Bond-order potential for simulations of extended defects in tungsten

We present a bond-order potential (BOP) for the bcc transition metal tungsten. The bond-order potentials are a real-space semiempirical scheme for the description of interatomic interactions based on the tight-binding approximation. In the hierarchy of atomic-scale-modeling methods the BOPs thus provide a direct bridge between electronic-structure and atomistic techniques. Two variants of the BOP were constructed and extensively tested against accurate first-principles methods in order to assess the potentials\u27 reliability and applicability. A comparison of the BOP with a central-force potential is used to demonstrate that a correct description of directional mixed covalent and metallic bonds is crucial for a successful and fully transferable model. The potentials are applied in studies of low-index surfaces, symmetrical tilt grain boundaries, and dislocations

On the incompatibility of strains and its application to mesoscopic studies of plasticity

Structural transitions are invariably affected by lattice distortions. If the body is to remain crack-free, the strain field cannot be arbitrary but has to satisfy the Saint-Venant compatibility constraint. Equivalently, an incompatibility constraint consistent with the actual dislocation network has to be satisfied in media with dislocations. This constraint can be incorporated into strain-based free energy functionals to study the influence of dislocations on phase stability. We provide a systematic analysis of this constraint in three dimensions and show how three incompatibility equations accommodate an arbitrary dislocation density. This approach allows the internal stress field to be calculated for an anisotropic material with spatially inhomogeneous microstructure and distribution of dislocations by minimizing the free energy. This is illustrated by calculating the stress field of an edge dislocation and comparing it with that of an edge dislocation in an infinite isotropic medium. We outline how this procedure can be utilized to study the interaction of plasticity with polarization and magnetization.Comment: 6 pages, 2 figures; will appear in Phys. Rev.

The influence of transition metal solutes on dislocation core structure and values of Peierls stress and barrier in tungsten

Several transition metals were examined to evaluate their potential for improving the ductility of tungsten. The dislocation core structure and Peierls stress and barrier of $1/2$ screw dislocations in binary tungsten-transition metal alloys (W$_{1-x}$TM$_{x}$) were investigated using first principles electronic structure calculations. The periodic quadrupole approach was applied to model the structure of $1/2$ dislocation. Alloying with transition metals was modeled using the virtual crystal approximation and the applicability of this approach was assessed by calculating the equilibrium lattice parameter and elastic constants of the tungsten alloys. Reasonable agreement was obtained with experimental data and with results obtained from the conventional supercell approach. Increasing the concentration of a transition metal from the VIIIA group, i.e. the elements in columns headed by Fe, Co and Ni, leads to reduction of the $C^\prime$ elastic constant and increase of elastic anisotropy A=$C_{44}/C^\prime$. Alloying W with a group VIIIA transition metal changes the structure of the dislocation core from symmetric to asymmetric, similar to results obtained for W$_{1-x}$Re$_{x}$ alloys in the earlier work of Romaner {\it et al} (Phys. Rev. Lett. 104, 195503 (2010))\comments{\cite{WRECORE}}. In addition to a change in the core symmetry, the values of the Peierls stress and barrier are reduced. The latter effect could lead to increased ductility in a tungsten-based alloy\comments{\cite{WRECORE}}. Our results demonstrate that alloying with any of the transition metals from the VIIIA group should have similar effect as alloying with Re.Comment: 12 pages, 8 figures, 3 table

Assessment of interatomic potentials for atomistic analysis of static and dynamic properties of screw dislocations in W

