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High temperature properties of ceria surfaces are important for many applications. Here we report the temperature dependences of surface energy for the (111) and (110) CeO2 obtained in the framework of the extended two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD). The method was used together with machinelearning potentials called moment tensor potentials (MTPs), which were fitted to the results of the ab initio MD calculations for (111) and (110) CeO2 at different temperatures. The parameters of MTPs training and fitting were tested and the optimal algorithm for the ceria systems was proposed. We found that the temperature increases from 0 K to 2100 K led to the decrease of the Helmholtz free energy of (111) CeO2 from 0.78 J/m2 to 0.64 J/m2. The energy of (110) CeO2 dropped from 1.19 J/m2 at 0 K to 0.92 J/m2 at 1800 K. We show that it is important to take anharmonicity into account as simple consideration of volume expansion gives wrong temperature dependences of the surface energies., Comment: 8 pages, 4 figures

This paper presents the Standalone Neural ODE (sNODE), a continuous-depth neural ODE model capable of describing a full deep neural network. This uses a novel nonlinear conjugate gradient (NCG) descent optimization scheme for training, where the Sobolev gradient can be incorporated to improve smoothness of model weights. We also present a general formulation of the neural sensitivity problem and show how it is used in the NCG training. The sensitivity analysis provides a reliable measure of uncertainty propagation throughout a network, and can be used to study model robustness and to generate adversarial attacks. Our evaluations demonstrate that our novel formulations lead to increased robustness and performance as compared to ResNet models, and that it opens up for new opportunities for designing and developing machine learning with improved explainability., Comment: 25 pages, 15 figures; typos corrected

The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous layers. The NODE is treated as an isolated entity describing the full network as opposed to earlier research, which embedded it between pre- and post-appended layers trained by conventional methods. The proposed parameter reconstruction is done for a general first order differential equation by minimizing a cost functional covering a variety of loss functions and penalty terms. A nonlinear conjugate gradient method (NCG) is derived for the minimization. Mathematical properties are stated for the differential equation and the cost functional. The adjoint problem needed is derived together with a sensitivity problem. The sensitivity problem can estimate changes in the network output under perturbation of the trained parameters. To preserve smoothness during the iterations the Sobolev gradient is calculated and incorporated. As a proof-of-concept, numerical results are included for a NODE and two synthetic datasets, and compared with standard gradient approaches (not based on NODEs). The results show that the proposed method works well for deep learning with infinite numbers of layers, and has built-in stability and smoothness., Comment: 26 pages, 3 figures

Catalysis has entered everyday life through a number of technological processes relying on different catalytic systems. The increasing demand for such systems requires rationalization of the use of their expensive components, like noble metal catalysts. As such, a catalyst with low noble metal concentration, in which each one of the noble atoms is active, would reach the lowest price possible. Nevertheless, there are no reactivity descriptors outlined for this type of low coordinated supported atoms. Using DFT calculations, we consider three diverse systems as models of single atom catalysts. We investigate monomers and bimetallic dimers of Ru, Rh, Pd, Ir and Pt on MgO(001), Cu adatom on thin Mo(001)-supported films (NaF, MgO and ScN) and single Pt adatoms on oxidized graphene surfaces. Reactivity of these metal atoms was probed by CO. In each case we see the interaction through the donation-backdonation mechanism. In some cases the CO adsorption energies can be linked to the position of the d-band center and the charge of the adatom. Higher positioned d-band center and less charged supported single atoms bind CO weaker. Also, in some cases metal atoms less strongly bonded to the substrate bind CO more strongly. The results suggest that the identification of common activity descriptor(s) for single metal atoms on foreign supports is a difficult task with no unique solution. However, it is also suggested that the stability of adatoms and strong anchoring to the support are prerequisites for the application of descriptor-based search for novel single atom catalysts., Comment: 19 pages, 6 figures, 66 references

