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Although various visual localization approaches exist, such as scene coordinate and pose regression, these methods often struggle with high memory consumption or extensive optimization requirements. To address these challenges, we utilize recent advancements in novel view synthesis, particularly 3D Gaussian Splatting (3DGS), to enhance localization. 3DGS allows for the compact encoding of both 3D geometry and scene appearance with its spatial features. Our method leverages the dense description maps produced by XFeat's lightweight keypoint detection and description model. We propose distilling these dense keypoint descriptors into 3DGS to improve the model's spatial understanding, leading to more accurate camera pose predictions through 2D-3D correspondences. After estimating an initial pose, we refine it using a photometric warping loss. Benchmarking on popular indoor and outdoor datasets shows that our approach surpasses state-of-the-art Neural Render Pose (NRP) methods, including NeRFMatch and PNeRFLoc., Comment: Project website at https://gsplatloc.github.io/

Nowadays superconducting radio frequency (SRF) cavities represent fundamental tools used for (Standard Model) particle acceleration, (beyond Standard Model) particle probing and long-lifetime photon preservation. We study the SRF frequency shift in the vicinity of the critical temperature $T_c$ and the quality factor mainly at low temperatures within the Dynes superconductor model. We scrutinize and use the local limit response to the external electromagnetic field. Our approach allows for a finer analysis of the peculiar behavior of the resonant frequency shift immensely close to $T_c$, observed in recent experiments. In the ideal dirty limit, we analytically elaborate on the width and depth of the resulting dip. Studying the sign of the slope of the resonant frequency shift at $T_c$ in the moderately clean regime reveals the role of the pair-breaking and pair-conserving disorder. Next, to find the relevance of our description, we compare and also fit our results with the recent experimental data from the N-doped Nb sample presented in [arXiv:2307.07905v1]. Our analysis remarkably complies with the experimental findings, especially concerning the dip width. We offer straightforward, homogeneous-disorder-based interpretation within the moderately clean regime. Assuming the same regime at low temperatures, we address details of the high-quality plateaus. Summing all up, this work presents (and studies the limits of) the simple effective description of the complex problem corresponding to the electromagnetic response in the superconductors combining homogeneous conventional pairing and two different kinds of disorder scattering., Comment: 16 pages, 13 figures, 2 appendices

We provide constructive necessary and sufficient conditions for a family of periodic wavelets to be a Parseval wavelet frame. The criterion generalizes unitary and oblique extension principles. The case of one wavelet generator and refinable functions being trigonometric polynomials is discussed in details., Comment: 21 pages

We study the energy gap $\Delta(T)$ within the Dynes superconductor theory. This model generalizes the Bardeen-Cooper-Schrieffer (BCS) approach by including the pair-breaking scattering, introducing the tunneling in-gap states up to a Fermi level. We analytically solve the energy gap equation in various limit cases. The solution provides simple tools for further studies, compared to more complex numerics, and highlights the basic characteristics of the theory. First, in the critical limit of pair-breaking scattering, we derive (inspired by the famous BCS ratio) $\Delta_0/T_c = \sqrt{2/3}\pi$. Next, we derive the dependence $ \Delta(T)$ close to critical temperature and look at its behavior for general (and also critical) pair-breaking scattering rate $\Gamma$. Furthermore, we compare our result - analytical dependence of $\Delta(T)$ - with the numerical solution of the gap equation assuming general temperature. We show the range of temperatures, for which the analytical approximation is valid. In the end, we introduce the heuristic formula of $\Delta(0\leq T\leq T_c)$, assuming general pair-breaking scattering, emphasizing its exact behavior close to $T_c$., Comment: 5 pages, 6 figures, 4 Appendices

We demonstrate an efficient swithcable spintronic THz emission from a Co(2nm)/Pt(2nm) bilayer split into a grating of micro- or nanostripes in applied external magnetic field of the order of 10mT. The THz signal is effectively emitted if the samples are magnetized perpendicular to the stripes direction and decreases upon a 90-degree rotation of a sample. The maximal 27-fold ratio of amplitude change is achieved for the sample with a $2 \mu m$ width of stripes. For the samples with easy magnetization axis directed perpendicular to stripes the THz signal is linearly polarized in the direction of the stripes and abruptly switches during the sample re-magnetization process. If the easy axis is along the stripes the THz source is almost switched off in a zero magnetic field., Comment: 6 pages, 6 figures