Screw dislocations in bcc metals display non-planar cores at zero temperature which result in high lattice friction and thermally activated strain rate behavior. In bcc W, electronic structure molecular statics calculations reveal a compact, non-degenerate core with an associated Peierls stress between 1.7 and 2.8 GPa. However, a full picture of the dynamic behavior of dislocations can only be gained by using more efficient atomistic simulations based on semiempirical interatomic potentials. In this paper we assess the suitability of five different potentials in terms of static properties relevant to screw dislocations in pure W. As well, we perform molecular dynamics simulations of stress-assisted glide using all five potentials to study the dynamic behavior of screw dislocations under shear stress. Dislocations are seen to display thermally-activated motion in most of the applied stress range, with a gradual transition to a viscous damping regime at high stresses. We find that one potential predicts a core transformation from compact to dissociated at finite temperature that affects the energetics of kink-pair production and impacts the mechanism of motion. We conclude that a modified embedded-atom potential achieves the best compromise in terms of static and dynamic screw dislocation properties, although at an expense of about ten-fold compared to central potentials

Stability estimates for resolvents, eigenvalues and eigenfunctions of elliptic operators on variable domains

We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\phi (\Omega)$ parametrized by Lipschitz homeomorphisms $\phi$ defined on a fixed reference domain $\Omega$. Given two open sets $\phi (\Omega)$, $\tilde \phi (\Omega)$ we estimate the variation of resolvents, eigenvalues and eigenfunctions via the Sobolev norm $\|\tilde \phi -\phi \|_{W^{1,p}(\Omega)}$ for finite values of $p$, under natural summability conditions on eigenfunctions and their gradients. We prove that such conditions are satisfied for a wide class of operators and open sets, including open sets with Lipschitz continuous boundaries. We apply these estimates to control the variation of the eigenvalues and eigenfunctions via the measure of the symmetric difference of the open sets. We also discuss an application to the stability of solutions to the Poisson problem.Comment: 34 pages. Minor changes in the introduction and the refercenes. Published in: Around the research of Vladimir Maz'ya II, pp23--60, Int. Math. Ser. (N.Y.), vol. 12, Springer, New York 201

Indian Ocean marine biogeochemical variability and its feedback on simulated South Asia climate

We investigate the effect of variable marine biogeochemical light absorption on Indian Ocean sea surface temperature (SST) and how this affects the South Asian climate. In twin experiments with a regional Earth system model, we found that the average SST is lower over most of the domain when variable marine biogeochemical light absorption is taken into account, compared to the reference experiment with a constant light attenuation coefficient equal to 0.06 m−1. The most significant deviations (more than 1 ∘C) in SST are observed in the monsoon season. A considerable cooling of subsurface layers occurs, and the thermocline shifts upward in the experiment with the activated biogeochemical impact. Also, the phytoplankton primary production becomes higher, especially during periods of winter and summer phytoplankton blooms. The effect of altered SST variability on climate was investigated by coupling the ocean models to a regional atmosphere model. We find the largest effects on the amount of precipitation, particularly during the monsoon season. In the Arabian Sea, the reduction of the transport of humidity across the Equator leads to a reduction of the large-scale precipitation in the eastern part of the basin, reinforcing the reduction of the convective precipitation. In the Bay of Bengal, it increases the large-scale precipitation, countering convective precipitation decline. Thus, the key impacts of including the full biogeochemical coupling with corresponding light attenuation, which in turn depends on variable chlorophyll a concentration, include the enhanced phytoplankton primary production, a shallower thermocline, and decreased SST and water temperature in subsurface layers, with cascading effects upon the model ocean physics which further translates into altered atmosphere dynamics

Interaction of the hydrogen sulfide system with the oxytocin system in the injured mouse heart.

