Resonance-based schemes for dispersive equations via decorated trees

We introduce a numerical framework for dispersive equations embedding their underlying resonance structure into the discretisation. This will allow us to resolve the nonlinear oscillations of the partial differential equation (PDE) and to approximate with high-order accuracy a large class of equations under lower regularity assumptions than classical techniques require. The key idea to control the nonlinear frequency interactions in the system up to arbitrary high order thereby lies in a tailored decorated tree formalism. Our algebraic structures are close to the ones developed for singular stochastic PDEs (SPDEs) with regularity structures. We adapt them to the context of dispersive PDEs by using a novel class of decorations which encode the dominant frequencies. The structure proposed in this article is new and gives a variant of the Butcher–Connes–Kreimer Hopf algebra on decorated trees. We observe a similar Birkhoff type factorisation as in SPDEs and perturbative quantum field theory. This factorisation allows us to single out oscillations and to optimise the local error by mapping it to the particular regularity of the solution. This use of the Birkhoff factorisation seems new in comparison to the literature. The field of singular SPDEs took advantage of numerical methods and renormalisation in perturbative quantum field theory by extending their structures via the adjunction of decorations and Taylor expansions. Now, through this work, numerical analysis is taking advantage of these extended structures and provides a new perspective on them.

Characteristics of megahertz resonant platform for evaluating sensitivity of photoacoustic contrast agent

A platform designed exclusively for evaluating photoacoustic contrast agents is required to prevent deviations in the results caused by differences in the architecture of photoacoustic imaging systems. In this paper, we managed to develop an evaluation system using a cost-efficient laser diode running in megahertz frequency band. To increase the output signal, an acoustic resonance structure is introduced where the sample liquid is filled in a glass capillary embedded in a soft phantom. The optimal width and interval of the excitation pulse were investigated and found to be 230 ns and 4.92 μs, respectively. Experimental results on inks and Indocyanine green verified the feasibility and effectiveness of the platform. Next, as a non-resonant platform, the glass capillary was replaced with a soft tube to examine the signal enhancement effect of the resonance. The signal-to-noise ratio was on average improved 2.5-fold by the resonance occurring in the glass capillary. The success in improving the signal-to-noise ratio may ensure the lower requirement on the laser power, which could consequently suppress the cost of the evaluation platform.

Excitation of the 6d 2D → 6p 2Po Radiative Transitions in the Pb+ Ion by Electron Impact

Results of experimental and theoretical investigation of electron-impact excitation of the 6s26d D2→6s26p P2o spectral transitions from the ground 6s26p P21/2o level in the Pb+ ion are presented. The experimental excitation functions for the transitions, measured by a VUV spectroscopy method, using the crossed electron and ion beams technique, reveal a rather distinct resonance structure resulting mainly from the electron decay of both atomic and ionic autoionizing states. The absolute values of the emission cross-sections, obtained by normalizing the experimental data at the incident electron energy 100 eV by those calculated using the Flexible Atomic Code software package, were found to be (0.35 ± 0.17) × 10–16 cm2 for the 6s26d D23/2 → 6s26p P21/2o (λ143.4 nm) transition and (0.19 ± 0.09) × 10–16 cm2 for the 6s26d D25/2 → 6s26p P23/2o (λ182.2 nm) transition.

Nonlinear nanoelectrodynamics of a Weyl metal

Chiral Weyl fermions with linear energy-momentum dispersion in the bulk accompanied by Fermi-arc states on the surfaces prompt a host of enticing optical effects. While new Weyl semimetal materials keep emerging, the available optical probes are limited. In particular, isolating bulk and surface electrodynamics in Weyl conductors remains a challenge. We devised an approach to the problem based on near-field photocurrent imaging at the nanoscale and applied this technique to a prototypical Weyl semimetal TaIrTe4. As a first step, we visualized nano-photocurrent patterns in real space and demonstrated their connection to bulk nonlinear conductivity tensors through extensive modeling augmented with density functional theory calculations. Notably, our nanoscale probe gives access to not only the in-plane but also the out-of-plane electric fields so that it is feasible to interrogate all allowed nonlinear tensors including those that remained dormant in conventional far-field optics. Surface- and bulk-related nonlinear contributions are distinguished through their “symmetry fingerprints” in the photocurrent maps. Robust photocurrents also appear at mirror-symmetry breaking edges of TaIrTe4 single crystals that we assign to nonlinear conductivity tensors forbidden in the bulk. Nano-photocurrent spectroscopy at the boundary reveals a strong resonance structure absent in the interior of the sample, providing evidence for elusive surface states.

Physico-Chemistry of Dinitrosyl Iron Complexes as a Determinant of Their Biological Activity

In this article we minutely discuss the so-called “oxidative” mechanism of mononuclear form of dinitrosyl iron complexes (M-DNICs) formations proposed by the author. M-DNICs are proposed to be formed from their building material—neutral NO molecules, Fe2+ ions and anionic non-thiol (L−) and thiol (RS−) ligands based on the disproportionation reaction of NO molecules binding with divalent ion irons in pairs. Then a protonated form of nitroxyl anion (NO−) appearing in the reaction is released from this group and a neutral NO molecule is included instead. As a result, M-DNICs are produced. Their resonance structure is described as [(L−)2Fe2+(NO)(NO+)], in which nitrosyl ligands are represented by NO molecules and nitrosonium cations in equal proportions. Binding of hydroxyl ions with the latter causes conversion of these cations into nitrite anions at neutral pH values and therefore transformation of DNICs into the corresponding high-spin mononitrosyl iron complexes (MNICs) with the resonance structure described as [(L−)2Fe2+(NO)]. In case of replacing L− by thiol-containing ligands, which are characterized by high π-donor activity, electron density transferred from sulfur atoms to iron-dinitrosyl groups neutralizes the positive charge on nitrosonium cations, which prevents their hydrolysis, ensuring relatively a high stability of the corresponding M-DNICs with the resonance structure [(RS−)2Fe2+ (NO, NO+)]. Therefore, M-DNICs with thiol-containing ligands, as well as their binuclear analogs (B-DNICs, respective resonance structure [(RS−)2Fe2+2 (NO, NO+)2]), can serve donors of both NO and NO+. Experiments with solutions of B-DNICs with glutathione or N-acetyl-L-cysteine (B-DNIC-GSH or B-DNIC-NAC) showed that these complexes release both NO and NO+ in case of decomposition in the presence of acid or after oxidation of thiol-containing ligands in them. The level of released NO was measured via optical absorption intensity of NO in the gaseous phase, while the number of released nitrosonium cations was determined based on their inclusion in S-nitrosothiols or their conversion into nitrite anions. Biomedical research showed the ability of DNICs with thiol-containing ligands to be donors of NO and NO+ and produce various biological effects on living organisms. At the same time, NO molecules released from DNICs usually have a positive and regulatory effect on organisms, while nitrosonium cations have a negative and cytotoxic effect.