N-heterocyclic carbene (NHC) iridium (III) complexes are considered as promising candidates for blue emitters in organic light-emitting diodes. They can play the roles of the emitter as well as of electron and hole transporters in the same emission layer. We investigate optical transitions in such complexes with account of geometry and electronic structure changes upon excitation or charging and exciton transfer between the complexes from first principles. It is shown that excitation of NHC iridium complexes is accompanied by a large reorganization energy $\sim$0.7 eV and a significant loss in the oscillator strength, which should lead to low exciton diffusion. Calculations with account of spin-orbit coupling reveal a small singlet-triplet splitting $\sim$0.1 eV, whereas the oscillator strength for triplet excitations is found to be an order of magnitude smaller than for the singlet ones. The contributions of the F\"orster and Dexter mechanisms are analyzed via the explicit integration of transition densities. It is shown that for typical distances between emitter complexes in the emission layer, the contribution of the Dexter mechanism should be negligible compared to the F\"orster mechanism. On the other hand, the ideal dipole approximation, although gives the correct order of the exciton coupling, fails to reproduce the result taking into account spatial distribution of the transition density. For charged NHC complexes, we find a number of optical transitions close to the emission peak of the blue emitter with high exciton transfer rates that can be responsible for exciton-polaron quenching. The nature of these transitions is analyzed., Comment: 20 pages, 7 figures

The potential energy surface (PES) of interlayer interaction of infinite twisted bilayer graphene is calculated for a set of commensurate moir\'e patterns using the registry-dependent Kolmogorov-Crespi empirical potential. The calculated PESs have the same shape for all considered moir\'e patterns with the unit cell size of the PES which is inversely related to the unit cell size of the moir\'e pattern. The amplitude of PES corrugations is found to decrease exponentially upon increasing the size of the moir\'e pattern unit cell. An analytical expression for such a PES including the first Fourier harmonics compatible with the symmetries of both layers is derived. It is shown that the calculated PESs can be approximated by the derived expression with the accuracy within 1%. This means that different physical properties associated with relative in-plane motion of graphene layers are interrelated and can be expressed analytically as functions of the amplitude of PES corrugations. In this way, we obtain the shear mode frequency, shear modulus, shear strength and barrier for relative rotation of the commensurate twisted layers to a fully incommensurate state for the considered moir\'e patterns. This barrier may possibly lead to the macroscopic robust superlubricity for twisted graphene bilayer with a commensurate moir\'e pattern. The conclusions made should be valid for diverse 2D systems of twisted commensurate layers., Comment: 9 pages, 3 figures; Supplemental Material: 2 pages, 1 figure

In the paper we design a Parseval wavelet frame with a compact support. The corresponding refinement mask uniformly approximates an arbitrary continuous periodic function $f$, $f(0)=1$, $|f(x)|^2+|f(x+\pi)|^2\le 1$. The refinable function has stable integer shifts., Comment: 6 pages. arXiv admin note: substantial text overlap with arXiv:2207.08252

Written for the book "Mathematicians from Saint Petersburg and their theorems"., Comment: english+russian

Graph comparison is a certain type of condition on metric space encoded by a finite graph. We show that any nontrivial graph comparison implies one of Alexandrov's comparisons. The proof gives a complete description of graphs with trivial graph comparisons., Comment: English+Russian, 7+7 pages, 11+11 figures

We show that trees and their products meet octahedron comparison., Comment: 4 pages, 4 figures

We investigate how parameters of the model of semi-infinite graphene based on a graphene nanoribbon under periodic boundary conditions affect the accuracy of ab initio calculations of reactions at graphene edges by the example of the first stage of reconstruction of zigzag graphene edges, formation of a pentagon-heptagon pair. It is shown that to converge properly the results, the nanoribbon should consist of at least 6 zigzag rows and periodic images of the pair along the nanoribbon axis should be separated by at least 6 hexagons. The converged reaction energy and activation barrier for formation of an isolated pentagon-heptagon pair are found to be -0.15 eV and 1.61 eV, respectively. It is also revealed that such defects reduce the graphene edge magnetization only locally but ordering of spins at opposite nanoribbon edges switches from the antiparallel (antiferromagnetic) to parallel one (ferromagnetic) upon increasing the defect density., Comment: 19 pages, 7 figures

Ab initio calculations are performed to study consecutive reconstruction of a zigzag graphene edge. According to the obtained energy profile along the reaction pathway, the first reconstruction step, formation of the first pentagon-heptagon pair, is the slowest one, while the growth of an already nucleated reconstructed edge domain should occur steadily at a much higher rate. Domains merge into one only in 1/4 of cases when they get in contact, while in the rest of the cases, residual defects are left. Structure, energy and magnetic properties of these defects are studied. It is found that spontaneous formation of pairs of residual defects (i.e. spontaneous domain nucleation) in the fully reconstructed edge is unlikely at temperatures below 1000 K. Using a kinetic model, we show that the average domain length is of several $\mathrm{\mu}$m at room temperature and it decreases exponentially upon increasing the temperature at which the reconstruction takes place., Comment: 5 pages, 4 figures

