Three-body bound states with zero-range interaction in the Bethe-Salpeter approach

The Bethe-Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body binding energies, Bethe-Salpeter amplitudes and light-front wave functions. Three different regimes are analyzed: ({\it i}) For weak enough two-body interaction the three-body system is unbound. ({\it ii}) For stronger two-body interaction a three-body bound state appears. It provides an interesting example of a deeply bound Borromean system. ({\it iii}) For even stronger two-body interaction this state becomes unphysical with a negative mass squared. However, another physical (excited) state appears, found previously in light-front calculations. The Bethe-Salpeter approach implicitly incorporates three-body forces of relativistic origin, which are attractive and increase the binding energy.Comment: 13 pages, 7 figure

Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space

The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by standard analytical and numerical methods, without relying on any ansatz or assumption. The results for the binding energies and transverse amplitudes are compared with the results computed in Euclidean space. A fair agreement between the calculations is found.Comment: 10 pages, 2 figures, version accepted for publication in Phys. Lett.

Bound state structure and electromagnetic form factor beyond the ladder approximation

We investigate the response of the bound state structure of a two-boson system, within a Yukawa model with a scalar boson exchange, to the inclusion of the cross-ladder contribution to the ladder kernel of the Bethe-Salpeter equation. The equation is solved by means of the Nakanishi integral representation and light-front projection. The valence light-front wave function and the elastic electromagnetic form factor beyond the impulse approximation, with the inclusion of the two-body current, generated by the cross-ladder kernel, are computed. The valence wave function and electromagnetic form factor, considering both ladder and ladder plus cross-ladder kernels, are studied in detail. Their asymptotic forms are found to be quite independent of the inclusion of the cross-ladder kernel, for a given binding energy. The asymptotic decrease of form factor agrees with the counting rules. This analysis can be generalized to fermionic systems, with a wide application in the study of the meson structure.Comment: 19 pages, 6 figures, submitted to Phys. Lett.

Outcomes of Vaginal Birth After Caesarean: Experience of a Portuguese Hospital

info:eu-repo/semantics/publishedVersio

Site-selective protein modification via disulfide rebridging for fast tetrazine/trans-cyclooctene bioconjugation

An inverse electron demand Diels–Alder reaction between tetrazine and trans-cyclooctene (TCO) holds great promise for protein modification and manipulation. Herein, we report the design and synthesis of a tetrazine-based disulfide rebridging reagent, which allows the site-selective installation of a tetrazine group into disulfide-containing peptides and proteins such as the hormone somatostatin (SST) and the antigen binding fragment (Fab) of human immunoglobulin G (IgG). The fast and efficient conjugation of the tetrazine modified proteins with three different TCO-containing substrates to form a set of bioconjugates in a site-selective manner was successfully demonstrated for the first time. Homogeneous, well-defined bioconjugates were obtained underlining the great potential of our method for fast bioconjugation in emerging protein therapeutics. The formed bioconjugates were stable against glutathione and in serum, and they maintained their secondary structure. With this work, we broaden the scope of tetrazine chemistry for site-selective protein modification to prepare well-defined SST and Fab conjugates with preserved structures and good stability under biologically relevant conditions

Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin–Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211–237) at low Strouhal number ( St ) and non-zero azimuthal wavenumbers ( m ). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency–wavenumber space where each dominates, finding lift-up to be dominant as St/m→0 . Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core

Stability of casein micelles cross-linked with genipin: a physicochemical study as a function of pH

Chemical or enzymatic cross-linking of casein micelles (CMs) increases their stability against dissociating agents. In this paper, a comparative study of stability between native CMs and CMs cross-linked with genipin (CMs-GP) as a function of pH is described. Stability to temperature and ethanol were investigated in the pH range 2.0-7.0. The size and the charge ($\zeta$-potential) of the particles were determined by dynamic light scattering. Native CMs precipitated below pH 5.5, CMs-GP precipitated from pH 3.5 to 4.5, whereas no precipitation was observed at pH 2.0-3.0 or pH 4.5-7.0. The isoelectric point of CMs-GP was determined to be pH 3.7. Highest stability against heat and ethanol was observed for CMs-GP at pH 2, where visible coagulation was determined only after 800 s at 140 $^\circ$C or 87.5% (v/v) of ethanol. These results confirmed the hypothesis that cross-linking by GP increased the stability of CMs.Comment: 5 pages, 2 figures, International Dairy Journal, 201