Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

Prediction of infrared light emission from pi-conjugated polymers: a diagrammatic exciton basis valence bond theory

There is currently a great need for solid state lasers that emit in the infrared, as this is the operating wavelength regime for applications in telecommunications. Existing $\pi$--conjugated polymers all emit in the visible or ultraviolet, and whether or not $\pi$--conjugated polymers that emit in the infrared can be designed is an interesting challenge. On the one hand, the excited state ordering in trans-polyacetylene, the $\pi$--conjugated polymer with relatively small optical gap, is not conducive to light emission because of electron-electron interaction effects. On the other hand, excited state ordering opposite to that in trans-polyacetylene is usually obtained by chemical modification that increases the effective bond-alternation, which in turn increases the optical gap. We develop a theory of electron correlation effects in a model $\pi$-conjugated polymer that is obtained by replacing the hydrogen atoms of trans-polyacetylene with transverse conjugated groups, and show that the effective on-site correlation in this system is smaller than the bare correlation in the unsubstituted system. An optical gap in the infrared as well as excited state ordering conducive to light emission is thereby predicted upon similar structural modifications.Comment: 15 pages, 15 figures, 1 tabl

Comparative study of deuterium retention and vacancy content of self-ion irradiated tungsten

Self-ion irradiation of pure tungsten with 2 MeV W ions provides a way of simulating microstructures generated by neutron irradiation in tungsten components of a fusion reactor. Transmission electron microscopy (TEM) has been used to characterize defects formed in tungsten samples by ion irradiation. It was found that tungsten irradiated to 0.85 dpa at relatively low temperatures develops a characteristic microstructure dominated by dislocation loops and black dots. The density and size distribution of these defects were estimated. Some of the samples exposed to self-ion irradiation were then implanted with deuterium. Thermal Desorption Spectrometry (TDS) analysis was performed to estimate the deuterium inventory as a function of irradiation damage and deuterium release as a function of temperature. Increase of inventory with increasing irradiation dose followed by slight decrease above 0.1 dpa was found. Application of Positron Annihilation Spectroscopy (PAS) to self-irradiated but not deuterium implanted samples enabled an assessment of the density of irradiation defects as a function of exposure to highenergy ions. The PAS results show that the density of defects saturates at doses in the interval from 0.085 to 0.425 displacements per atom (dpa). These results are discussed in the context of recent theoretical simulations exhibiting the saturation of defect microstructure in the high irradiation exposure limit. The saturation of damage found in PAS agrees with the simulation data described in the paper. (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )Peer reviewe

A theoretical investigation of the low lying electronic structure of poly(p-phenylene vinylene)

The two-state molecular orbital model of the one-dimensional phenyl-based semiconductors is applied to poly(p-phenylene vinylene). The energies of the low-lying excited states are calculated using the density matrix renormalization group method. Calculations of both the exciton size and the charge gap show that there are both Bu and Ag excitonic levels below the band threshold. The energy of the 1Bu exciton extrapolates to 2.60 eV in the limit of infinite polymers, while the energy of the 2Ag exciton extrapolates to 2.94 eV. The calculated binding energy of the 1Bu exciton is 0.9 eV for a 13 phenylene unit chain and 0.6 eV for an infinite polymer. This is expected to decrease due to solvation effects. The lowest triplet state is calculated to be at ca. 1.6 eV, with the triplet-triplet gap being ca. 1.6 eV. A comparison between theory, and two-photon absorption and electroabsorption is made, leading to a consistent picture of the essential states responsible for most of the third-order nonlinear optical properties. An interpretation of the experimental nonlinear optical spectroscopies suggests an energy difference of ca. 0.4 eV between the vertical energy and ca. 0.8 eV between the relaxed energy, of the 1Bu exciton and the band gap, respectively.Comment: LaTeX, 19 pages, 7 eps figures included using epsf. To appear in Physical Review B, 199

Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries

We present a numerical study of 2D random-bond Potts ferromagnets. The model is studied both below and above the critical value $Q_c=4$ which discriminates between second and first-order transitions in the pure system. Two geometries are considered, namely cylinders and square-shaped systems, and the critical behavior is investigated through conformal invariance techniques which were recently shown to be valid, even in the randomness-induced second-order phase transition regime Q>4. In the cylinder geometry, connectivity transfer matrix calculations provide a simple test to find the range of disorder amplitudes which is characteristic of the disordered fixed point. The scaling dimensions then follow from the exponential decay of correlations along the strip. Monte Carlo simulations of spin systems on the other hand are generally performed on systems of rectangular shape on the square lattice, but the data are then perturbed by strong surface effects. The conformal mapping of a semi-infinite system inside a square enables us to take into account boundary effects explicitly and leads to an accurate determination of the scaling dimensions. The techniques are applied to different values of Q in the range 3-64.Comment: LaTeX2e file with Revtex, revised versio

