Geodesics on Lie groups: Euler equations and totally geodesic subgroup

The geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler-Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given. The setting works both in the classical nite dimensional case, and in the category of in nite dimensional Fr echet Lie groups, in which di eomorphism groups are included. Using the framework we give new examples of both nite and in nite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving di eomorphisms is totally geodesic. The paper also gives a general framework for the representation of Euler-Arnold equations in arbitrary choice of dual pairing

Quantum Statistical Calculations and Symplectic Corrector Algorithms

The quantum partition function at finite temperature requires computing the trace of the imaginary time propagator. For numerical and Monte Carlo calculations, the propagator is usually split into its kinetic and potential parts. A higher order splitting will result in a higher order convergent algorithm. At imaginary time, the kinetic energy propagator is usually the diffusion Greens function. Since diffusion cannot be simulated backward in time, the splitting must maintain the positivity of all intermediate time steps. However, since the trace is invariant under similarity transformations of the propagator, one can use this freedom to "correct" the split propagator to higher order. This use of similarity transforms classically give rises to symplectic corrector algorithms. The split propagator is the symplectic kernel and the similarity transformation is the corrector. This work proves a generalization of the Sheng-Suzuki theorem: no positive time step propagators with only kinetic and potential operators can be corrected beyond second order. Second order forward propagators can have fourth order traces only with the inclusion of an additional commutator. We give detailed derivations of four forward correctable second order propagators and their minimal correctors.Comment: 9 pages, no figure, corrected typos, mostly missing right bracket

Wide-angle perfect absorber/thermal emitter in the THz regime

We show that a perfect absorber/thermal emitter exhibiting an absorption peak of 99.9% can be achieved in metallic nanostructures that can be easily fabricated. The very high absorption is maintained for large angles with a minimal shift in the center frequency and can be tuned throughout the visible and near-infrared regime by scaling the nanostructure dimensions. The stability of the spectral features at high temperatures is tested by simulations using a range of material parameters.Comment: Submitted to Phys. Rev. Let

Low-Temperature Solution-Processed Electron Transport Layers for Inverted Polymer Solar Cells

© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimProcessing temperature is highlighted as a convenient means of controlling the optical and charge transport properties of solution processed electron transport layers (ETLs) in inverted polymer solar cells. Using the well-studied active layer – poly(3-hexylthiophene-2,5-diyl):indene-C60 bisadduct – the influence of ETL processing temperatures from 25 to 450 °C is shown, reporting the role of crystallinity, structure, charge transport, and Fermi level (EF) on numerous device performance characteristics. It has been determined that an exceptionally low temperature processed ETL (110 °C) increases device power conversion efficiency by a factor greater than 50% compared with a high temperature (450 °C) processed ETL. Modulations in device series and shunt resistance, induced by changes in the ETL transport properties, are observed in parallel to significant changes in device open circuit voltage attributed to changes on the EF of the ETLs. This work highlights the importance of interlayer control in multilayer photovoltaic devices and presents a convenient material compatible with future flexible and roll-to-roll processes

Breaking tolerance in transgenic mice expressing the human TSH receptor A-subunit: thyroiditis, epitope spreading and adjuvant as a 'double edged sword'.

Transgenic mice with the human thyrotropin-receptor (TSHR) A-subunit targeted to the thyroid are tolerant of the transgene. In transgenics that express low A-subunit levels (Lo-expressors), regulatory T cell (Treg) depletion using anti-CD25 before immunization with adenovirus encoding the A-subunit (A-sub-Ad) breaks tolerance, inducing extensive thyroid lymphocytic infiltration, thyroid damage and antibody spreading to other thyroid proteins. In contrast, no thyroiditis develops in Hi-expressor transgenics or wild-type mice. Our present goal was to determine if thyroiditis could be induced in Hi-expressor transgenics using a more potent immunization protocol: Treg depletion, priming with Complete Freund's Adjuvant (CFA) + A-subunit protein and further Treg depletions before two boosts with A-sub-Ad. As controls, anti-CD25 treated Hi- and Lo-expressors and wild-type mice were primed with CFA+ mouse thyroglobulin (Tg) or CFA alone before A-sub-Ad boosting. Thyroiditis developed after CFA+A-subunit protein or Tg and A-sub-Ad boosting in Lo-expressor transgenics but Hi- expressors (and wild-type mice) were resistant to thyroiditis induction. Importantly, in Lo-expressors, thyroiditis was associated with the development of antibodies to the mouse TSHR downstream of the A-subunit. Unexpectedly, we observed that the effect of bacterial products on the immune system is a "double-edged sword". On the one hand, priming with CFA (mycobacteria emulsified in oil) plus A-subunit protein broke tolerance to the A-subunit in Hi-expressor transgenics leading to high TSHR antibody levels. On the other hand, prior treatment with CFA in the absence of A-subunit protein inhibited responses to subsequent immunization with A-sub-Ad. Consequently, adjuvant activity arising in vivo after bacterial infections combined with a protein autoantigen can break self-tolerance but in the absence of the autoantigen, adjuvant activity can inhibit the induction of immunity to autoantigens (like the TSHR) displaying strong self-tolerance

Numerical Implementation of Gradient Algorithms

A numerical method for computational implementation of gradient dynamical systems is presented. The method is based upon the development of geometric integration numerical methods, which aim at preserving the dynamical properties of the original ordinary differential equation under discretization. In particular, the proposed method belongs to the class of discrete gradients methods, which substitute the gradient of the continuous equation with a discrete gradient, leading to a map that possesses the same Lyapunov function of the dynamical system, thus preserving the qualitative properties regardless of the step size. In this work, we apply a discrete gradient method to the implementation of Hopfield neural networks. Contrary to most geometric integration methods, the proposed algorithm can be rewritten in explicit form, which considerably improves its performance and stability. Simulation results show that the preservation of the Lyapunov function leads to an improved performance, compared to the conventional discretization.Spanish Government project no. TIN2010-16556 Junta de Andalucía project no. P08-TIC-04026 Agencia Española de Cooperación Internacional para el Desarrollo project no. A2/038418/1

Symplectic integrators for index one constraints

We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity constraints nondegenerate in the velocities, such as those arising in sub-Riemannian geometry and control theory.Comment: 13 pages, accepted in SIAM J Sci Compu