A boundary integral based method for the stable reconstruction of missing boundary data is presented for the governing hyperbolic equation of elastodynamics in annular planar domains. Cauchy data in the form of the solution and traction is reconstructed on the inner boundary curve from the similar data given on the outer boundary. The ill-posed data reconstruction problem is reformulated as a sequence of boundary integral equations using the Laguerre transform with respect to time and employing a single-layer approach for the stationary problem. Singularities of the involved kernels in the integrals are analysed and made explicit, and standard quadrature rules are used for discretisation. Tikhonov regularization is employed for the stable solution of the obtained linear system. Numerical results are included showing that the outlined approach can be turned into a practical working method for finding the missing data., Comment: 26 pages, 2 Figures, 8 Tables

New electrode materials for alkaline-ion batteries are a timely topic. Among many promising candidates, V2O5 is one of the most interesting cathode materials. While having very high theoretical capacity, in practice, its performance is hindered by low stability and poor conductivity. As regards theoretical descriptions of V2O5, common DFT-GGA calculations fail to reproduce both the electronic and crystal structure. While the band gap is underestimated, the interlayer spacing is overestimated as weak dispersion interactions are not properly described within GGA. Here we show that the combination of the DFT+U method and semi-empirical D2 correction can compensate for the drawbacks of the GGA approximation when it comes to the modelling of V2O5. When compared to common PBE calculations, with a modest increase of the computational cost, PBE+U+D2 fully reproduced the experimental band gap of V2O5, while the errors in the lattice parameters are only a few percent. Using the proposed PBE+U+D2 methodology we studied V2O5 doped with 3d elements (from Sc to Zn). We show that both the structural and electronic parameters are affected by doping. Most importantly, a significant increase of conductivity is expected upon doping, which is of great importance for the application of V2O5 in metal-ion batteries., Comment: 20 pages, 8 figures, 2 tables, 56 references, Supplementary Information included, submitted to Physical Chemistry Chemical Physics

The Monte Carlo event generator HYDJET++ is one of the few generators, designed for the calculations of heavy-ion collisions at ultrarelativistic energies, which combine treatment of soft hydro-like processes with the description of jets traversing the hot and dense partonic medium. The model is employed to study the azimuthal anisotropy phenomena, dihadron angular correlations and event-by-event (EbyE) fluctuations of the anisotropic flow in Pb+Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV. The interplay of soft and hard processes describes the violation of the mass hierarchy of meson and baryon elliptic and triangular flows at p_T > 2 GeV/c, the fall-off of the flow harmonics at intermediate transverse momenta, and the worsening of the number-of-constituent-quark (NCQ) scaling of elliptic/triangular flow at LHC compared to RHIC energies. The cross-talk of v_2 and v_3 leads to emergence of higher order harmonics in the model and to appearance of the ridge structure in dihadron angular correlations in a broad pseudorapidity range. HYDJET++ possesses also the dynamical EbyE fluctuations of the anisotropic flow. The model results agree well with the experimental data., Comment: 8 pages, 6 figures, contribution to Proceedings of the Winter Workshop on Nuclear Dynamics 2016

The rare-earths are known to have intriguing changes of the valence, depending on chemical surrounding or geometry. Here we make predictions from theory that combines density functional theory with atomic multiplet-theory, on the transition of valence when transferring from the atomic divalent limit to the trivalent bulk, passing through different sized clusters, of selected rare-earths. We predict that Tm clusters show an abrupt change from pure divalent to pure trivalent at a size of 6 atoms, while Sm and Tb clusters are respectively pure divalent and trivalent up to 8 atoms. Larger Sm clusters are argued to likely make a transition to a mixed valent, or trivalent, configuration. The valence of all rare-earth clusters, as a function of size, is predicted from interpolation of our calculated results. We argue that the here predicted behavior is best analyzed by spectroscopic measurements, and provide theoretical spectra, based on dynamical mean field theory, in the Hubbard-I approximation, to ease experimental analysis.

