F. John's stability conditions vs. A. Carasso's SECB constraint for backward parabolic problems

In order to solve backward parabolic problems F. John [{\it Comm. Pure. Appl. Math.} (1960)] introduced the two constraints "$\|u(T)\|\le M$" and $\|u(0) - g \| \le \delta$ where $u(t)$ satisfies the backward heat equation for $t\in(0,T)$ with the initial data $u(0).$ The {\it slow-evolution-from-the-continuation-boundary} (SECB) constraint has been introduced by A. Carasso in [{\it SIAM J. Numer. Anal.} (1994)] to attain continuous dependence on data for backward parabolic problems even at the continuation boundary $t=T$. The additional "SECB constraint" guarantees a significant improvement in stability up to $t=T.$ In this paper we prove that the same type of stability can be obtained by using only two constraints among the three. More precisely, we show that the a priori boundedness condition $\|u(T)\|\le M$ is redundant. This implies that the Carasso's SECB condition can be used to replace the a priori boundedness condition of F. John with an improved stability estimate. Also a new class of regularized solutions is introduced for backward parabolic problems with an SECB constraint. The new regularized solutions are optimally stable and we also provide a constructive scheme to compute. Finally numerical examples are provided.Comment: 15 pages. To appear in Inverse Problem

Unsteady undular bores in fully nonlinear shallow-water theory

We consider unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the leading-order fully nonlinear dispersive terms. This system contains one horizontal space dimension and time and can be systematically derived from the full Euler equations for irrotational flows with a free surface using a standard long-wave asymptotic expansion. In this context the system was first derived by Su and Gardner. It coincides with the one-dimensional flat-bottom reduction of the Green-Naghdi system and, additionally, has recently found a number of fluid dynamics applications other than the present context of shallow-water gravity waves. We then use the Whitham modulation theory for a one-phase periodic travelling wave to obtain an asymptotic analytical description of an undular bore in the Su-Gardner system for a full range of "depth" ratios across the bore. The positions of the leading and trailing edges of the undular bore and the amplitude of the leading solitary wave of the bore are found as functions of this "depth ratio". The formation of a partial undular bore with a rapidly-varying finite-amplitude trailing wave front is predicted for ``depth ratios'' across the bore exceeding 1.43. The analytical results from the modulation theory are shown to be in excellent agreement with full numerical solutions for the development of an undular bore in the Su-Gardner system.Comment: Revised version accepted for publication in Phys. Fluids, 51 pages, 9 figure

New limit on the mass of 9.4-keV solar axions emitted in an M1 transition in 83^{83}Kr nuclei

A search for resonant absorption of the solar axion by $^{83}\rm{Kr}$ nuclei was performed using the proportional counter installed inside the low-background setup at the Baksan Neutrino Observatory. The obtained model independent upper limit on the combination of isoscalar and isovector axion-nucleon couplings $|g_3-g_0|\leq 1.69\times 10^{-6}$ allowed us to set the new upper limit on the hadronic axion mass of $m_{A}\leq 130$ eV (95\% C.L.) with the generally accepted values $S$=0.5 and $z$=0.56.Comment: 5 pages, 2 figures, Proceedings of the 10th Patras Workshop on Axions, WIMPs and WISP 29 June - 4 July 2014, CERN, Geneva, Switzerlan

A unified hyperbolic formulation for viscous fluids and elastoplastic solids

We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the classical continuum models, such as the Navier-Stokes for example, is that the finite length scale of the continuum particles is not ignored but kept in the model in order to semi-explicitly describe the essence of any flows, that is the process of continuum particles rearrangements. To allow the continuum particle rearrangements, we admit the deformability of particle which is described by the distortion field. The ability of media to flow is characterized by the strain dissipation time which is a characteristic time necessary for a continuum particle to rearrange with one of its neighboring particles. It is shown that the continuum particle length scale is intimately connected with the dissipation time. The governing equations are represented by a system of first order hyperbolic PDEs with source terms modeling the dissipation due to particle rearrangements. Numerical examples justifying the reliability of the proposed approach are demonstrated.Comment: 6 figure

Magnetoelectric ordering of BiFeO3 from the perspective of crystal chemistry

In this paper we examine the role of crystal chemistry factors in creating conditions for formation of magnetoelectric ordering in BiFeO3. It is generally accepted that the main reason of the ferroelectric distortion in BiFeO3 is concerned with a stereochemical activity of the Bi lone pair. However, the lone pair is stereochemically active in the paraelectric orthorhombic beta-phase as well. We demonstrate that a crucial role in emerging of phase transitions of the metal-insulator, paraelectric-ferroelectric and magnetic disorder-order types belongs to the change of the degree of the lone pair stereochemical activity - its consecutive increase with the temperature decrease. Using the structural data, we calculated the sign and strength of magnetic couplings in BiFeO3 in the range from 945 C down to 25 C and found the couplings, which undergo the antiferromagnetic-ferromagnetic transition with the temperature decrease and give rise to the antiferromagnetic ordering and its delay in regard to temperature, as compared to the ferroelectric ordering. We discuss the reasons of emerging of the spatially modulated spin structure and its suppression by doping with La3+.Comment: 18 pages, 5 figures, 3 table

Measurement of the cross-section and charge asymmetry of WW bosons produced in proton-proton collisions at s=8\sqrt{s}=8 TeV with the ATLAS detector

This paper presents measurements of the $W^+ \rightarrow \mu^+\nu$ and $W^- \rightarrow \mu^-\nu$ cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables, submitted to EPJC. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13

Search for chargino-neutralino production with mass splittings near the electroweak scale in three-lepton final states in √s=13 TeV pp collisions with the ATLAS detector

A search for supersymmetry through the pair production of electroweakinos with mass splittings near the electroweak scale and decaying via on-shell W and Z bosons is presented for a three-lepton final state. The analyzed proton-proton collision data taken at a center-of-mass energy of √s=13  TeV were collected between 2015 and 2018 by the ATLAS experiment at the Large Hadron Collider, corresponding to an integrated luminosity of 139  fb−1. A search, emulating the recursive jigsaw reconstruction technique with easily reproducible laboratory-frame variables, is performed. The two excesses observed in the 2015–2016 data recursive jigsaw analysis in the low-mass three-lepton phase space are reproduced. Results with the full data set are in agreement with the Standard Model expectations. They are interpreted to set exclusion limits at the 95% confidence level on simplified models of chargino-neutralino pair production for masses up to 345 GeV

Search for direct stau production in events with two hadronic tau-leptons in root s=13 TeV pp collisions with the ATLAS detector

A search for the direct production of the supersymmetric partners ofτ-leptons (staus) in final stateswith two hadronically decayingτ-leptons is presented. The analysis uses a dataset of pp collisions corresponding to an integrated luminosity of139fb−1, recorded with the ATLAS detector at the LargeHadron Collider at a center-of-mass energy of 13 TeV. No significant deviation from the expected StandardModel background is observed. Limits are derived in scenarios of direct production of stau pairs with eachstau decaying into the stable lightest neutralino and oneτ-lepton in simplified models where the two staumass eigenstates are degenerate. Stau masses from 120 GeV to 390 GeV are excluded at 95% confidencelevel for a massless lightest neutralino