Modeling of diffusion of injected electron spins in spin-orbit coupled microchannels

We report on a theoretical study of spin dynamics of an ensemble of spin-polarized electrons injected in a diffusive microchannel with linear Rashba and Dresselhaus spin-orbit coupling. We explore the dependence of the spin-precession and spin-diffusion lengths on the strengths of spin-orbit interaction and external magnetic fields, microchannel width, and orientation. Our results are based on numerical Monte Carlo simulations and on approximate analytical formulas, both treating the spin dynamics quantum-mechanically. We conclude that spin-diffusion lengths comparable or larger than the precession-length occur i) in the vicinity of the persistent spin helix regime for arbitrary channel width, and ii) in channels of similar or smaller width than the precession length, independent of the ratio of Rashba and Dresselhaus fields. For similar strengths of the Rashba and Dresselhaus fields, the steady-state spin-density oscillates or remains constant along the channel for channels parallel to the in-plane diagonal crystal directions. An oscillatory spin-polarization pattern tilted by 45$^{\circ}$ with respect to the channel axis is predicted for channels along the main cubic crystal directions. For typical experimental system parameters, magnetic fields of the order of Tesla are required to affect the spin-diffusion and spin-precession lengths.Comment: Replaced with final version (some explanations and figures improved). 8 pages, 6 figure

Guidelines for the use of cell lines in biomedical research

Cell-line misidentification and contamination with microorganisms, such as mycoplasma, together with instability, both genetic and phenotypic, are among the problems that continue to affect cell culture. Many of these problems are avoidable with the necessary foresight, and these Guidelines have been prepared to provide those new to the field and others engaged in teaching and instruction with the information necessary to increase their awareness of the problems and to enable them to deal with them effectively. The Guidelines cover areas such as development, acquisition, authentication, cryopreservation, transfer of cell lines between laboratories, microbial contamination, characterisation, instability and misidentification. Advice is also given on complying with current legal and ethical requirements when deriving cell lines from human and animal tissues, the selection and maintenance of equipment and how to deal with problems that may arise

Component-based reduced basis for parametrized symmetric eigenproblems

Background: A component-based approach is introduced for fast and flexible solution of parameter-dependent symmetric eigenproblems. Methods: Considering a generalized eigenproblem with symmetric stiffness and mass operators, we start by introducing a “ σ-shifted” eigenproblem where the left hand side operator corresponds to an equilibrium between the stiffness operator and a weighted mass operator, with weight-parameter σ>0. Assuming that σ=λ n >0, the nth real positive eigenvalue of the original eigenproblem, then the shifted eigenproblem reduces to the solution of a homogeneous linear problem. In this context, we can apply the static condensation reduced basis element (SCRBE) method, a domain synthesis approach with reduced basis (RB) approximation at the intradomain level to populate a Schur complement at the interdomain level. In the Offline stage, for a library of archetype subdomains we train RB spaces for a family of linear problems; these linear problems correspond to various equilibriums between the stiffness operator and the weighted mass operator. In the Online stage we assemble instantiated subdomains and perform static condensation to obtain the “ σ-shifted” eigenproblem for the full system. We then perform a direct search to find the values of σ that yield singular systems, corresponding to the eigenvalues of the original eigenproblem. Results: We provide eigenvalue a posteriori error estimators and we present various numerical results to demonstrate the accuracy, flexibility and computational efficiency of our approach. Conclusions: We are able to obtain large speed and memory improvements compared to a classical Finite Element Method (FEM), making our method very suitable for large models commonly considered in an engineering context.United States. Air Force Office of Scientific Research (OSD/AFOSR/MURI Grant FA9550-09-1-0613)United States. Office of Naval Research (ONR Grant N00014-11-1-0713)Deshpande Center for Technological Innovation (grant)Switzerland. Commission for Technology and Innovation (CTI