Triangular flow $v_3$ of identified and inclusive particles in Pb+Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV is studied as a function of centrality and transverse momentum within the \textsc{hydjet++} model. The model enables one to investigate the influence of both hard processes and final-state interactions on the harmonics of particle anisotropic flow. Decays of resonances are found to increase the magnitude of the $v_3(p_{\rm T})$ distributions at $p_{\rm T} \geq 2$ GeV/$c$ and shift their maxima to higher transverse momenta. The $p_{\rm T}$-integrated triangular flow, however, becomes slightly weakened for all centralities studied. The resonance decays also modify the spectra towards the number-of-constituent-quark scaling fulfillment for the triangular flow, whereas jets are the main source of the scaling violation at the energies available at the CERN Large Hadron Collider (LHC). Comparison with the corresponding spectra of elliptic flow reveals that resonance decays and jets act in a similar manner on both $v_3(p_{\rm T})$ and $v_2(p_{\rm T})$ behavior. Obtained results are also confronted with the experimental data on differential triangular flow of identified hadrons, ratio $v_3^{1/3}(p_{\rm T}) / v_2^{1/2}(p_{\rm T})$ and $p_{\rm T}$-integrated triangular flow of charged hadrons., Comment: revised version

In this work we examine critically the electronic structure of the rare-earth elements by use of the so-called Hubbard I approximation. From the theoretical side all measured features of both occupied and unoccupied states are reproduced, without significant deviations between observations and theory. We also examine cohesive properties like the equilibrium volume and bulk modulus, where we find, in general, a good agreement between theory and measurements. In addition we have reproduced the spin and orbital moments of these elements, as they are reflected from measurements of the saturation moment. We have also employed the Hubbard I approximation to extract the interatomic exchange parameters of an effective spin Hamiltonian for the heavy rare earths. We show that the Hubbard I approximation gives results which are consistent with calculations where $4f$ electrons are treated as core states for Gd. The latter approach was also used to address the series of the heavy/late rare-earths. Via Monte Carlo simulations we obtained ordering temperatures which reproduce measurements within about $20\%$. We have further illustrated the accuracy of these exchange parameters by comparing measured and calculated magnetic configurations for the heavy rare earths and the magnon dispersion for Gd. The Hubbard I approximation is compared to other theories of the electronic structure, and we argue that it is superior. We discuss the relevance of our results in general, and how this makes it possible to treat the electronic structure of materials containing rare-earth elements, such as permanent magnets, magnetostrictive compounds, photovoltaics, optical fibers, topological insulators, and molecular magnets., Comment: 21 pages, 14 figures, 2 tables, 4 appendices

Segregation, precipitation, and phase separation in Fe-Cr systems is investigated. Monte Carlo simulations using semiempirical interatomic potential, first-principles total energy calculations, and experimental spectroscopy are used. In order to obtain a general picture of the relation of the atomic interactions and properties of Fe-Cr alloys in bulk, surface, and interface regions several complementary methods has to be used. Using Exact Muffin-Tin Orbitals method the effective chemical potential as a function of Cr content (0-15 at.% Cr) is calculated for a surface, second atomic layer and bulk. At ~10 at.% Cr in the alloy the reversal of the driving force of a Cr atom to occupy either bulk or surface sites is obtained. The Cr containing surfaces are expected when the Cr content exceeds ~10 at.%. The second atomic layer forms about 0.3 eV barrier for the migration of Cr atoms between bulk and surface atomic layer. To get information on Fe-Cr in larger scales we use semiempirical methods. Using combined Monte Carlo molecular dynamics simulations, based on semiempirical potential, the precipitation of Cr into isolated pockets in bulk Fe-Cr and the upper limit of the solubility of Cr into Fe layers in Fe/Cr layer system is studied. The theoretical predictions are tested using spectroscopic measurements. Hard X-ray photoelectron spectroscopy and Auger electron spectroscopy investigations were carried out to explore Cr segregation and precipitation in Fe/Cr double layer and Fe_0.95Cr_0.05 and Fe_0.85Cr_0.15 alloys. Initial oxidation of Fe-Cr was investigated experimentally at 10^-8 Torr pressure of the spectrometers showing intense Cr_2O_3 signal. Cr segregation and the formation of Cr rich precipitates were traced by analysing the experimental spectral intensities with respect to annealing time, Cr content, and kinetic energy of the exited electron., Comment: 16 pages, 14 figures, 52 references

