Kalman filters for assimilating near-surface observations into the Richards equation – Part 3: Retrieving states and parameters from laboratory evaporation experiments

Abstract. The purpose of this work is to evaluate the performance of a dual Kalman filter procedure in retrieving states and parameters of a one-dimensional soil water budget model based on the Richards equation, by assimilating near-surface soil water content values during evaporation experiments carried out under laboratory conditions. The experimental data set consists of simultaneously measured evaporation rates, soil water content and matric potential profiles. The parameters identified by assimilating the data measured at 1 and 2 cm soil depths are in very good agreement with those obtained by exploiting the observations carried out in the entire soil profiles. A reasonably good correspondence has been found between the parameter values obtained from the proposed assimilation technique and those identified by applying a non-sequential parameter estimation method. The dual Kalman filter also performs well in retrieving the water state in the porous system. Bias and accuracy of the predicted state profiles are affected by observation depth changes, particularly for the experiments involving low state vertical gradients. The assimilation procedure proved flexible and very stable in both experimental cases, independently from the selected initial conditions and the involved uncertainty

Kalman filters for assimilating near-surface observations into the Richards equation – Part 1: Retrieving state profiles with linear and nonlinear numerical schemes

Abstract. This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations into a one-dimensional Richards equation governing soil water flow in soil. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms in retrieving matric pressure head profiles when they are implemented with different numerical schemes of the Richards equation; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve matric pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. Our first objective is achieved by implementing a Standard Kalman Filter (SKF) algorithm with both an explicit finite difference scheme (EX) and a Crank-Nicolson (CN) linear finite difference scheme of the Richards equation. The Unscented (UKF) and Ensemble Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward Euler finite difference scheme. To accomplish the second objective, an analogous framework is applied, with the exception of replacing SKF with the Extended Kalman Filter (EKF) in combination with a CN numerical scheme, so as to handle the nonlinearity of the observation equation. While the EX scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieval algorithm implemented with a CN scheme is found to be computationally more feasible and accurate than those implemented with the backward Euler scheme, at least for the examined one-dimensional problem. The UKF appears to be as feasible as the EnKF when one has to handle nonlinear numerical schemes or additional nonlinearities arising from the observation equation, at least for systems of small dimensionality as the one examined in this study

Ultrasound-assisted synthesis of copper-based catalysts for the electrocatalytic CO2 reduction: Effect of ultrasound irradiation, precursor concentration and calcination temperature

The reduction of high CO2 concentrations in the atmosphere is an imperative task to reduce the consequences of the greenhouse effect on our planet. Developing active and selective materials for electrochemical CO2 reduction towards value-added products is mandatory to bring this technology to a practical application. This work studied the effect of assisting Cu and Zn oxides co-precipitation with sonochemistry. Different factors were investigated: the ultrasounds (US) amplitude, the effect of US irradiation time during either precipitation or ageing processes, the precursor concentration and calcination temperature. The synthesised catalysts were tested for the electrocatalytic CO2 reduction reaction in a Rotating Disk Electrode (RDE) system. Faradaic efficiencies >14% towards alcohols were obtained using US-assisted synthesised Cu-based catalysts. Instead, with the US-prepared CupperZinc-based catalysts, the selectivity towards H-2 and C-1 products (CO and formate) was improved, and the syngas productivity was increased by >.1.4-fold compared to the non-sonicated one. The alcohols production of the best Cu-catalyst was also confirmed on scalable electrodes. Controlling the synthesis conditions allowed to tune the physicochemical properties of the nanoparticles, including specific surface area, porosity, crystallite size and phases. Mesoporous materials with a mean pores size of around 25 nm were found to induce a better CO2 diffusion and CO retention time in the porous network, improving the *CO intermediate adsorption at active sites, promoting its dimerisation and thus enhancing the selectivity towards C2+ alcohols. The here reported results open the way for new electrocatalysts designs with properly tuned porosity for the selective CO2 conversion to different valuable products

Pasti-Sorokin-Tonin Actions in the Presence of Sources

Pasti, Sorokin and Tonin have recently constructed manifestly Lorentz-invariant actions for self-dual field strengths and for Maxwell fields with manifest electromagnetic duality. Using the method of Deser, Gomberoff, Henneaux and Teitelboim, we generalize these actions in the presence of sources.Comment: 6 pages, LaTe

Directed paths on hierarchical lattices with random sign weights

We study sums of directed paths on a hierarchical lattice where each bond has either a positive or negative sign with a probability $p$. Such path sums $J$ have been used to model interference effects by hopping electrons in the strongly localized regime. The advantage of hierarchical lattices is that they include path crossings, ignored by mean field approaches, while still permitting analytical treatment. Here, we perform a scaling analysis of the controversial ``sign transition'' using Monte Carlo sampling, and conclude that the transition exists and is second order. Furthermore, we make use of exact moment recursion relations to find that the moments always determine, uniquely, the probability distribution $P(J)$. We also derive, exactly, the moment behavior as a function of $p$ in the thermodynamic limit. Extrapolations ($n\to 0$) to obtain for odd and even moments yield a new signal for the transition that coincides with Monte Carlo simulations. Analysis of high moments yield interesting ``solitonic'' structures that propagate as a function of $p$. Finally, we derive the exact probability distribution for path sums $J$ up to length L=64 for all sign probabilities.Comment: 20 pages, 12 figure