This is the final version. Available from the publisher via the DOI in this record.BACKGROUND: Both the hydrogen sulfide/cystathionine-γ-lyase (H2S/CSE) and oxytocin/oxytocin receptor (OT/OTR) systems have been reported to be cardioprotective. H2S can stimulate OT release, thereby affecting blood volume and pressure regulation. Systemic hyper-inflammation after blunt chest trauma is enhanced in cigarette smoke (CS)-exposed CSE-/- mice compared to wildtype (WT). CS increases myometrial OTR expression, but to this point, no data are available on the effects CS exposure on the cardiac OT/OTR system. Since a contusion of the thorax (Txt) can cause myocardial injury, the aim of this post hoc study was to investigate the effects of CSE-/- and exogenous administration of GYY4137 (a slow release H2S releasing compound) on OTR expression in the heart, after acute on chronic disease, of CS exposed mice undergoing Txt. METHODS: This study is a post hoc analysis of material obtained in wild type (WT) homozygous CSE-/- mice after 2-3 weeks of CS exposure and subsequent anesthesia, blast wave-induced TxT, and surgical instrumentation for mechanical ventilation (MV) and hemodynamic monitoring. CSE-/- animals received a 50 μg/g GYY4137-bolus after TxT. After 4h of MV, animals were exsanguinated and organs were harvested. The heart was cut transversally, formalin-fixed, and paraffin-embedded. Immunohistochemistry for OTR, arginine-vasopressin-receptor (AVPR), and vascular endothelial growth factor (VEGF) was performed with naïve animals as native controls. RESULTS: CSE-/- was associated with hypertension and lower blood glucose levels, partially and significantly restored by GYY4137 treatment, respectively. Myocardial OTR expression was reduced upon injury, and this was aggravated in CSE-/-. Exogenous H2S administration restored myocardial protein expression to WT levels. CONCLUSIONS: This study suggests that cardiac CSE regulates cardiac OTR expression, and this effect might play a role in the regulation of cardiovascular function.German Research FoundationIGradUUlm University (Herta-Narthorff-Programm

Defect-induced incompatibility of elastic strains: dislocations within the Landau theory of martensitic phase transformations

In dislocation-free martensites the components of the elastic strain tensor are constrained by the Saint-Venant compatibility condition which guarantees continuity of the body during external loading. However, in dislocated materials the plastic part of the distortion tensor introduces a displacement mismatch that is removed by elastic relaxation. The elastic strains are then no longer compatible in the sense of the Saint-Venant law and the ensuing incompatibility tensor is shown to be proportional to the gradients of the Nye dislocation density tensor. We demonstrate that the presence of this incompatibility gives rise to an additional long-range contribution in the inhomogeneous part of the Landau energy functional and to the corresponding stress fields. Competition amongst the local and long-range interactions results in frustration in the evolving order parameter (elastic) texture. We show how the Peach-Koehler forces and stress fields for any distribution of dislocations in arbitrarily anisotropic media can be calculated and employed in a Fokker-Planck dynamics for the dislocation density. This approach represents a self-consistent scheme that yields the evolutions of both the order parameter field and the continuous dislocation density. We illustrate our method by studying the effects of dislocations on microstructure, particularly twinned domain walls, in an Fe-Pd alloy undergoing a martensitic transformation.Comment: 24 pages, submitted to Phys. Rev. B (changes from v1 include mainly incorporation of discrete slip systems; densities of crystal dislocations are now tracked explicitly

The mixed problem for the Laplacian in Lipschitz domains

We consider the mixed boundary value problem or Zaremba's problem for the Laplacian in a bounded Lipschitz domain in R^n. We specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We assume that the boundary between the sets where we specify Dirichlet and Neumann data is a Lipschitz surface. We require that the Neumann data is in L^p and the Dirichlet data is in the Sobolev space of functions having one derivative in L^p for some p near 1. Under these conditions, there is a unique solution to the mixed problem with the non-tangential maximal function of the gradient of the solution in L^p of the boundary. We also obtain results with data from Hardy spaces when p=1.Comment: Version 5 includes a correction to one step of the main proof. Since the paper appeared long ago, this submission includes the complete paper, followed by a short section that gives the correction to one step in the proo

Modelling avalanches in martensites

Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation, fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling.Comment: Chapter in the book "Avalanches in Functional Materials and Geophysics", edited by E. K. H. Salje, A. Saxena, and A. Planes. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-45612-6_