Application of hpDGFEM to mechanisms at channel microband electrodes

We extend our earlier work (Harriman et al., Oxford University Computing Laboratory Technical Report NA04/19) on hp-DGFEM for disc electrodes to the case of reaction mechanisms to the increasingly popular channel microband electrode configuration. We present results for the simple E reaction mechanism (convection-diffusion equation), for the ECE and EC2E reaction mechanisms (linear and nonlinear systems of reaction-convection- diffusion equations, respectively) and for the DISP1 and DISP2 reaction mechanisms (linear and nonlinear coupled systems of reaction-convection-diffusion equations, respectively). In all cases we demonstrate excellent agreement with previous results using relatively coarse meshes and without the need for streamline-diffusion stabilisation, even at high flow rates

Approximation of linear functionals using an hp-adaptive discontinuous Galerkin finite element method

We consider the problem of computing a linear functional of the solution of an elliptic partial differential equation to within a given tolerance. We drive an a posteriori error bound for the linear functional and use this as the basis of an hp-adaptive discontinuous Galerkin finite element algorithm to deliver the functional to within a prescribed error tolerance

Measurements of strongly-anisotropic g-factors for spins in single quantum states

We have measured the full angular dependence, as a function of the direction of magnetic field, for the Zeeman splitting of individual energy states in copper nanoparticles. The g-factors for spin splitting are highly anisotropic, with angular variations as large as a factor of five. The angular dependence fits well to ellipsoids. Both the principal-axis directions and g-factor magnitudes vary between different energy levels within one nanoparticle. The variations agree quantitatively with random-matrix theory predictions which incorporate spin-orbit coupling.Comment: 4 pages, 3 figures, 2 in colo

The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method

We describe how a discontinuous Galerkin finite element method with interior penalty can be used to compute the solution to an elliptic partial differential equation and a linear functional of this solution can be evaluated. We show that, in order to have an adjoint consistent method and thus obtain optimal rates of convergence of the functional, a symmetric interior penalty Galerkin method must be used and, when the functional depends on the derivative of the solution of the PDE, an equivalent formulation of the functional must be used

Finite element solution of a membrane covered electrode problem

Membrane covered oxygen sensors, or Clark electrodes, are used for monitoring the concentration of oxygen in blood. The operation of such sensors is governed by the diffusion equation with different diffusion coefficients in different sub-domains. The form of the boundary conditions and the material interface conditions means that the derivative of the solution has discontinuities which restrict the convergence of standard numerical methods on regular meshes. We describe and computationally compare adaptive finite element methods based on continuous and discontinuous basis functions to overcome this problem

Mechanical Response of He- Implanted Amorphous SiOC/ Crystalline Fe Nanolaminates

This study investigates the microstructural evolution and mechanical response of sputter-deposited amorphous silicon oxycarbide (SiOC)/crystalline Fe nanolaminates, a single layer SiOC film, and a single layer Fe film subjected to ion implantation at room temperature to obtain a maximum He concentration of 5 at. %. X-ray diffraction and transmission electron microscopy indicated no evidence of implantation-induced phase transformation or layer breakdown in the nanolaminates. Implantation resulted in the formation of He bubbles and an increase in the average size of the Fe grains in the individual Fe layers of the nanolaminates and the single layer Fe film, but the bubble density and grain size were found to be smaller in the former. By reducing the thicknesses of individual layers in the nanolaminates, bubble density and grain size were further decreased. No He bubbles were observed in the SiOC layers of the nanolaminates and the single layer SiOC film. Nanoindentation and scanning probe microscopy revealed an increase in the hardness of both single layer SiOC and Fe films after implantation. For the nanolaminates, changes in hardness were found to depend on the thicknesses of the individual layers, where reducing the layer thickness to 14 nm resulted in mitigation of implantation-induced hardening

Pseudocontact shifts and paramagnetic susceptibility in semiempirical and quantum chemistry theories

