by Dobrushin.^(37,38) We also present some refinements and extensions of both arguments, including a generalization of the Lovász local lemma that allows for soft dependencies. In addition, we prove some general properties of the partition function of a repulsive lattice gas, most of which are consequences of the alternating-sign property for the Mayer coefficients. We conclude with a brief discussion of the repulsive lattice gas on countably infinite graphs.     

Effects of the 3d transition metal doping on the structural,electronic, and magnetic properties of BeO nanotubesEffects of the 3d transition metal doping on the structural,electronic, and magnetic properties of BeO nanotubesEffects of the 3d transition metal doping on the structural,electronic, and magnetic properties of BeO nanotubes

First-principles calculations have been performed on the structural, electronic, and magnetic properties of seven 3d transition-metal （TM） impurities （V, Cr, Mn, Fe, Co, Ni, and Cu） doped armchair （5,5） and zigzag （8,0） beryllium oxide nanotubes （BeONTs）. The results show that there exists a structural distortion around the 3d TM impurities with respect to the pristine BeONTs. The magnetic moment increases for V- and Cr-doped BeONTs and reaches a maximum for Mn-doped BeONT, and then decreases for Fe-, Co-, Ni-, and Cu-doped BeONTs successively, consistent with the predicted trend of Hund＇s rule to maximize the magnetic moments of the doped TM ions. However, the values of the magnetic moments are smaller than the predicted values of Hund＇s rule due to the strong hybridization between the 2p orbitals of the near O and Be ions of BeONTs and the 3d orbitals of the TM ions. Furthermore, the V-, Co-, and Ni-doped （5,5） and （8,0） BeONTs with half-metal ferromagnetism and thus 100% spin polarization character are good candidates for spintronic applications.     

Existence,regularity, and asymptotic behavior of the solutions to the Ginzburg-Landau equations on ℝ3

This paper studies the solutions of the Ginzburg-Landau equations on ³ in the presence of an arbitrarily distributed external magnetic field. The existence and regularity of the solutions at the lowest energy level are established. The solutions found are in the Coulomb gauge. If the external field is sufficiently regular, the solutions are shown to have nice asymptotic decay properties at infinity.     

What are the correct L‐subshell photoionization cross sections for quantitative X‐ray spectroscopy?

For fundamental parameter‐based, quantitative X‐ray fluorescence, X‐ray photoelectron spectroscopy or Auger electron spectroscopy, it is crucial to accurately know the photoionization cross sections (PCS). This atomic probability to absorb the exciting photon and eject a photoelectron, in general, followed by a subsequent decay resulting in the emission of a fluorescence photon or an Auger electron, strongly depends on the electron configuration and photon energy. Two contrary models for the photon energy dependence of the L‐subshell PCS, or the 2s, 2p ½ and 2p 3/2; energy levels, respectively, exist in the literature, and an experimental verification was not available until recently. In this work, the two models for calculating the PCS are discussed, and their influence on quantitative experiments is demonstrated by means of the fluorescence production cross sections for the three L shells. Depending on the excitation conditions, these fluorescence production cross sections and, thus, the derived quantitative results can differ significantly if the wrong PCS model is employed. Copyright © 2016 John Wiley & Sons, Ltd.     

The ζ-Determinant and the Additivity of the η-Invariant on the Smooth, Self-Adjoint Grassmannian

In this paper we discuss the existence of the ‘-determinant of a Dirac operator \Dd\Dd on a compact manifold with boundary. We show that the determinant is well defined in the case of the operator \Dd\Dd with a domain determined by a boundary condition from the smooth, self-adjoint Grassmannian \Grass_￥^*(\Dd)\Grass_{\infty}^*(\Dd) discussed in the papers [5, 13, 29]. We prove a generalization of a pasting formula for the m-invariant (see [34]). The results of the paper are used in the recent proof of the projective equality of the ‘-determinant and Quillen determinant on \Grass_￥^*(\Dd)\Grass_{\infty}^*(\Dd) (see [30, 31]).     

Ions,bubbles, and vortices at the superfluid λ-transition

A vortex-ring theory of the superfluid -transition is reviewed, and new results are presented for the vortex density and for the superfluid density of helium in confined geometries. Possible experiments using ion probes to detect the thermally excited vortices are discussed. It appears that the usual helium ions are not suitable for this purpose, and that larger ion complexes such as multielectron bubbles will need to be employed. An experiment to stably trap multielectron bubbles with acoustic standing waves is outlined.