Decoherence due to contacts in ballistic nanostructures

The active region of a ballistic nanostructure is an open quantum-mechanical system, whose nonunitary evolution (decoherence) towards a nonequilibrium steady state is determined by carrier injection from the contacts. The purpose of this paper is to provide a simple theoretical description of the contact-induced decoherence in ballistic nanostructures, which is established within the framework of the open systems theory. The active region's evolution in the presence of contacts is generally non-Markovian. However, if the contacts' energy relaxation due to electron-electron scattering is sufficiently fast, then the contacts can be considered memoryless on timescales coarsened over their energy relaxation time, and the evolution of the current-limiting active region can be considered Markovian. Therefore, we first derive a general Markovian map in the presence of a memoryless environment, by coarse-graining the exact short-time non-Markovian dynamics of an abstract open system over the environment memory-loss time, and we give the requirements for the validity of this map. We then introduce a model contact-active region interaction that describes carrier injection from the contacts for a generic two-terminal ballistic nanostructure. Starting from this model interaction and using the Markovian dynamics derived by coarse-graining over the effective memory-loss time of the contacts, we derive the formulas for the nonequilibrium steady-state distribution functions of the forward and backward propagating states in the nanostructure's active region. On the example of a double-barrier tunneling structure, the present approach yields an I-V curve with all the prominent resonant features. The relationship to the Landauer-B\"{u}ttiker formalism is also discussed, as well as the inclusion of scattering.Comment: Published versio

Fake news and critical thinking in information evaluation

In the post-truth era we are constantly bombarded with “news” which is fabricated, distorted, and massaged information, published with the intention to deceive and mislead others. Such “news” has come to be known as “fake news”. The influence of fake news can have profound socio-political and cultural effects when translated into action. The ability to distinguish between real facts, fabricated stories, rumours, propaganda, or opinions is of paramount importance. The rapid proliferation of information through social media is now the norm. In this paper we consider the challenge of preparing students, in developing skills for recognising mis-information, dis-information and mal-information. We argue that critical thinking for evaluating information should now be considered a basic literacy, equally important to literacy itself, as well as information and information technology literacies. In this paper we revisit Bloom’s taxonomy of cognitive skills and represent what a learner can achieve at each level. We customise the traditional moral and ethical concepts suggested by the US Content Subcommittee of the ImpactCS Steering Committee to flag the ethical concerns over mis-information, dis-information and mal-information. We report on current levels of awareness and practices at the authors’ five higher education institutions, and reveal varying levels of awareness of the significance of critical literacy and different practices in each location. The paper concludes with an outline of future work

Self-consistent Wigner distribution function study of gate-voltage controlled triple-barrier resonant tunnelling diode

The electron transport through the triple-barrier resonant tunnelling diode (TBRTD) have been studied by the self-consistent numerical method for the Wigner-Poisson problem. The electron flow through the TBRTD can be controlled by the gate voltage applied to one of the potential well regions. For different gate voltage values we have determined the current-voltage characteristics, potential energy profiles, and electron density distribution. We have found the enhancement of the peak-to-valley ratio (up to $\sim$10), the appearance of the linear current versus bias voltage behaviour within the negative-differential resistance region, and the bistability of the current-voltage characteristics. The analysis of the self-consistent potential energy profiles and electron density distribution allowed us to provide a physical interpretation of these properties.Comment: 13 pages, 7 figure

Reduced Basis Approximation and a Posteriori Error Estimation for the Parametrized Unsteady Boussinesq Equations

In this paper we present reduced basis (RB) approximations and associated rigorous a posteriori error bounds for the parametrized unsteady Boussinesq equations. The essential ingredients are Galerkin projection onto a low-dimensional space associated with a smooth parametric manifold — to provide dimension reduction; an efficient proper orthogonal decomposition–Greedy sampling method for identification of optimal and numerically stable approximations — to yield rapid convergence; accurate (online) calculation of the solution-dependent stability factor by the successive constraint method — to quantify the growth of perturbations/residuals in time; rigorous a posteriori bounds for the errors in the RB approximation and associated outputs — to provide certainty in our predictions; and an offline–online computational decomposition strategy for our RB approximation and associated error bound — to minimize marginal cost and hence achieve high performance in the real-time and many-query contexts. The method is applied to a transient natural convection problem in a two-dimensional "complex" enclosure — a square with a small rectangle cutout — parametrized by Grashof number and orientation with respect to gravity. Numerical results indicate that the RB approximation converges rapidly and that furthermore the (inexpensive) rigorous a posteriori error bounds remain practicable for parameter domains and final times of physical interest.United States. Air Force Office of Scientific Research (Grant FA9550-07-1-0425)United States. Department of Defense. Office of the Secretary of Defense (United States. Air Force Office of Scientific Research Grant FA9550-09-1-0613