The low-lying excitations of polydiacetylene

The Pariser-Parr-Pople Hamiltonian is used to calculate and identify the nature of the low-lying vertical transition energies of polydiacetylene. The model is solved using the density matrix renormalisation group method for a fixed acetylenic geometry for chains of up to 102 atoms. The non-linear optical properties of polydiacetylene are considered, which are determined by the third-order susceptibility. The experimental 1Bu data of Giesa and Schultz are used as the geometric model for the calculation. For short chains, the calculated E(1Bu) agrees with the experimental value, within solvation effects (ca. 0.3 eV). The charge gap is used to characterise bound and unbound states. The nBu is above the charge gap and hence a continuum state; the 1Bu, 2Ag and mAg are not and hence are bound excitons. For large chain lengths, the nBu tends towards the charge gap as expected, strongly suggesting that the nBu is the conduction band edge. The conduction band edge for PDA is agreed in the literature to be ca. 3.0 eV. Accounting for the strong polarisation effects of the medium and polaron formation gives our calculated E(nBu) ca. 3.6 eV, with an exciton binding energy of ca. 1.0 eV. The 2Ag state is found to be above the 1Bu, which does not agree with relaxed transition experimental data. However, this could be resolved by including explicit lattice relaxation in the Pariser- Parr-Pople-Peierls model. Particle-hole separation data further suggest that the 1Bu, 2Ag and mAg are bound excitons, and that the nBu is an unbound exciton.Comment: LaTeX, 23 pages, 4 postscript tables and 8 postscript figure

Theory of excited state absorptions in phenylene-based π\pi-conjugated polymers

Within a rigid-band correlated electron model for oligomers of poly-(paraphenylene) (PPP) and poly-(paraphenylenevinylene) (PPV), we show that there exist two fundamentally different classes of two-photon A$_g$ states in these systems to which photoinduced absorption (PA) can occur. At relatively lower energies there occur A$_g$ states which are superpositions of one electron - one hole (1e--1h) and two electron -- two hole (2e--2h) excitations, that are both comprised of the highest delocalized valence band and the lowest delocalized conduction band states only. The dominant PA is to one specific member of this class of states (the mA$_g$). In addition to the above class of A$_g$ states, PA can also occur to a higher energy kA$_g$ state whose 2e--2h component is {\em different} and has significant contributions from excitations involving both delocalized and localized bands. Our calculated scaled energies of the mA$_g$ and the kA$_g$ agree reasonably well to the experimentally observed low and high energy PAs in PPV. The calculated relative intensities of the two PAs are also in qualitative agreement with experiment. In the case of ladder-type PPP and its oligomers, we predict from our theoretical work a new intense PA at an energy considerably lower than the region where PA have been observed currently. Based on earlier work that showed that efficient charge--carrier generation occurs upon excitation to odd--parity states that involve both delocalized and localized bands, we speculate that it is the characteristic electronic nature of the kA$_g$ that leads to charge generation subsequent to excitation to this state, as found experimentally.Comment: Revtex4 style, 2 figures inserted in the text, three tables, 10 page

Новый Каталог ледников России по спутниковым данным (2016–2019 гг.)

The new Inventory of the Russian glaciers has been created at the Institute of Geography of the Russian Academy of Sciences mainly on the basis of the Sentinel 2 satellite images for 2016–2019 with the aim of assessing the current state of glacier systems and as a basis for monitoring and re-inventorying. Delineation of glacier outlines was manually made to reduce uncertainties, especially for small glaciers. The database structure is compatible with the global and national glacier archives and includes the main glacial parameters. Additionally a classification of possible catastrophic phenomena of glacial genesis was developed: dynamically unstable glaciers, glacier lakes, icebergs, etc. The data base is available online (www.glacrus.ru). At present, there are 22 glacial systems in Russia with a total area of 54,518 km2. The largest glacial systems by area are located in the Arctic archipelagos: Novaya Zemlya, Severnaya Zemlya, and Franz Josef Land. The glacial systems of the Caucasus, Kamchatka, and Altai are the largest by area in the continental part of Russia. The main group consists of 13 small glacial systems, the area of which does not exceed 100 km2. They are located in different glaciological zones: from the De Long Islands in the Arctic to the Eastern Sayan in southern Siberia. Since the compilation of the USSR glacier Inventory (1965–1982), the area of glaciers has decreased by 5,594 km2, or 9.3%. The area of polar glaciers has decreased in smaller degree than that of glaciers in mountainous regions. The results of our research confirm the trend of reducing the area of glaciers throughout the Russian territory. The magnitude and rate of changes depend on local climatic and orographic features. The exception is the glaciers of the volcanic regions of Kamchatka, the area of which has increased or remained unchanged.Создан Каталог ледников России на основе спутниковых снимков Sentinel‑2 (2016–2019 гг.) (www.glacrus.ru). Он содержит информацию о 22-х ледниковых системах общей площадью 54 518 км2. По сравнению с Каталогом ледников СССР (1965–1982 гг.) площадь ледников на территории России уменьшилась на 5594 км2, или на 9,3%. Величина и скорость изменений в разных районах сильно отличаются и зависят от местных климатических и орографических особенностей

Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates

In this paper we will review the main results concerning the issue of stability for the determination unknown boundary portion of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and selfcontained proofs. We prove that such problems are severely ill-posed in the sense that under a priori regularity assumptions on the unknown boundaries, up to any finite order of differentiability, the continuous dependence of unknown boundary from the measured data is, at best, of logarithmic type