Multi-soliton dynamics of anti-self-dual gauge fields

We study dynamics of multi-soliton solutions of anti-self-dual Yang-Mills equations for G = GL(2, ℂ) in four-dimensional spaces. The one-soliton solution can be interpreted as a codimension-one soliton in four-dimensional spaces because the principal peak of action density localizes on a three-dimensional hyperplane. We call it the soliton wall. We prove that in the asymptotic region, the n-soliton solution possesses n isolated localized lumps of action density, and interpret it as n intersecting soliton walls. More precisely, each action density lump is essentially the same as a soliton wall because it preserves its shape and “velocity” except for a position shift of principal peak in the scattering process. The position shift results from the nonlinear interactions of the multi-solitons and is called the phase shift. We calculate the phase shift factors explicitly and find that the action densities can be real-valued in three kind of signatures. Finally, we show that the gauge group can be G = SU(2) in the Ultrahyperbolic space 𝕌 (the split signature (+, +, −, −)). This implies that the intersecting soliton walls could be realized in all region in N=2 string theories. It is remarkable that quasideterminants dramatically simplify the calculations and proofs.

Interaction between equatorial stratospheric Kelvin waves and gravity waves in a QBO phase

<p>An interaction between Kelvin waves and gravity waves (GWs) in the tropical stratosphere is investigated using the global weather-forecasting model ICON with a horizontal grid spacing of ~160 km. To represent GWs in ICON, the Multi-Scale Gravity Wave Model (MS-GWaM) is used as a subgrid-scale parameterization, which is a prognostic model that explicitly calculates the evolution of GW action density in phase space. The simulation is initialized on a day in the QBO phase of the easterly maximum at ~20 hPa, so that Kelvin waves can propagate vertically throughout the lower stratosphere during the simulation. We show that Kelvin waves with zonal-wind amplitudes of about 10 m s<sup>-1</sup> can largely affect the distribution of GW drag, by disturbing the local wind shear. Moreover, due to the zonal asymmetry in the activity of tropospheric convection, which is the source of GWs in the tropics, this effect of Kelvin waves can also influence the zonal mean of GW drag. The effect seems to be large when a strong convective system, from which large-amplitude GWs are generated, propagates eastward in the troposphere together with a phase of stratospheric Kelvin wave aloft. In our case, such an interaction causes a zonal-mean GW drag of ~0.26 m s<sup>-1</sup> d<sup>-1</sup> at ~20 hPa for a week during an early phase of the easterly-to-westerly transition of the QBO. The result emphasizes the importance of a correct representation of large-scale waves as well as subgrid-scale GWs in QBO simulations.</p>

Yang-Mills Equations of General Connections and a Certain Solutions in the Quaternionic Hopf Fibration Over Four-Sphere

We investigate a version of Yang-Mills theory by means of general connections. In order to deduce a basic equation, which we regard as a version of Yang-Mills equation, we construct a self-action density using the curvature of general connections. The most different point from the usual theory is that the solutions are given in pairs of two general connections. This enables us to get nontrivial solutions as general connections. Especially, in the quaternionic Hopf fibration over four-sphere, we demonstrate that there certainly exist nontrivial solutions, which are made by twisting the well-known BPST anti-instanton.

New soliton solutions of anti-self-dual Yang-Mills equations

We study exact soliton solutions of anti-self-dual Yang-Mills equations for G = GL(2) in four-dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special kinds of one-soliton solutions whose action density TrFμνFμν can be real-valued. These solitons are shown to be new type of domain walls in four dimension by explicit calculation of the real-valued action density. Our results are successful applications of the Darboux transformation developed by Nimmo, Gilson and Ohta. More surprisingly, integration of these action densities over the four-dimensional spaces are suggested to be not infinity but zero. Furthermore, whether gauge group G = U(2) can be realized on our solition solutions or not is also discussed on each real space.

ANTIOXIDATIVE AND INHIBITION POTENCY OF CYNODONTIN

The antioxidant activity of cynodontin was studied in the absence and the presence of free radical species. This in silico study was performed in water and benzene, with the aim to simulate polar and non-polar environment. To determine the most probable mechanism of antioxidant action, density functional theory (DFT) was employed. The change in reaction enthalpy of cynodontin with three different free radicals (hydroxyl, hydroperoxyl, and methyl peroxyl radical) were examined and presented. SET-PT (Single Electron Transfer – Proton Transfer) mechanism is not an operative mechanism of antioxidant action. The obtained results imply that the possible mechanism of antioxidant action in water is SPLET (Sequential Proton Loss Electron Transfer), while in benzene HAT (Hydrogen atom transfer) and SPLET are competitive mechanisms. The molecular docking study was performed in order to estimate the inhibition potency of the investigated compound toward human leukocyte elastase (HLE). The obtained results indicate that numerous interactions determine the inhibition activity towards the investigated protein.