A metric space is said to be all-set-homogeneous if any of its partial isometries can be extended to a genuine isometry. We give a classification of a certain subclass of all-set-homogeneous length spaces., Comment: English+Russian, 4+4 pages, 1+1 figure

We present a code modularization approach to design efficient and massively parallel cubic and linear-scaling solvers for electronic structure calculations using atomic orbitals. The modular implementation of the orbital minimization method, in which linear algebra and parallelization issues are handled via external libraries, is demonstrated in the SIESTA code. The DBCSR and ScaLAPACK libraries are used for algebraic operations with sparse and dense matrices, respectively. The MatrixSwitch and libOMM libraries, recently developed within the Electronic Structure Library, facilitate switching between different matrix formats and implement the energy minimization. We show results comparing the performance of several cubic-scaling algorithms, and also demonstrate the parallel performance of the linear-scaling solvers, and their supremacy over the cubic-scaling solvers for insulating systems with sizes of several hundreds of atoms., Comment: 13 pages, 10 figures

In the paper we design a Parseval wavelet frame with a compact support and many vanishing moments. The corresponding refinement mask approximates an arbitrary continuous periodic function $f$, $f(0)=1$. The refinable function has stable integer shifts., Comment: 8 pages

We prove weak convergence of curvature tensors of Riemannian manifolds for converging noncollapsing sequences with a lower bound on sectional curvature., Comment: 34 pages, 4 figures

We give an if-and-only-if condition on a five-point metric spaces that admit embeddings into nonnegatively curved Riemannian manifolds., Comment: 19 pages, 37 figures

The potential energy surface (PES) of interlayer interaction of twisted bilayer graphene with vacancies in one of the layers is investigated via density functional theory (DFT) calculations with van der Waals corrections. These calculations give a non-negligible magnitude of PES corrugation of 28 meV per vacancy and barriers for relative sliding of the layers of 7 - 8 meV per vacancy for the moir\'e pattern with coprime indices (2,1) (twist angle 21.8$^\circ$). At the same time, using the semiempirical potential fitted to the DFT results, we confirm that twisted bilayer graphene without defects exhibits superlubricity for the same moir\'e pattern and the magnitude of PES corrugation for the infinite bilayer is below the calculation accuracy. Our results imply that atomic-scale defects restrict the superlubricity of 2D layers and can determine static and dynamic tribological properties of these layers in a superlubric state. We also analyze computationally cheap approaches that can be used for modeling of tribological behavior of large-scale systems with defects. The adequacy of using state-of-the-art semiempirical potentials for interlayer interaction and approximations based on the first spatial Fourier harmonics for the description of interaction between graphene layers with defects is discussed., Comment: 11 pages, 4 figures

Since fullerene formation occurs under conditions where direct observation of atomic-scale reactions is not possible, modeling is the only way to reveal atomistic mechanisms which can lead to selection of abundant fullerene isomers (like C60-Ih). In the present paper we review the results obtained for different atomistic mechanisms by various modeling techniques. Although it seems that atomic-scale processes related to odd fullerenes (such as growth by consecutive insertions of single carbon atoms and rearrangements of the sp$^2$ structure promoted by extra sp atoms) provide the main contribution to selection of abundant isomers, at the moment there is no conclusive evidence in favor of any particular atomistic mechanism. Thus, the following multiscale modeling strategy to solve the mystery of the high yield of abundant fullerene isomers is suggested. On the one hand, sets of reactions between fullerene isomers can be described using theoretical graph techniques. On the other hand, reaction schemes can be revealed by classical molecular dynamics simulations with subsequent refinement of the activation barriers by ab initio calculations. Based on the reaction sets with the reaction probabilities derived in this way, the different atomistic mechanisms of abundant fullerene isomer selection can be compared by kinetic models., Comment: 20 pages, 4 figures

We experimentally studied a clusterization process in a system of polyamide tracers that are used for visualizing the flow of liquids on their surface. It was shown that in a surface structure system appearing on the water surface a Pareto distribution is formed for normalized cluster density and it is well described by a C/x^(-n) power-law function. One can suggest that the growth of a surface structure is defined by the action of surface tension forces, and the number of surface structures decreases exponentially, while maintaining their total surface area. We show experimentally the significant role of background liquid flows on the surface in the clusterization process, Comment: 12 pages, 8 figures