The LHC data on azimuthal anisotropy harmonics from PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair are analyzed and interpreted in the framework of the HYDJET++ model. The cross-talk of elliptic $v_2$ and triangular $v_3$ flow in the model generates both even and odd harmonics of higher order. Comparison with the experimental data shows that this mechanism is able to reproduce the $p_{\rm T}$ and centrality dependencies of quadrangular flow $v_4$, and also the basic trends for pentagonal $v_5$ and hexagonal $v_6$ flows., Comment: 12 pages including 13 figures as EPS-files; prepared using LaTeX package for publication in the European Physical Journal C

Partial contributions of elliptic v_2 and triangular v_3 flows to the hexagonal v_6 flow are studied within the HYDJET++ model for Pb+Pb collisions at sqrt{s}=2.76 TeV. Scaling of the ratio v_6^{1/6}{Psi_2} / v_2^{1/2}{Psi_2} in the elliptic flow plane, Psi_2, is predicted in the range 1 < p_T < 4 GeV/c for semicentral and semiperipheral collisions. Jets increase this ratio by about 10% and also cause its rise at p_T > 3.5 GeV/c. The part of v_6 coming from v_2 is instantly increasing as the reaction becomes more peripheral, whereas the contribution of v_3 to v_6 drops. This behavior explains the experimentally observed increase of correlations between second and sixth harmonics and decrease of correlations between third and sixth harmonics with rising impact parameter $b$. Our study favors the idea that basic features of the hexagonal flow can be understood in terms of the interplay of elliptic and triangular flows., Comment: Final version

The Monte Carlo HYDJET++ model, that combines parametrized hydrodynamics with jets, is employed to study formation of second v_2 and fourth v_4 components of the anisotropic flow in ultrarelativistic heavy-ion collisions at energies of the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC), sqrt{s}=200 AGeV and sqrt{s}=2.76 ATeV, respectively. It is shown that the quenched jets contribute to the soft part of the v_2(p_T) and v_4(p_T) spectra. The jets increase the ratio v_4/v_2^2 thus leading to deviations of the ratio from the value of 0.5 predicted by the ideal hydrodynamics. Together with the event-by-event fluctuations, the influence of jets can explain quantitatively the ratio v_4/v_2^2 at p_T < 2 GeV/c for both energies and qualitatively the rise of its high-p_T tail at LHC. Jets are also responsible for violation of the number-of-constituent-quark (NCQ) scaling at LHC despite the fact that the scaling is fulfilled for the hydro-part of particle spectra., Comment: minor corrections, as published in Phys. Rev. C

We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information from a supplementary temperature measurement at a given single instant of time. In the multi-dimensional case, we use Carleman estimates for parabolic equations to obtain a uniqueness result. The given data and the solution domain are sufficiently smooth such that the required norms and the derivatives of the conductivity, the source and the solution of the parabolic heat equation exist and are continuous throughout the solution domain. These assumptions can be further relaxed using more involved estimates and techniques but these lengthy details are not included. Instead, in the special case of the one-dimensional heat equation, we give an alternative and rather straightforward proof of uniqueness of the inverse problem, based on integral representations of the solution together with density results for solutions of the corresponding adjoint problem. In this case, the required regularity conditions on the conductivity, source and the solution of the parabolic heat equation are weakened to classes of integrable functions. Keywords: uniqueness; spacewise conductivity and source; final time measurements; heat equation; Carleman estimates., Comment: Submitted in October of 2012

Iron-chromium forms the basis of most of the stainless steel grades in the markets. Recently new insights into the physical and chemical properties of Fe-Cr based alloys have been obtained. Some of the new results are quite unexpected and call for further investigations. The present study addresses the magnetic contribution in the atomic driving forces behind the chemical composition in Fe-Cr alloyed with Al, Ti, V, Mn, Co, Ni, and Mo. Using the ab initio exact muffin-tin orbitals method and an Ising-type spin model, it is found that the magnetic moment of the solute atom combined with the induced changes in the magnetic moments of the host atoms form the main framework in determining the mixing energy and chemical potentials of low-Cr Fe-Cr based alloys. The results obtained in the present work are related to tuning of the microstructure and corrosion protection of low-Cr steels., Comment: 7 pages 6 figures