On the physical mechanisms of the two-way coupling between a surface wave field and a circulation consisting of a roll and streak

The governing equations of a surface wave field and a coexisting roll–streak circulation typical of Langmuir circulations or submesoscale frontal circulations are derived to better describe their two-way interactions. The gradients and vertical velocities of the roll–streak circulation induce wave refraction, amplitude modulation and higher-order waves. These changes then produce wave–wave nonlinear forces and divergence of the wave-induced mass transport, both of which in turn affect the circulation. To accurately represent these processes, both a wave theory and a wave-averaged theory are developed without relying on any extrapolation, any spatiotemporal mapping or an approximation that treats the wave-induced mass divergence as being concentrated at the surface. This wave theory finds seven types of current-induced higher-order wave motions. It also determines the wave dynamics such as the governing equation of the wave action density valid in the presence of the complex circulation. The evolution of the wave action density is clearly affected by the upwelling or downwelling. The new wave-averaged theory presents the governing equations of the wave-averaged circulation which satisfies the wave-averaged mass conservation. This circulation is different from the circulation considered to satisfy the mass conservation in the Craik–Leibovich theory, and the difference becomes critical when the wave field evolves due to refraction. In this case, compared to the Craik–Leibovich theory, long waves are more important and also the rolls are more weakly forced.

WAVES AND STRONGLY SHEARED CURRENTS: EXTENSIONS TO COASTAL OCEAN MODELS

Significant progress has been made in the numerical modeling of wave-current interaction during the past decade. Typical coastal circulation and wave models, however, still only employ theoretical formulations which take depth-uniform mean flows into account, with realistic, non-uniform flows treated as being depth uniform through some chosen averaging procedure. Depending on the choice of average over depth, significant errors may arise in the estimation of properties such as group velocity and action density in realistic conditions. These errors, in turn, are fed back into the circulation model through incorrect representation of the vertical structure of wave forcing. A new framework for wave-current interaction theory for strongly sheared mean flows has been developed using vortex force formalism by Dong (2016). The resulting formulation leads to a conservation law for wave action identical to that of Voronovich (1976), and to expressions for wave-averaged forces in the Craik-Leibovich vortex force formalism. In this study, we are completing the development of a coupled NHWAVE/SWAN which implements the wave forcing formulation of Dong (2016) in a wave-averaged version of the non-hydrostatic model NHWAVE (Ma et al., 2012). The SWAN model is also being extended to incorporate a better representation of frequency and direction-dependent group velocity and intrinsic frequency in the neighborhood of the spectral peak, thus improving on the present practice of using quantities evaluated only at the spectral peak. The resulting model is being tested against field data collected in several recent experiments involving strong, vertically sheared currents in river mouths or straits.

On the Generalized Kinetic Equation for Surface Gravity Waves, Blow-Up and Its Restraint

This article is concerned with the non-linear interaction of homogeneous random ocean surface waves. Under this umbrella, numerous kinetic equations have been derived to study the evolution of the spectral action density, each employing slightly different assumptions. Using analytical and numerical tools, and providing exact formulas, we demonstrate that the recently derived generalized kinetic equation exhibits blow up in finite time for certain degenerate quartets of waves. This is discussed in light of the assumptions made in the derivation, and this equation is contrasted with other kinetic equations for the spectral action density.

Interactions between Mesoscale and Submesoscale Gravity Waves and Their Efficient Representation in Mesoscale-Resolving Models

As present weather forecast codes and increasingly many atmospheric climate models resolve at least part of the mesoscale flow, and hence also internal gravity waves (GWs), it is natural to ask whether even in such configurations subgrid-scale GWs might impact the resolved flow and how their effect could be taken into account. This motivates a theoretical and numerical investigation of the interactions between unresolved submesoscale and resolved mesoscale GWs, using Boussinesq dynamics for simplicity. By scaling arguments, first a subset of submesoscale GWs that can indeed influence the dynamics of mesoscale GWs is identified. Therein, hydrostatic GWs with wavelengths corresponding to the largest unresolved scales of present-day limited-area weather forecast models are an interesting example. A large-amplitude WKB theory, allowing for a mesoscale unbalanced flow, is then formulated, based on multiscale asymptotic analysis utilizing a proper scale-separation parameter. Purely vertical propagation of submesoscale GWs is found to be most important, implying inter alia that the resolved flow is only affected by the vertical flux convergence of submesoscale horizontal momentum at leading order. In turn, submesoscale GWs are refracted by mesoscale vertical wind shear while conserving their wave-action density. An efficient numerical implementation of the theory uses a phase-space ray tracer, thus handling the frequent appearance of caustics. The WKB approach and its numerical implementation are validated successfully against submesoscale-resolving simulations of the resonant radiation of mesoscale inertia GWs by a horizontally as well as vertically confined submesoscale GW packet.

SU(3) Yang Mills theory at small distances and fine lattices

We investigate the SU(3) Yang Mills theory at small gradient flow time and at short distances. Lattice spacings down to a = 0.015 fm are simulated with open boundary conditions to allow topology to flow in and out. We study the behaviour of the action density E(t) close to the boundaries, the feasibility of the small flow-time expansion and the extraction of the Λ-parameter from the static force at small distances. For the latter, significant deviations from the 4-loop perturbative β-function are visible at α ≈ 0.2. We still can extrapolate to extract roΛ.