Healing of a hole in a carbon nanotube under electron irradiation in HRTEM at room temperature is demonstrated using molecular dynamics simulations with the CompuTEM algorithm. Formation of an amorphous patch is observed in all simulation runs. The amorphous patch is formed in the absence of external carbon adatoms only via reconstruction of the carbon bond network. It consists mainly of 5-, 6- and 7-membered rings and causes a small bottleneck. In addition, further growth of the initial amorphous patch under electron irradiation takes place. Two-coordinated atoms are found to play a crucial role in the latter process, analogous to autocatalisys of rearrangements of rings in fullerenes. The principal rearrangements in the presence of two-coordinated atoms can be described as generalized sp-defect migration: a bond is broken between two three-coordinated atoms and one of them forms a new bond with a nearby two-coordinated atom. If the new and former two-coordinated atoms are not bonded, the reaction leads both to displacement of the sp defect and changes in rings of the sp$^2$ carbon structure. Migration by hopping of two-coordinated atoms and other reactions involving simultaneous breakage of two bonds are also detected but much rarely. Long-living two-coordinated atoms in the patch structure and related fast growth of the patch are observed in more than half of the simulation runs. Since the amorphous patch and bottleneck affect the electronic properties of the nanotube, such nanotubes can be perspective for nanoelectronic applications., Comment: 9 pages, 5 figures

The dynamics of memristive device in response to neuron-like signals and coupling electronic neurons via memristive device has been investigated theoretically and experimentally. The simplest experimental system consists of electronic circuit based on the FitzHugh-Nagumo model and metal-oxide memristive device. The hardware-software complex based on commercial data acquisition system is implemented for the imitation of signal from presynaptic neuron`s membrane and synaptic signal transmission between neurons. The main advantage of our system is that it uses real time dynamics of memristive device. Electrical response of memristive device shows its behavioral flexibility that allows presenting a memristive device as an active synapse. This means an internal adjustment of the parameters of memristive device that leads to modulation of neuron-like signals. Physics-based dynamical model of memristor is developed in MATLAB for numerical simulation of such a memristive interface to describe and predict experimentally observed regularities of synchronization of neuron-like oscillators. FitzHugh-Nagumo circuits time series with a linear or stepwise increase in the signal amplitude are used to study the memristor response and coupling of neuron-like oscillators taking into account the stochasticity of memristor model to compare the numerical and experimental data. The observed forced synchronization modes characterize the dynamic complexity of the memristive device, which requires further description using high-order dynamical models. The developed memristive interface will provide high efficiency in the imitation of the synaptic connection due to its stochastic nature and can be used to increase the flexibility of neuronal connections for neuroprosthetic challenges.

Molecular dynamics simulations show that a graphene nanoribbon with alternating regions which are one and three hexagons wide can transform into a hybrid 1D nanoobject with alternating double chains and polycyclic regions under electron irradiation in HRTEM. A scheme of synthesis of such a nanoribbon using Ullmann coupling and dehydrogenation reactions is proposed. The reactive REBO-1990EVC potential is adapted for simulations of carbon-hydrogen systems and is used in combination with the CompuTEM algorithm for modeling of electron irradiation effects. The atomistic mechanism of formation of the new hybrid 1D nanoobject is found to be the following. Firstly hydrogen is removed by electron impacts. Then spontaneous breaking of bonds between carbon atoms leads to decomposition of narrow regions of the graphene nanoribbon into double chains. Simultaneously thermally activated growth of polycyclic regions occurs. Density functional theory calculations give barriers along the growth path of polycyclic regions consistent with this mechanism. Electronic properties of the new 1D nanoobject are shown to be strongly affected by the edge magnetism and make this nanostructure promising nanoelectronic and spintronic applications. The way of synthesis the 1D nanoobject proposed here can be considered as an example of the general three-stage strategy of production of nanoobjects and macromolecules. 1) precursors are synthesized by traditional chemical method, 2) precursors are placed in HRTEM with the electron energy that is sufficient only to remove hydrogen atoms, 3) as a result of hydrogen removal, the precursors become unstable or metastable and transform into new nanoobjects or macromolecules., Comment: 17 pages, 10 figures in the paper; 5 pages and 3 figures in the supplementary information