Mesoscopic rings with Spin-Orbit interactions

A didactic description of charge and spin equilibrium currents on mesoscopic rings in the presence of Spin-Orbit interaction is presented. Emphasis is made on the non trivial construction of the correct Hamiltonian in polar coordinates, the calculation of eigenvalues and eigenfunctions and the symmetries of the ground state properties. Spin currents are derived following an intuitive definition and then a more thorough derivation is built upon the canonical Lagrangian formulation that emphasizes the SU(2) gauge structure of the transport problem of spin 1/2 fermions in spin-orbit active media. The quantization conditions that follow from the constraint of single-valued Pauli spinors are also discussed. The targeted students are those of a graduate Condensed Matter Physics course

Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace

A simple BRST-closed expression for the color-ordered super-Yang-Mills 5-point amplitude at tree-level is proposed in pure spinor superspace and shown to be BRST-equivalent to the field theory limit of the open superstring 5-pt amplitude. It is manifestly cyclic invariant and each one of its five terms can be associated to the five Feynman diagrams which use only cubic vertices. Its form also suggests an empirical method to find superspace expressions in the cohomology of the pure spinor BRST operator for higher-point amplitudes based on their kinematic pole structure. Using this method, Ansaetze for the 6- and 7-point 10D super-Yang-Mills amplitudes which map to their 14 and 42 color-ordered diagrams are conjectured and their 6- and 7-gluon expansions are explicitly computed.Comment: 14 pages, harvmac, v4: trivial edits in the text to comply with JHEP refere

Towards an integrated moisture-safe retrofit process for traditional buildings in policy and industry

Improving the energy efficiency of traditional buildings, which represent a large proportion of the building stock in the UK, is necessary to meet national targets on greenhouse gas emissions and alleviate fuel poverty. Traditional dwellings in the UK are defined as hard-to-treat homes because insulating them is not cost-effective or might lead to moisture-related issues. This has led to efforts from policy-makers and organisations towards minimizing moisture risk in the energy-efficient retrofit of traditional buildings. This paper presents an overview of the work done towards a moisture-safe retrofit in the UK in the past ten years, focusing on the Government's policies and the work and legacy of the late Neil May, one of the pioneers in sustainable traditional buildings in the UK

Deflection of ultra high energy cosmic rays by the galactic magnetic field: from the sources to the detector

We report the results of 3D simulations of the trajectories of ultra-high energy protons and Fe nuclei (with energies $E = 4 \times 10^{19}$ and $2.5 \times 10^{20} eV$) propagating through the galactic magnetic field from the sources to the detector. A uniform distribution of anti-particles is backtracked from the detector, at the Earth, to the halo of the Galaxy. We assume an axisymmetric, large scale spiral magnetic field permeating both the disc and the halo. A normal field component to the galactic plane ($B_z$) is also included in part of the simulations. We find that the presence of a large scale galactic magnetic field does not generally affect the arrival directions of the protons, although the inclusion of a $B_z$ component may cause significant deflection of the lower energy protons ($E = 4 \times 10^{19}$ eV). Error boxes larger than or equal to $\sim 5^{\circ}$ are most expected in this case. On the other hand, in the case of heavy nuclei, the arrival direction of the particles is strongly dependent on the coordinates of the particle source. The deflection may be high enough ($> 20^{\circ}$) as to make extremely difficult any identification of the sources unless the real magnetic field configuration is accurately determined. Moreover, not every incoming particle direction is allowed between a given source and the detector. This generates sky patches which are virtually unobservable from the Earth. In the particular case of the UHE events of Yakutsk, Fly's Eye, and Akeno, they come from locations for which the deflection caused by the assumed magnetic field is not significant.Comment: LaTeX + 2 postscript figures - Color versions of both figures (highly recommended) available via anonymous ftp at ftp://capc07.ast.cam.ac.uk/pub/uhecr_gmf as fig*.g

The One-loop Open Superstring Massless Five-point Amplitude with the Non-Minimal Pure Spinor Formalism

We compute the massless five-point amplitude of open superstrings using the non-minimal pure spinor formalism and obtain a simple kinematic factor in pure spinor superspace, which can be viewed as the natural extension of the kinematic factor of the massless four-point amplitude. It encodes bosonic and fermionic external states in supersymmetric form and reduces to existing bosonic amplitudes when expanded in components, therefore proving their equivalence. We also show how to compute the kinematic structures involving fermionic states.Comment: 38 pages, harvmac TeX, v2: fix typo in (4.2) and add referenc