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

Copper In Douglas-Fir and Associated Dielectric Changes

The dielectric constant, loss tangent, and AC resistivity of 60 Douglas-fir (Psendotsuga menziesii (Mirb.) Franco) heartwood specimens were determined at 100 Hz, 1 kHz, 50 kHz, and 100 kHz before and after treatment with copper sulphate solutions. The copper retentions, based on oven-dry weight before treatment, ranged from 1 to 7%.Of the three electrical properties, AC resistivity changed most as a result of treatment. This change, a factor of 7, occurred at 100 Hz and with specimens at an estimated 20% moisture content. A statistical analysis showed even changes of this magnitude are insufficient to form a basis for a nondestructive method for estimating copper retention in wood

A Static condensation Reduced Basis Element method: approximation and a posteriori error estimation

We propose a new reduced basis element-cum-component mode synthesis approach for parametrized elliptic coercive partial differential equations. In the Offline stage we construct a Library of interoperable parametrized reference components relevant to some family of problems; in the Online stage we instantiate and connect reference components (at ports) to rapidly form and query parametric systems. The method is based on static condensation at the interdomain level, a conforming eigenfunction “port” representation at the interface level, and finally Reduced Basis (RB) approximation of Finite Element (FE) bubble functions at the intradomain level. We show under suitable hypotheses that the RB Schur complement is close to the FE Schur complement: we can thus demonstrate the stability of the discrete equations; furthermore, we can develop inexpensive and rigorous (system-level) a posteriori error bounds. We present numerical results for model many-parameter heat transfer and elasticity problems with particular emphasis on the Online stage; we discuss flexibility, accuracy, computational performance, and also the effectivity of the a posteriori error bounds.United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613)MIT-Singapore International Design Cente

A Laplace transform certified reduced basis method; application to the heat equation and wave equation

We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accuracy and efficiency of the approach.United States. Air Force Office of Scientific Research (Grant FA9550-07-1-0425)United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0613

Certified reduced basis model validation: A frequentistic uncertainty framework

We introduce a frequentistic validation framework for assessment — acceptance or rejection — of the consistency of a proposed parametrized partial differential equation model with respect to (noisy) experimental data from a physical system. Our method builds upon the Hotelling T[superscript 2] statistical hypothesis test for bias first introduced by Balci and Sargent in 1984 and subsequently extended by McFarland and Mahadevan (2008). Our approach introduces two new elements: a spectral representation of the misfit which reduces the dimensionality and variance of the underlying multivariate Gaussian but without introduction of the usual regression assumptions; a certified (verified) reduced basis approximation — reduced order model — which greatly accelerates computational performance but without any loss of rigor relative to the full (finite element) discretization. We illustrate our approach with examples from heat transfer and acoustics, both based on synthetic data. We demonstrate that we can efficiently identify possibility regions that characterize parameter uncertainty; furthermore, in the case that the possibility region is empty, we can deduce the presence of “unmodeled physics” such as cracks or heterogeneities.United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613)MIT-Singapore International Design Cente

High-fidelity real-time simulation on deployed platforms

We present a certified reduced basis method for high-fidelity real-time solution of parametrized partial differential equations on deployed platforms. Applications include in situ parameter estimation, adaptive design and control, interactive synthesis and visualization, and individuated product specification. We emphasize a new hierarchical architecture particularly well suited to the reduced basis computational paradigm: the expensive Offline stage is conducted pre-deployment on a parallel supercomputer (in our examples, the TeraGrid machine Ranger); the inexpensive Online stage is conducted “in the field” on ubiquitous thin/inexpensive platforms such as laptops, tablets, smartphones (in our examples, the Nexus One Android-based phone), or embedded chips. We illustrate our approach with three examples: a two-dimensional Helmholtz acoustics “horn” problem; a three-dimensional transient heat conduction “Swiss Cheese” problem; and a three-dimensional unsteady incompressible Navier–Stokes low-Reynolds-number “eddy-promoter” problem.United States. Air Force Office of Scientific Research (Grant FA9550-07-1-0425)United States. Air Force Office of Scientific Research (OSD Grant FA9550-09-1-0613)National Science Foundation (U.S.) (University of Texas at Austin. Texas Advanced Computing Center Grant TG-ASC100016

THE INFLUENCE OF FOLIAR FERTILIZATION WITH ORGANIC FERTILIZERS ON THE YIELD AND THE CHEMICAL CONTENT OF POTATOES GROWN IN STRUMICA REGION

The effect of foliar fertilization with organic fertilizers on the yield and the chemical content of potatoes grown in Strumica region were studied, in the period from the year of 2011-2012. The experiment was set in four variants and three repetitions. The variants in the experiment were: Control (no-fertilizing variant); Humusil (organic matter 1.86%; organic carbon 1.08%; humin acids 0.14%; N 224 mg/L; P2O5 71 mg/L; K2O 1024 mg/L; CaO 180 mg/L); Humustim (organic matter 58.63 %; dry matter 12.38 %; humin acids 20.40 %; fulvo acids 2.15%; N 3%; P2O5 1.02%; K2O 7.92%; Ca 3.70 %; Mg 1.03%); Ingrasamant foliar (N 0 %; P2O5 130 g/L; K2O 130 g/L; ME in helate form and plant extracts 0.005 g/L). The experiment was arranged in 12 rows and in each variant and repetition was involved 100 plants, total in all experiment were involved 1200 plants. The planting was made in rows at a distance of 60 cm row by row and 20 cm in the rows. The row’s length was 20 m. Three foliar treatments were applied with given above fertilizers at a concentration of 0.4%. The soil where the experiment was carried had a good fertility with nitrogen, phosphorus and potassium. The foliar fertilization had a positive influence on potatoes yield in all of the variants treated with different organic fertilizers. The highest potatoes yield of 54.62 t ha-1 was established in variant 4. The foliar fertilization had a positive influence on the chemical content of tubers potato, too. In three variants treated with different fertilizers, higher content of all tested parameters was found, compared to the control untreated variant. The highest average content of vitamin C (2.60 mg/100g), phosphorus (0.90 %), and potassium (1.30 %) was determined in the tubers potato in variant 3

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

A natural-norm Successive Constraint Method for inf-sup lower bounds

We present a new approach for the construction of lower bounds for the inf-sup stability constants required in a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations. We combine the “linearized” inf-sup statement of the natural-norm approach with the approximation procedure of the Successive Constraint Method (SCM): the former (natural-norm) provides an economical parameter expansion and local concavity in parameter—a small(er) optimization problem which enjoys intrinsic lower bound properties; the latter (SCM) provides a systematic optimization framework—a Linear Program (LP) relaxation which readily incorporates continuity and stability constraints. The natural-norm SCM requires a parameter domain decomposition: we propose a greedy algorithm for selection of the SCM control points as well as adaptive construction of the optimal subdomains. The efficacy of the natural-norm SCM is illustrated through numerical results for two types of non-coercive problems: the Helmholtz equation (for acoustics, elasticity, and electromagnetics), and the convection–diffusion equation.United States. Air Force Office of Scientific Research (Grant No. FA 9550-07-1-0425