To explain recent experiment showing the role of odd fullerenes in formation of abundant fullerene isomers a reactive molecular dynamics (MD) study has been performed. Three types of bond rearrangement reactions are found by MD simulations at 3000 K in odd fullerenes which contain an extra sp atom among all other sp$^2$ atoms. The first type is sto-chastic sp-defect migration analogous to exchange mechanism of adatom migration on a surface. The second type cor-responds to changes in the ring configuration of the sp$^2$-structure assisted by the sp atom which can lead to annealing of seven-membered rings or separation of five-membered rings. The third type is formation of short-living one-coordinated atoms or two additional sp atoms. Annihilation of a pair of sp defects has been also observed in the MD simulations. It is shown that the frequency of sp-defect migration at a lower temperature, as estimated from performed density functional theory calculations of the barriers of sp-defect migration events, is sufficient to deliver the sp atom to defects of sp$^2$ structure during the fullerene formation time. Based on these results, we propose to supplement the self-organization paradigm of fullerene formation by the following four-stage atomistic mechanism of formation of abundant isomers of fullerenes: 1) attachment of single carbon atoms, 2) sp-defect migration to sp$^2$-structure defects, 3) sp$^2$-defect annealing assisted by the sp atom and 4) subsequent annihilation of pairs of sp defects., Comment: 12 pages and 4 figures in the paper; 7 pages and 4 figures in the supporting information

We give another proof of Toyoda's theorem that describes 5-point subpaces in CAT(0) length spaces, Comment: 9 pages, 8 figures

In the paper we obtain sufficient conditions for a trigonometric polynomial to be a refinement mask corresponding to a tight wavelet frame. The condition is formulated in terms of the roots of a mask. In particular, it is proved that any trigonometric polynomial can serve as a mask if its associated algebraic polynomial has only negative roots (at least one of them, of course, equals $-1$)., Comment: 11 pages

We show that locally homogeneous $\mathcal{C}^0$-Riemannian manifolds are smooth., Comment: 18 pages

We propose a hypothesis that the potential energy surface (PES) of interlayer interaction in diverse 2D materials can be universally described by the first spatial Fourier harmonics. This statement (checked previously for the interactions between graphene and hexagonal boron nitride layers in different combinations) is verified in the present paper for the case of hydrofluorinated graphene (HFG) bilayer with hydrogen bonding between fluorine and hydrogen at the interlayer interface. The PES for HFG bilayer is obtained through density functional theory calculations with van der Waals corrections. An analytical expression based on the first Fourier harmonics describing the PES which corresponds to the symmetry of HFG layers is derived. It is found that the calculated PES can be described by the first Fourier harmonics with the accuracy of 3\% relative to the PES corrugation. The shear mode frequency, shear modulus and barrier for relative rotation of the layers to incommensurate states of HFG bilayer are estimated. Additionally it is shown that HFG bilayer is stable relative to the formation of HF molecules as a result of chemical reactions between the layers., Comment: 12 pages, 3 figures

It is shown that at a description of a binary solution, in the presence of a liquid phase of variable composition and a stoichiometric solid phase, the concept of chemical potential can be introduced for stoichiometry, which qualitatively describes the dynamics of the re-distribution of the impurity at the contact of the phases. A model describing the slow dynamics of diffusion processes in an initially inhomogeneous sample is proposed. In the model under study, it is shown that the interaction of the impurity and the phase composition of the mixture, when deviating from equilibrium, leads to the development of instability, known as spinodal decay and mathematically described by the Cahn-Hilliard equation. Within the framework of this model system, a dispersion relation is constructed, from which the growth rate of unstable fluctuations from time is found and the influence of the model parameters on the instability value is investigated. The detected instability can explain the processes of slow non-monotonic relaxation that occurs when melting glass-forming metal alloys.

Matched wavelets interpolating equidistant data are designed. These wavelets form Riesz bases. Meyer wavelets that interpolate data on a particular uniform lattice are found., Comment: 7 pages

A review of the present status, recent enhancements, and applicability of the SIESTA program is presented. Since its debut in the mid-nineties, SIESTA's flexibility, efficiency and free distribution has given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of SIESTA combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a real-space grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here we describe the more recent implementations on top of that core scheme, which include: full spin-orbit interaction, non-repeated and multiple-contact ballistic electron transport, DFT+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient Van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as Wannier90 and the second-principles modelling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering SIESTA runs, and various postprocessing utilities. SIESTA has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low level libraries, as well as data standards and support for them, in particular the PSML definition and library for transferable pseudopotentials, and the interface to the ELSI library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments., Comment: 29 pages, 23 figures