An archetypical spin-glass metallic alloy, Cu0.83Mn0.17, is studied by means of an ab-initio based approach. First-principles calculations are employed to obtain effective chemical, strain-induced and magnetic exchange interactions, as well as static atomic displacements, and the interactions are subsequently used in thermodynamic simulations. It is shown that the calculated atomic and magnetic short-range order accurately reproduces the results of neutron-scattering experiments. In particular, it is confirmed that the alloy exhibits a tendency toward ordering and the corresponding ordered phase is revealed. The magnetic structure is represented by spin-spiral clusters accompanied by weaker ferromagnetic short-range correlations. The spin-glass transition temperature obtained in Monte Carlo simulations by a finite-size scaling technique, 57 K, is in reasonable agreement with experimental data, 78 K., Comment: 36 pages, 12 figures

The high-pressure structural behaviour of the fluoroperovskite KMgF_3 is investigated by theory and experiment. Density functional calculations were performed within the local density approximation and the generalized gradient approximation for exchange and correlation effects, as implemented within the full-potential linear muffin-tin orbital method. In situ high-pressure powder x-ray diffraction experiments were performed up to a maximum pressure of 40 GPa using synchrotron radiation. We find that the cubic Pm\bar{3}m crystal symmetry persists throughout the pressure range studied. The calculated ground state properties -- the equilibrium lattice constant, bulk modulus and elastic constants -- are in good agreement with experimental results. By analyzing the ratio between the bulk and shear modulii, we conclude that KMgF_3 is brittle in nature. Under ambient conditions, KMgF_3 is found to be an indirect gap insulator with the gap increasing under pressure., Comment: 4 figures

The high-pressure structural behavior of lanthanum monochalcogenides is investigated by theory and experiment. Theory comprises density functional calculations of LaS, LaSe and LaTe with the general gradient approximation for exchange and correlation effects, as implemented within the full-potential linear muffin-tin orbital method. The experimental studies consist of high-pressure angle dispersive x-ray diffraction investigations of LaS and LaSe up to a maximum pressure of 41 GPa. A structural phase transition from the NaCl type to CsCl type crystal structure is found to occur in all cases. The experimental transition pressures are 27-28 GPa and 19 GPa, for LaS and LaSe, respectively, while the calculated transition pressures are 29 GPa, 21 GPa and 10 GPa for LaS, LaSe and LaTe, respectively. The calculated ground state properties such as equilibrium lattice constant, bulk modulus and its pressure derivative, and Debye temperatures are in good agreement with experimental results. Elastic constants are predicted from the calculations., Comment: Phys. Rev. B 75, 184108 (2007)

In this work, the mechanism of Li insertion in $\eta '$-Cu$_6$Sn$_5$ to form Li$_2$CuSn is discussed in detail, based on both theoretical calculations and experimental results. The mechanism is investigated by means of first principles calculations, with the full potential linearized augmented plane wave method, in combination with {\it in situ} X-ray diffraction experiments. The $\eta '$-Cu$_6$Sn$_5$ structure, as well as its lithiated products, have been optimized and the electronic charge density calculated in order to study the change in bond character on lithiation. The average insertion voltage of the $\eta '$-Cu$_6$Sn$_5$-Li$_2$CuSn transformation has been calculated to be 0.378V in good agreement with the experimental value., Comment: 11 pages and 6 figures accepted for publication in J. Electr. Chem Soc. 2003

We have calculated from first principles the electronic structure of 0.5 monolayer upto 5 monolayer thick Fe layers on top of a GaAs (100) surface. We find the Fe magnetic moment to be determined by the Fe-As distance. As segregates to the top of the Fe film, whereas Ga most likely is found within the Fe film. Moreover, we find an asymmetric in-plane contraction of our unit-cell along with an expansion perpendicular to the surface. We predict the number of Fe 3d-holes to increase with increasing Fe thickness on $p$-doped GaAs., Comment: 9 pages, 14 figures, submitted to PRB

The lattice dynamical properties of Li$_x$BC are calculated for several values of $x$ using density functional perturbation theory. We find that the electron-phonon coupling parameter $\lambda$ increases monotonically with decreasing $x$ to a maximum value of 1.4 for $x=0.125$ owing to the increasing radius of multiply-nested Fermi surface cylinders. The B-C bond-stretching phonon modes have frequencies which are 28% higher than the equivalent modes in MgB$_2$. This combination results in a $T_c$ of about 65 K for $x=0.5$., Comment: 6 pages, 5 figures

