Towards massless sector of tensionless strings on AdS(5)

A Formal Higher Spin Gravity in five dimensions is constructed. It was shown recently that constructing formally consistent classical equations of motion of higher spin gravities is equivalent to finding a certain deformation of a given higher spin algebra. A strong homotopy algebra encoding the interaction vertices then follows. We propose two different and novel realizations of the deformed higher spin algebra in the case of five dimensions: one in terms of the universal enveloping algebra of $su(2,2)$ and the other by means of oscillator variables. Both the new realizations are amenable to supersymmetric extensions and the $\mathcal{N}=8$ case underlies the massless sector of tensionless strings

More on Quantum Chiral Higher Spin Gravity

Chiral Higher Spin Gravity is unique in being the smallest higher spin extension of gravity and in having a simple local action both in flat and (anti)-de Sitter spaces. It must be a closed subsector of any other higher spin theory in four dimensions, which makes it an important building block and benchmark. Using the flat space version for simplicity, we perform a thorough study of quantum corrections in Chiral Theory, which strengthen our earlier results arXiv:1805.00048. Even though the interactions are naively non-renormalizable, we show that there are no UV-divergences in two-, three- and four-point amplitudes at one loop thanks to the higher spin symmetry. We also give arguments that the AdS Chiral Theory should exhibit similar properties. It is shown that Chiral Theory admits Yang-Mills gaugings with $U(N)$, $SO(N)$ and $USp(N)$ groups, which is reminiscent of the Chan-Paton symmetry in string theory

Boundary homogenization for target search problems

In this review, we describe several approximations in the theory of Laplacian transport near complex or heterogeneously reactive boundaries. This phenomenon, governed by the Laplace operator, is ubiquitous in fields as diverse as chemical physics, hydrodynamics, electrochemistry, heat transfer, wave propagation, self-organization, biophysics, and target search. We overview the mathematical basis and various applications of the effective medium approximation and the related boundary homogenization when a complex heterogeneous boundary is replaced by an effective much simpler boundary. We also discuss the constant-flux approximation, the Fick-Jacobs equation, and other mathematical tools for studying the statistics of first-passage times to a target. Numerous examples and illustrations are provided to highlight the advantages and limitations of these approaches

Diffusion towards a nanoforest of absorbing pillars

Spiky coatings (also known as nanoforests or Fakir-like surfaces) have found many applications in chemical physics, material sciences and biotechnology, such as superhydrophobic materials, filtration and sensing systems, selective protein separation, to name but a few. In this paper, we provide a systematic study of steady-state diffusion towards a periodic array of absorbing cylindrical pillars protruding from a flat base. We approximate a periodic cell of this system by a circular tube containing a single pillar, derive an exact solution of the underlying Laplace equation, and deduce a simple yet exact representation for the total flux of particles onto the pillar. The dependence of this flux on the geometric parameters of the model is thoroughly analyzed. In particular, we investigate several asymptotic regimes such as a thin pillar limit, a disk-like pillar, and an infinitely long pillar. Our study sheds a light onto the trapping efficiency of spiky coatings and reveals the roles of pillar anisotropy and diffusional screening. Further extensions of the proposed solution are described, including time-dependent diffusion

Estimation of Scalar Field Distribution in the Fourier Domain

In this paper we consider the problem of estimation of scalar field distribution collected from noisy measurements. The field is modelled as a sum of Fourier components/modes, where the number of modes retained and estimated determines in a natural way the approximation quality. An algorithm for estimating the modes using an online optimization approach is presented, under the assumption that the noisy measurements are quantized. The algorithm can estimate time-varying fields through the introduction of a forgetting factor. Simulation studies demonstrate the effectiveness of the proposed approach

Slip length for a viscous flow over spiky surfaces

For a model of a 3D coating composed of a bi-periodic system of parallel riblets with gaps we analytically derive an approximate formula for the effective slip length (an offset from the flat surface at which the flow velocity would extrapolate to zero) as a function of the geometry of the system (riblet period, riblet height, and relative gap size). This formula is valid for an arbitrary fraction of gaps (i.e from narrow riblets to narrow gaps) and agrees with the known analytical results for the 2D periodic coating of riblets without gaps

Blocker effect on diffusion resistance of a membrane channel. Dependence on the blocker geometry

Being motivated by recent progress in nanopore sensing, we develop a theory of the effect of large analytes, or blockers, trapped within the nanopore confines, on diffusion flow of small solutes. The focus is on the nanopore diffusion resistance which is the ratio of the solute concentration difference in the reservoirs connected by the nanopore to the solute flux driven by this difference. Analytical expressions for the diffusion resistance are derived for a cylindrically symmetric blocker whose axis coincides with the axis of a cylindrical nanopore in two limiting cases where the blocker radius changes either smoothly or abruptly. Comparison of our theoretical predictions with the results obtained from Brownian dynamics simulations shows good agreement between the two

On the effect of far impurities on the density of states of two-dimensional electron gas in a strong magnetic field

The effect of impurities situated at different distances from a two-dimensional electron gas on the density of states in a strong magnetic field is analyzed. Based on the exact result of Brezin, Gross, and Itzykson, we calculate the density of states in the whole energy range, assuming the Poisson distribution of impurities in the bulk. It is shown that in the case of small impurity concentration the density of states is qualitatively different from the model case when all impurities are located in the plane of the two-dimensional electron gas.Comment: 6 pages, 1 figure, submitted to JETP Letter

Measurement of the geomagnetic field in the ionosphere using radar methods

A new method for measuring the geomagnetic field in the ionosphere by the integrated use of vertical sounding radar (ionosonde) and incoherent scatter radar, its capabilities and features of the technical implementation, as well as the first results of an experimental test are considered.Розглянуто новий спосіб вимірювання геомагнітного поля в іоносфері шляхом інтегрального використання радару вертикального зондування (іонозонду) і радару некогерентного розсіяння, його можливості й особливості технічної реалізації, а також перші результати експериментального випробування

Spectroscopic evidence for strong correlations between local superconducting gap and local Altshuler-Aronov density-of-states suppression in ultrathin NbN films

Disorder has different profound effects on superconducting thin films. For a large variety of materials, increasing disorder reduces electronic screening which enhances electron-electron repulsion. These fermionic effects lead to a mechanism described by Finkelstein: when disorder combined to electron-electron interactions increases, there is a global decrease of the superconducting energy gap $\Delta$ and of the critical temperature $T_c$, the ratio $\Delta$/$k_BT_c$ remaining roughly constant. In addition, in most films an emergent granularity develops with increasing disorder and results in the formation of inhomogeneous superconducting puddles. These gap inhomogeneities are usually accompanied by the development of bosonic features: a pseudogap develops above the critical temperature $T_c$ and the energy gap $\Delta$ starts decoupling from $T_c$. Thus the mechanism(s) driving the appearance of these gap inhomogeneities could result from a complicated interplay between fermionic and bosonic effects. By studying the local electronic properties of a NbN film with scanning tunneling spectroscopy (STS) we show that the inhomogeneous spatial distribution of $\Delta$ is locally strongly correlated to a large depletion in the local density of states (LDOS) around the Fermi level, associated to the Altshuler-Aronov effect induced by strong electronic interactions. By modelling quantitatively the measured LDOS suppression, we show that the latter can be interpreted as local variations of the film resistivity. This local change in resistivity leads to a local variation of $\Delta$ through a local Finkelstein mechanism. Our analysis furnishes a purely fermionic scenario explaining quantitatively the emergent superconducting inhomogeneities, while the precise origin of the latter remained unclear up to now.Comment: 11 pages, 4 figure