First-principles electronic structure calculations are very widely used thanks to the many successful software packages available. Their traditional coding paradigm is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, from the compiler up, with the exception of linear-algebra and message-passing libraries. This model has been quite successful for decades. The rapid progress in methodology, however, has resulted in an ever increasing complexity of those programs, which implies a growing amount of replication in coding and in the recurrent re-engineering needed to adapt to evolving hardware architecture. The Electronic Structure Library (\esl) was initiated by CECAM (European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure programs and redesign them as free, open-source libraries. They include "heavy-duty" ones with a high degree of parallelisation, and potential for adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by scientists when implementing new ideas. It is a community effort, undertaken by developers of various successful codes, now facing the challenges arising in the new model. This modular paradigm will improve overall coding efficiency and enable specialists (computer scientists or computational scientists) to use their skills more effectively. It will lead to a more sustainable and dynamic evolution of software as well as lower barriers to entry for new developers., Comment: Revised version as finally accepted by J. Chem. Phys. to appear within the Special Topic in Electronic Structure Software (version prior to JCP's typesetting and proofs)

The analytical two-chain Frenkel-Kontorova model is used to describe domain wall networks in bilayer graphene upon biaxial stretching of one of the layers. We show that the commensurate-incommensurate phase transition leading to formation of a regular triangular domain wall network at the relative biaxial elongation of $3.0\cdot 10^{-3}$ is followed by the transition to another incommensurate phase with a striped network at the elongation of $3.7\cdot 10^{-3}$. The reentrant transition to the phase with a triangular domain wall network is predicted for the elongation $\sim10^{-2}$., Comment: 6 pages, 3 figures

The parameters of the triangular domain wall network in bilayer graphene with a simultaneously twisted and biaxially stretched bottom layer are studied using the two-chain Frenkel-Kontorova model. It is demonstrated that if the graphene layers are free to rotate, they prefer to stay co-aligned upon stretching the bottom layer and the regular triangular network of tensile domain walls is formed upon the commensurate-incommensurate phase transition. If the angle between the layers is fixed, the regular triangular network of shear domain walls is observed at zero elongation of the bottom layer. Upon stretching the bottom layer, however, the domain walls transform into the tensile ones and the size of the commensurate domains decreases. We also show that the parameters of the isosceles triangular domain wall network in twisted bilayer graphene under shear strain can be determined through purely geometrical considerations. Experimental analysis of the orientation of domain walls and period of the triangular network would, on the one hand, contribute to understanding of the interlayer interaction of graphene layers, and, on the other hand, serve for detection of relative strains and rotation between the layers. Vice versa external strains can be used to control the parameters of the triangular domain wall network and, therefore, electronic properties of twisted bilayer graphene., Comment: 13 pages, 6 figures

Over the last years extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high-degree of precision. An appealing and challenging route towards engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, providing an unique framework allowing to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory framework. The present article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, like the new theoretical framework of quantum electrodynamics density-functional formalism (QEDFT) for the description of novel light-matter hybrid states. Those advances, and other being released soon as part of the Octopus package, will enable the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (QED-materials).

The two-chain Frenkel-Kontorova model is applied for an analytical description of the energy and structure of the network of domain walls in bilayer graphene. Using this approach, the commensurate-incommensurate phase transition upon biaxial stretching of one of the graphene layers is considered. We demonstrate that formation of the equilateral triangular network of domain walls becomes energetically favourable above the critical relative biaxial elongation of the bottom layer of $3.0\cdot 10^{-3}$. It is shown that the optimal period of the triangular network of domain walls is inversely proportional to the difference between the biaxial elongation of the bottom layer and the critical elongation as long as it is much greater than the width of domain walls. Quantitative estimates of the contribution of a single dislocation node to the system energy and the period of the network of domain walls are obtained. Experimental measurements of the period could help to verify the energy of the fully incommensurate state (such as obtained by relative rotation of the layers) with respect to the commensurate one., Comment: 9 pages, 5 figures

Photo-active systems are characterized by their capacity of absorbing light energy and transforming it. Usually, more than one chromophore is involved in the light absorption and excitation transport processes in complex systems. Linear-Response Time-Dependent Density Functional (LR-TDDFT) is commonly used to identify excitation energies and transition properties by solving well-known Casida's equation for single molecules. However, this methodology is not useful in practice when dealing with multichromophore systems. In this work, we extend our local density decomposition method that enables to disentangle individual contributions into the absorption spectrum to computation of exciton dynamic properties, such as exciton coupling parameters. We derive an analytical expression for the transition density from Real-Time Propagation TDDFT (P-TDDFT) based on Linear Response theorems. We demonstrate the validity of our method to determine transition dipole moments, transition densities and exciton coupling for systems of increasing complexity. We start from the isolated benzaldehyde molecule, perform a distance analysis for $\pi$-stacked dimers and finally map the exciton coupling for a 14 benzaldehyde cluster., Comment: 32 pages, 8 figures; added references in introductions, typos fixed