We present a microscopic theory of superfluid $^4$He, formulated using the overall experimental observations as input information. With the theory of a consistent basis, we answer all of the essential questions regarding He II., Comment: 42 pages, 10 figures; contact email (JXZJ): jxzj@mailaps.org; related paper of the authors: 1) (superfluidity mechanism): cond-mat/0206339; 2) J. de Physique IV, vol. 10, Pr7-181 (2000)

Based on a first principles treatment of the excitation states we show that superfluidity of superfluid $^4$He (He II) results from a reduction in the number of phonon wavevector $K$ states $\N2(K)$ to a level that is negligibly low when the fluid is confined e.g. in a narrow channel, yet wider than the helium atom correlation length, $\Lambda$. This is as a result of the $K$ discretization, a manifestation of the quantum confinement effect (QCE). The predicted relative viscosity of a confined superfluid has the characteristic order of magnitude of experimental data ($<10^{-6}$). Furthermore, we show that at the edges of the resulting energy gaps, the $\N2(K)$ presents discontinuity. When its corresponding energy exceeds the (first) gap, the superfluid flow exhibits a critical velocity $v_c$. Our evaluation of $v_c(d)$ versus the channel width $d$, constrained to satisfy energy conservation, is in good quantitative agreement with experimental data for channels with $d>10^{-6}$ m. Meanwhile, a sharp turn about $K\propto$ $ v_c$ in $\N2(K)$ resembles very well that of the experimental overshoot data. For narrower channels of $d<10^{-6}$ m $\le \Lambda$ in which the phonon excitation picture becomes inadequate, we instead represent the excitation in terms of single atoms with an effective mass, which yields a $v_c(d)$ in close agreement with experiment. Accordingly, the reduction in the number of atomic states results in superfluidity. The theoretical finding in this work, which can be termed the {\bf QCE superfluidity mechanism}, provides a consistent explanation for this puzzling phenomenon, the non-dissipative, superfluidity motion, of He II and could have a significant impact also on the understanding of other superfluids., Comment: Submitted to Physical Review B (2001); 14 pages, 3 figures. Contact : J.X.Zheng-Johansson . Related paper by J. X. Zheng-Johansson and B. Johansson appeared in "Dynamics in Confinement", edited by B. Frick, R. Zorn and H. Buttner, J. de Physique IV, vol. 10, Pr7-181 (2000)

An approach which allows to include the corrections from non-orthogonality of electron states in contacts and quantum dots is developed. Comparison of the energy levels and charge distributions of electrons in 1D quantum dot (QD) in equilibrium, obtained within orthogonal (OR) and non-orthogonal representations (NOR), with the exact ones shows that the NOR provides a considerable improvement, for levels below the top of barrier. The approach is extended to non-equilibrium states. A derivation of the tunneling current through a single potential barrier is performed using equations of motion for correlation functions. A formula for transient current derived by means of the diagram technique for Hubbard operators is given for the problem of QD with strongly correlated electrons interacting with electrons in contacts. The non-orthogonality renormalizes the tunneling matrix elements and spectral weights of Green functions (GFs)., Comment: 3 pages, 1 table, 1 figure

The mechanism of f-electron delocalization is investigated within the multi-orbital Anderson lattice model by means of diagrammatic perturbation theory from the atomic limit. The derived equations couple the intra-atomic transition energies, their spectral weights and population numbers of the many-electron states. Its self-consistent solution for praseodymium metal shows that the delocalization can be caused by external pressure via a resonant mixing of f- and conduction electrons in the vicinity of the the Fermi surface. It is also found that: 1. An increase of mixing leads to a decrease of the physical values of the Hubbard interactions, $U^*$, the reduction, however, is small. 2. The initial Hubbard U is split by renormalization into a set of different physical values of $U^*_{i,j}$. 3. The gain in cohesive energy together with the f-sum rule cause a transfer of spectral weight, which is decisive for the delocalization of \f-electrons. 4. The correlated Fermionic quasi particles have their bandwidth slightly reduced compared to the ones obtained by means of the Kohn-Sham equation., Comment: 10 figures