Pseudocontact shifts are traditionally described as a function of the anisotropy of the paramagnetic susceptibility tensor, according to the semiempirical theory mainly developed by Kurland and McGarvey (R.J. Kurland and B.R. McGarvey, J. Magn. Reson. 2, 286 (1970)). The paramagnetic susceptibility tensor is required to be symmetric. Applying point-dipole approximation to the quantum chemistry theory of hyperfine shift, pseudocontact shifts are found to scale with a non-symmetric tensor that differs by a factor g/ge from the paramagnetic susceptibility tensor derived within the semiempirical framework. We analyze the foundations of the Kurland-McGarvey pseudocontact shift expression and recall that it is inherently based on the Russell-Saunders (LS) coupling approximation for the spin-orbit coupling. We show that the difference between the semiempirical and quantum chemistry pseudocontact shift expressions arises directly from the different treatment of the orbital contribution to the hyperfine coupling

Causality re-established

Causality never gained the status of a "law" or "principle" in physics. Some recent literature even popularized the false idea that causality is a notion that should be banned from theory. Such misconception relies on an alleged universality of reversibility of laws of physics, based either on determinism of classical theory, or on the multiverse interpretation of quantum theory, in both cases motivated by mere interpretational requirements for realism of the theory. Here, I will show that a properly defined unambiguous notion of causality is a theorem of quantum theory, which is also a falsifiable proposition of the theory. Such causality notion appeared in the literature within the framework of operational probabilistic theories. It is a genuinely theoretical notion, corresponding to establish a definite partial order among events, in the same way as we do by using the future causal cone on Minkowski space. The causality notion is logically completely independent of the misidentified concept of "determinism", and, being a consequence of quantum theory, is ubiquitous in physics. In addition, as classical theory can be regarded as a restriction of quantum theory, causality holds also in the classical case, although the determinism of the theory trivializes it. I then conclude arguing that causality naturally establishes an arrow of time. This implies that the scenario of the "Block Universe" and the connected "Past Hypothesis" are incompatible with causality, and thus with quantum theory: they both are doomed to remain mere interpretations and, as such, not falsifiable, similar to the hypothesis of "super-determinism". This article is part of a discussion meeting issue "Foundations of quantum mechanics and their impact on contemporary society".Comment: Presented at the Royal Society of London, on 11/12/ 2017, at the conference "Foundations of quantum mechanics and their impact on contemporary society". To appear on Philosophical Transactions of the Royal Society

Ultrafast electronic energy transfer beyond the weak coupling limit in a proximal but orthogonal molecular dyad

Electronic energy transfer (EET) from a donor to an acceptor is an important mechanism that controls the light harvesting efficiency in a wide variety of systems, including artificial and natural photosynthesis and contemporary photovoltaic technologies. The detailed mechanism of BET at short distances or large angles between the donor and acceptor is poorly understood. Here the influence of the orientation between the donor and acceptor on EET is explored using a molecule with two nearly perpendicular chromophores. Very fast EET with a time constant of 120 fs is observed, which is at least 40 times faster than the time predicted by Coulombic coupling calculations. Depolarization of the emission signal indicates that the transition dipole rotates through ca. 64 degrees, indicating the near orthogonal nature of the EET event. The rate of EET is found to be similar to structural relaxation rates in the photoexcited oligothiophene donor alone, which suggests that this initial relaxation brings the dyad to a conical intersection where the excitation jumps to the acceptor.PostprintPeer reviewe

Successive Combination Jet Algorithm For Hadron Collisions

Jet finding algorithms, as they are used in $e^+ e^-$ and hadron collisions, are reviewed and compared. It is suggested that a successive combination style algorithm, similar to that used in $e^+ e^-$ physics, might be useful also in hadron collisions, where cone style algorithms have been used previously.Comment: 18 pages plus four uuencoded postscript figures, REVTEX 3.0, CERN-TH.6860/9