The capacity of popular classical interatomic potentials to describe elastic properties of graphene is tested. The Tersoff potential, Brenner reactive bond-order potentials REBO-1990, REBO-2000, REBO-2002 and AIREBO as well as LCBOP, PPBE-G, ReaxFF-CHO and ReaxFF-C2013 are considered. Linear and non-linear elastic response of graphene under uniaxial stretching is investigated by static energy calculations. The Young's modulus, Poisson's ratio and high-order elastic moduli are verified against the reference data available from experimental measurements and ab initio studies. The density functional theory calculations are performed to complement the reference data on the effective Young's modulus and Poisson's ratio at small but finite elongations. It is observed that for all the potentials considered, the elastic energy deviates remarkably from the simple quadratic dependence already at elongations of several percent. Nevertheless, LCBOP provides the results consistent with the reference data and thus realistically describes in-plane deformations of graphene. Reasonable agreement is also observed for the computationally cheap PPBE-G potential. REBO-2000, AIREBO and REBO-2002 give a strongly non-linear elastic response with a wrong sign of the third-order elastic modulus and the corresponding results are very far from the reference data. The ReaxFF potentials drastically overestimate the Poisson's ratio. Furthermore, ReaxFF-C2013 shows a number of numerical artefacts at finite elongations. The bending rigidity of graphene is also obtained by static energy calculations for large-diameter carbon nanotubes. The best agreement with the experimental and ab initio data in this case is achieved using the REBO-2000, REBO-2002 and ReaxFF potentials. Therefore, none of the considered potentials adequately describes both in-plane and out-of-plane deformations of graphene., Comment: 17 pages, 2 figures

We show that bounded self-contracted curves are rectifiable in metric spaces with weak lower curvature bound in a sense we introduce in this article. This class of spaces is wide and includes, for example, finite-dimensional Alexandrov spaces of curvature bounded below and Berwald spaces of nonnegative flag curvature. (To be more precise, our condition is regarded as a strengthened doubling condition and holds also for a certain class of metric spaces with upper curvature bound.) We also provide the non-embeddability of large snowflakes into (balls in) metric spaces in the same class. We follow the strategy of the last author's previous paper based on the small rough angle condition, where spaces with upper curvature bound are considered. The results in this article show that such a strategy applies to spaces with lower curvature bound as well., Comment: A goofy mistake in formulations of Theorem 2 and 4 is fixed

Voltage control of ferromagnetism on the nanometer scale is highly appealing for the development of novel electronic devices. Here a key challenge is to implement and combine low power consumption, high operation speed, reliable reversibility and compatibility with semiconductor technology. Hybrid structures based on the assembly of ferromagnetic and semiconducting building blocks are attractive candidates in that respect as such systems bring together the properties of the isolated constituents: They are expected to show magnetic order as a ferromagnet and to be electrically tunable as a semiconductor. Here we demonstrate the electrical control of the exchange coupling in a hybrid consisting of a ferromagnetic Co layer and a semiconductor CdTe quantum well, separated by a thin non-magnetic (Cd,Mg)Te barrier. The effective magnetic field of the exchange interaction reaches up to 2.5 Tesla and can be turned on and off by application of 1 V bias across the heterostructure. The mechanism of this electric field control is essentially different from the conventional concept, in which wavefunctions are spatially redistributed to vary the exchange interaction, requiring high field strengths. Here we address instead control of the novel exchange mechanism that is mediated by elliptically polarized phonons emitted from the ferromagnet, i.e. the phononic ac Stark effect. An essential parameter of this coupling is the splitting between heavy and light hole states in the quantum well which can be varied by the electric field induced band bending. Thereby the splitting can be tuned with respect to the magnon-phonon resonance energy in the ferromagnet, leading to maximum coupling for flat band conditions. Our results demonstrate the feasibility of electrically controlled exchange coupling in hybrid semiconductor nanostructures at quite moderate electric field strengths., Comment: 25 pages, 5 figures, supplementary material

We present several deep learning models for assessing the morphometric fidelity of deep grey matter region models extracted from brain MRI. We test three different convolutional neural net architectures (VGGNet, ResNet and Inception) over 2D maps of geometric features. Further, we present a novel geometry feature augmentation technique based on a parametric spherical mapping. Finally, we present an approach for model decision visualization, allowing human raters to see the areas of subcortical shapes most likely to be deemed of failing quality by the machine. Our training data is comprised of 5200 subjects from the ENIGMA Schizophrenia MRI cohorts, and our test dataset contains 1500 subjects from the ENIGMA Major Depressive Disorder cohorts. Our final models reduce human rater time by 46-70%. ResNet outperforms VGGNet and Inception for all of our predictive tasks., Comment: Accepted to Shape in Medical Imaging (ShapeMI) workshop at MICCAI 2018. arXiv admin note: substantial text overlap with arXiv:1707.06353

