Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.

Reaction of Copper(II) Chloroacetate with Pyrazole. Synthesis of a One-Dimensional Coordination Polymer and Unexpected Dehydrochlorination Reaction

The reaction of copper(II) chloroacetate (1d) with pyrazole (Hpz) mainly yielded the mononuclear compound [Cu(μ-ClCH2COO)2(Hpz)2] (2m), which self-assembled generating a one-dimensional coordination polymer. Moreover, the concomitant isolation of the tetranuclear [{Cu2(μ-pz)(μ-OCH2COO)(Hpz)(MeOH)}2(μ-ClCH2COO)2] (3t) and hexanuclear [{Cu3(μ3-OH)(μ-pz)3(Hpz)2}2(μ-ClCH2COO)2](Cl)2 (4h) species evidenced the occurrence of a peculiar, previously unreported, dehydrochlorination reaction and the formation of the trinuclear triangular moiety [Cu3(μ3-OH)(μ-pz)3]. Theoretical calculations based on density functional theory including solvation effects indicate a possible pathway for the formation of 3t. Interestingly, besides the energy minimum corresponding to 3t, a further relative energy minimum is found for a species which can be considered a possible reaction intermediate.

The benefits of one-dimensional detectors for high-pressure powder X-ray diffraction

High-pressure powder X-ray diffraction is a fundamental technique for investigating structural responses to externally applied force. Synchrotron sources and two-dimensional detectors are required. In contrast to this conventional setup, high-resolution beamlines equipped with one-dimensional detectors could offer much better resolved peaks but cannot deliver accurate structure factors because they only sample a small portion of the Debye rings, which are usually inhomogeneous and spotty because of the small amount of sample. In this study, a simple method to overcome this problem is presented and successfully applied to solving the structure of an L-serine polymorph from powder data. A comparison of the obtained high-resolution high-pressure data with conventional data shows that this technique, providing up to ten times better angular resolution, can be of advantage for indexing, for lattice parameter refinement, and even for structure refinement and solution in special cases.

One dimensional exciton luminescence induced by extended defects in nonpolar (Al,Ga)N/GaN quantum wells

In this study, we present the optical properties of nonpolar GaN/(Al,Ga)N single quantum wells (QWs) grown on either a- or m-plane GaN templates for Al contents set below 15%. In order to reduce the density of extended defects, the templates have been processed using the epitaxial lateral overgrowth technique. As expected for polarization-free heterostructures, the larger the QW width for a given Al content, the narrower the QW emission line. In structures with an Al content set to 5 or 10%, we also observe emission from excitons bound to the intersection of I1-type basal plane stacking faults (BSFs) with the QW. Similarly to what is seen in bulk material, the temperature dependence of BSF-bound QW exciton luminescence reveals intra-BSF localization. A qualitative model evidences the large spatial extension of the wavefunction of these BSF-bound QW excitons, making them extremely sensitive to potential fluctuations located in and away from BSF. Finally, polarization-dependent measurements show a strong emission anisotropy for BSF-bound QW excitons, which is related to their one-dimensional character and that confirms that the intersection between a BSF and a GaN/(Al,Ga)N QW can be described as a quantum wire.

Numerical analysis of axisymmetric shells by one-dimensional continuum elements suitable for high frequency excitations

Axisymmetric shells are analyzed by means of one-dimensional continuum elements by using the analogy between the bending of shells and the bending of beams on elastic foundation. The mathematical model is formulated in the frequency domain. Because the solution of the governing equations of vibration of beams are exact, the spatial discretization only depends on geometrical or material considerations. For some kind of situations, for example, for high frequency excitations, this approach may be more convenient than other conventional ones such as the finite element method.

Analytical solution to the one-dimensional non-uniform absorption of solar radiation in uncoated and coated single glass panes

The analytical solution to the one-dimensional absorption–conduction heat transfer problem inside a single glass pane is presented, which correctly takes into account all the relevant physical phenomena: the appearance of multiple reflections, the spectral distribution of solar radiation, the spectral dependence of optical properties, the presence of possible coatings, the non-uniform nature of radiation absorption, and the diffusion of heat by conduction across the glass pane. Additionally to the well established and known direct absorptance αe, the derived solution introduces a new spectral quantity called direct absorptance moment βe, that indicates where in the glass pane is the absorption of radiation actually taking place. The theoretical and numerical comparison of the derived solution with existing approximate thermal models for the absorption–conduction problem reveals that the latter ones work best for low-absorbing uncoated single glass panes, something not necessarily fulfilled by modern glazings.

One-dimensional self-similar solution of the dynamics of axisymmetric slender liquid bridges

In this paper the dynamics of axisymmetric, slender, viscous liquid bridges having volume close to the cylindrical one, and subjected to a small gravitational field parallel to the axis of the liquid bridge, is considered within the context of one-dimensional theories. Although the dynamics of liquid bridges has been treated through a numerical analysis in the inviscid case, numerical methods become inappropriate to study configurations close to the static stability limit because the evolution time, and thence the computing time, increases excessively. To avoid this difficulty, the problem of the evolution of these liquid bridges has been attacked through a nonlinear analysis based on the singular perturbation method and, whenever possible, the results obtained are compared with the numerical ones.

One-dimensional linear analysis of the compound jet

The stability of an infinitely long compound liquid column is analysed by using a one-dimensional inviscid slice model. Results obtained from this one-dimensional linear analysis are applicable to the study of compound capillary jets, which are used in the ink-jet printing technique. Stability limits and the breaking regimes of such fluid configurations are established, and, whenever possible, theoretical results are compared with experimental ones.

One-dimensional linear analysis of the liquid injection or removal in a liquid bridge

The filling-withdrawal process of a long liquid bridge is analyzed using a one-dimensional linearized model for the dynamics of the liquid column. To carry out this study, a well-known standard operational method (Laplace transform) has been used, and time variation of both liquid velocity field and interface shape are obtained.

Adsorption from a one-dimensional lattice gas and the Brunauer–Emmett–Teller equation

An exact treatment of adsorption from a one-dimensional lattice gas is used to eliminate and correct a well-known inconsistency in the Brunauer–Emmett–Teller (B.E.T.) equation—namely, Gibbs excess adsorption is not taken into account and the Gibbs integral diverges at the transition point. However, neither model should be considered realistic for experimental adsorption systems.

Observation via one-dimensional 13Calpha NMR of local conformational substates in thermal unfolding equilibria of a synthetic analog of the GCN4 leucine zipper.

Synthesis of a 33-residue, capped leucine zipper analogous to that in GCN4 is reported. Histidine and arginine residues are mutated to lysine to reduce the unfolding temperature. CD and ultracentrifugation studies indicate that the molecule is a two-stranded coiled coil under benign conditions. Versions of the same peptide are made with 99% 13Calpha at selected sites. One-dimensional 13C NMR spectra are assigned by inspection and used to study thermal unfolding equilibria over the entire transition from 8 to 73 degrees C. Spectra at the temperature extremes establish the approximate chemical shifts for folded and unfolded forms at each labeled site. Resonances for each amino acid appear at both locations at intermediate T, indicating that folded and unfolded forms interconvert slowly (> >2 ms) on the NMR time scale. Moreover, near room temperature, the structured form's resonance is double at several, but not all, sites, indicating at least two slowly interconverting, structured, local conformational substates. Analysis of the dynamics is possible. For example, near room temperature at the Val-9, Ala-24, and Gly-31 positions, the equilibrium constant for interconversion of the two structured forms is near unity and the time scale is > or= 10-20 ms.