On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Diffusion boundary layers ameliorate the negative effects of ocean acidification on the temperate coralline macroalga Arthrocardia corymbosa

Anthropogenically-modulated reductions in pH, termed ocean acidification, could pose a major threat to the physiological performance, stocks, and biodiversity of calcifiers and may devalue their ecosystem services. Recent debate has focussed on the need to develop approaches to arrest the potential negative impacts of ocean acidification on ecosystems dominated by calcareous organisms. In this study, we demonstrate the role of a discrete (i.e. diffusion) boundary layer (DBL), formed at the surface of some calcifying species under slow flows, in buffering them from the corrosive effects of low pH seawater. The coralline macroalga Arthrocardia corymbosa was grown in a multifactorial experiment with two mean pH levels (8.05 'ambient' and 7.65 a worst case 'ocean acidification' scenario projected for 2100), each with two levels of seawater flow (fast and slow, i.e. DBL thin or thick). Coralline algae grown under slow flows with thick DBLs (i.e., unstirred with regular replenishment of seawater to their surface) maintained net growth and calcification at pH 7.65 whereas those in higher flows with thin DBLs had net dissolution. Growth under ambient seawater pH (8.05) was not significantly different in thin and thick DBL treatments. No other measured diagnostic (recruit sizes and numbers, photosynthetic metrics, %C, %N, %MgCO3) responded to the effects of reduced seawater pH. Thus, flow conditions that promote the formation of thick DBLs, may enhance the subsistence of calcifiers by creating localised hydrodynamic conditions where metabolic activity ameliorates the negative impacts of ocean acidification.

On the non-slip boundary condition enforcement in SPH methods.

The implementation of boundary conditions is one of the points where the SPH methodology still has some work to do. The aim of the present work is to provide an in-depth analysis of the most representative mirroring techniques used in SPH to enforce boundary conditions (BC) along solid profiles. We specifically refer to dummy particles, ghost particles, and Takeda et al. [1] boundary integrals. A Pouseuille flow has been used as a example to gradually evaluate the accuracy of the different implementations. Our goal is to test the behavior of the second-order differential operator with the proposed boundary extensions when the smoothing length h and other dicretization parameters as dx/h tend simultaneously to zero. First, using a smoothed continuous approximation of the unidirectional Pouseuille problem, the evolution of the velocity profile has been studied focusing on the values of the velocity and the viscous shear at the boundaries, where the exact solution should be approximated as h decreases. Second, to evaluate the impact of the discretization of the problem, an Eulerian SPH discrete version of the former problem has been implemented and similar results have been monitored. Finally, for the sake of completeness, a 2D Lagrangian SPH implementation of the problem has been also studied to compare the consequences of the particle movement

On the Controversy About the Presence of Grain Boundary Sliding in Mg AZ31

Highly-textured, rolled AZ31 sheet material shows a significant drop in the plastic anisotropy (r-value; r=εw/εt) in tension between 25°C and 200°C. This behavior was initially explained as a result of the increased activity of non-basal slip with increased temperature. Other authors suggested, however, that the mechanism resp onsible for this phenomenon was the activation of grain boundary sliding (GBS). Here, in-situ ten sile tests have been carried out in an SEM at various temperatures in order to obtain further evi dence of the role of GBS during moderate to high temperature deformation of Mg alloys, which remains highly controversial.

On the free-boundary for an elliptic inverse nonlocal problem arising in the nuclear fusion. A numerical approach

We consider a mathematical model related to the stationary regime of a plasma magnetically confined in a Stellarator device in the nuclear fusion. The mathematical problem may be reduced to an nonlinear elliptic inverse nonlocal two dimensional free{boundary problem. The nonlinear terms involving the unknown functions of the problem and its rearrangement. Our main goal is to determinate the existence and the estimate on the location and size of region where the solution is nonnegative almost everywhere (corresponding to the plasma region in the physical model)

Governors Island, Vicksburg Military Park, Niagara Falls Heritage Area, and Craters of the Moon Preserve bills : hearing before the Subcommittee on National Parks of the Committee on Energy and Natural Resources, United States Senate, One Hundred Seventh Congress, first session on S. 689, to convey certain federal properties on Governors Island, New York; S. 1175, to modify the boundary of Vicksburg National Military Park to include the property known as Pemberton's Headquarters, and for other purposes; S. 1227, to authorize the Secretary of the Interior to conduct a study on the suitability and feasibility of establishing the Niagara Falls National Heritage Area in the state of New York, and for other purposes; H.R. 601, to redesignate certain lands within the Craters of the Moon National Monument, and for other purposes, July 31, 2001.

Shipping list no.: 2002-0096-P.

A Discourse on the lives and characters of Thomas Jefferson and John Adams : who both died on the Fourth of July, 1826 /

Mode of access: Internet.

Commutation tables for joint annuities & survivorship assurances, based on the Carlisle mortality at 3, 3 1/2, 4, 5, and 6 per cent interest, with tables of annuities & assurances on single lives, and other useful tables, and an introduction on their construction & use.

Mode of access: Internet.

The history and antiquities of dissenting churches and meeting houses, in London, Westminster, and Southwark : including the lives of their ministers, from the rise of nonconformity to the present time : with an appendix on the origin, progress, and present state of Christianity in Britain /

Includes bibliographical references and index.

The life of our blessed Lord and Saviour Jesus Christ : together with the lives of his holy apostles, evangelists, and other primitive martyrs, and a dissertation on the evidences of Christianity /

Mode of access: Internet.

On the utilization of the concept of boundary impedance in vibrations of bars

"Materials Laboratory, Contract no. AF 33(616)-5426, Project no. 7360."