The method for production of atomic chains by heating of graphene nanoribbons (GNRs) is proposed and studied by molecular dynamics simulations. The Brenner potential is revised to adequately describe formation of atomic chains, edges and vacancy migration in graphene. A fundamentally different behavior is observed for zigzag-edge GNRs with 3 and 4 atomic rows (3 and 4-ZGNRs) at 2500 K: formation of triple, double and single carbon chains with the length of hundreds of atoms in 3-ZGNRs and edge reconstruction with only short chains and GNR width reduction in 4-ZGNRs. The chain formation mechanism in 3-ZGNRs is revealed by analysis of bond reorganization reactions and is based on the interplay of two processes. The first one is breaking of bonds between 3 zigzag atomic rows leading to triple chain formation. The second one is bond breaking within the same zigzag atomic row, which occurs predominantly through generation of pentagons with subsequent bond breaking in pentagons and results in single or double chain formation. The DFT calculations of the barriers for relevant reactions are consistent with the mechanism proposed. The possibility of chain-based nanoelectronic devices with a controllable number of chains is discussed., Comment: 43 pages, 9 figures

We show that if a Riemannian manifold satisfies (3,3)-bipolar comparisons and has an open flat subset then it is flat. The same holds for a version of MTW where the perpendicularity is dropped. In particular we get that the (3,3)-bipolar comparison is strictly stronger than the Alexandrov comparison.

Magneto-optical response, i.e. optical response in the presence of a magnetic field, is commonly used for characterization of materials and in optical communications. However, quantum mechanical description of electric and magnetic fields in crystals is not straightforward as the position operator is ill defined. We present a reformulation of the density matrix perturbation theory for time-dependent electromagnetic fields under periodic boundary conditions, which allows us to treat the orbital magneto-optical response of solids at the \textit{ab initio} level. The efficiency of the computational scheme proposed is comparable to standard linear-response calculations of absorption spectra and the results of tests for molecules and solids agree with the available experimental data. A clear signature of the valley Zeeman effect is revealed in the continuum magneto-optical spectrum of a single layer of hexagonal boron nitride. The present formalism opens the path towards the study of magneto-optical effects in strongly driven low-dimensional systems., Comment: 12 pages, 3 figures

In this paper we present the results of the spectral studies of erosive discharge with tin alloy electrodes and of the generated JFs, and experimentally determine internal energy of JFs using the calorimetric technique., Comment: 5 pages, 3 figures This report was presented at AIS-2018 conference

A directional time-frequency localization measure for functions defined on the $d$-dimensional Euclidean space is introduced. A connection between this measure and its periodic counterpart is established. For a class of functions, an optimization problem for finding the optimal direction, along which a function is best or worst localized, is solved., Comment: 20 pages

Single-layer and bilayer carbon and hexagonal boron nitride nanoscrolls as well as nanoscrolls made of bilayer graphene/hexagonal boron nitride heterostructure are considered. Structures of stable states of the corresponding nanoscrolls prepared by rolling single-layer and bilayer rectangular nanoribbons are obtained based on the analytical model and numerical calculations. The lengths of nanoribbons for which stable and energetically favorable nanoscrolls are possible are determined. Barriers to rolling of single-layer and bilayer nanoribbons into nanoscrolls and barriers to nanoscroll unrolling are calculated. Based on the calculated barriers nanoscroll lifetimes in the stable state are estimated. Elastic constants for bending of graphene and hexagonal boron nitride layers used in the model are found by density functional theory calculations., Comment: 9 pages, 6 figures

This paper studies how dependent typed events can be used to treat verb phrase anaphora. We introduce a framework that extends Dependent Type Semantics (DTS) with a new atomic type for neo-Davidsonian events and an extended @-operator that can return new events that share properties of events referenced by verb phrase anaphora. The proposed framework, along with illustrative examples of its use, are presented after a brief overview of the necessary background and of the major challenges posed by verb phrase anaphora.

We define a new type of metric comparison similar to the comparison of Alexandrov. We show that it has strong connections to continuity of optimal transport between regular measures on a Riemannian manifold, in particular to the so called MTW condition introduced by Xi-Nan Ma, Neil Trudinger and Xu-Jia Wang., Comment: 25 pages, 16 figures