Semi-invariant Riemannian metrics in hydrodynamics

Many models in mathematical physics are given as non-linear partial differential equation of hydrodynamic type; the incompressible Euler, KdV, and Camassa–Holm equations are well-studied examples. A beautiful approach to well-posedness is to go from the Eulerian to a Lagrangian description. Geometrically it corresponds to a geodesic initial value problem on the infinite-dimensional group of diffeomorphisms with a right invariant Riemannian metric. By establishing regularity properties of the Riemannian spray one can then obtain local, and sometimes global, existence and uniqueness results. There are, however, many hydrodynamic-type equations, notably shallow water models and compressible Euler equations, where the underlying infinite-dimensional Riemannian structure is not fully right invariant, but still semi-invariant with respect to the subgroup of volume preserving diffeomorphisms. Here we study such metrics. For semi-invariant metrics of Sobolev Hk-type we give local and some global well-posedness results for the geodesic initial value problem. We also give results in the presence of a potential functional (corresponding to the fluid’s internal energy). Our study reveals many pitfalls in going from fully right invariant to semi-invariant Sobolev metrics; the regularity requirements, for example, are higher. Nevertheless the key results, such as no loss or gain in regularity along geodesics, can be adopted

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

Sensitivity of IceCube-DeepCore to neutralino dark matter in the MSSM-25

We analyse the sensitivity of IceCube-DeepCore to annihilation of neutralino dark matter in the solar core, generated within a 25 parameter version of the minimally supersymmetric standard model (MSSM-25). We explore the 25-dimensional parameter space using scanning methods based on importance sampling and using DarkSUSY 5.0.6 to calculate observables. Our scans produced a database of 6.02 million parameter space points with neutralino dark matter consistent with the relic density implied by WMAP 7-year data, as well as with accelerator searches. We performed a model exclusion analysis upon these points using the expected capabilities of the IceCube-DeepCore Neutrino Telescope. We show that IceCube-DeepCore will be sensitive to a number of models that are not accessible to direct detection experiments such as SIMPLE, COUPP and XENON100, indirect detection using Fermi-LAT observations of dwarf spheroidal galaxies, nor to current LHC searches.Comment: 15 pages, 13 figures. V2: Additional comparisons are made to limits from Fermi-LAT observations of dwarf spheroidal galaxies and to the 125 GeV Higgs signal from the LHC. The spectral hardness section has been removed. Matches version accepted for publication in JCAP. V3: Typos correcte

Dynamic energy system modeling using hybrid physics-based and machine learning encoder–decoder models

Three model configurations are presented for multi-step time series predictions of the heat absorbed by the water and steam in a thermal power plant. The models predict over horizons of 2, 4, and 6 steps into the future, where each step is a 5-minute increment. The evaluated models are a pure machine learning model, a novel hybrid machine learning and physics-based model, and the hybrid model with an incomplete dataset. The hybrid model deconstructs the machine learning into individual boiler heat absorption units: economizer, water wall, superheater, and reheater. Each configuration uses a gated recurrent unit (GRU) or a GRU-based encoder–decoder as the deep learning architecture. Mean squared error is used to evaluate the models compared to target values. The encoder–decoder architecture is over 11% more accurate than the GRU only models. The hybrid model with the incomplete dataset highlights the importance of the manipulated variables to the system. The hybrid model, compared to the pure machine learning model, is over 10% more accurate on average over 20 iterations of each model. Automatic differentiation is applied to the hybrid model to perform a local sensitivity analysis to identify the most impactful of the 72 manipulated variables on the heat absorbed in the boiler. The models and sensitivity analyses are used in a discussion about optimizing the thermal power plant

Anomalous AMS radiocarbon ages for foraminifera from high-deposition-rate ocean sediments

Radiocarbon ages on handpicked foraminifera from deep-sea cores are revealing that areas of rapid sediment accumulation are in some cases subject to hiatuses, reworking and perhaps secondary calcite deposition. We present here an extreme example of the impacts of such disturbances. The message is that if precise chronologies or meaningful benthic planktic age differences are to be obtained, then it is essential to document the reliability of radiocarbon ages by making both comparisons between coexisting species of planktomc foraminifera and detailed down-core sequences of measurements

Corona discharge experiments in admixtures of N2 and CH4: a laboratory simulation of Titan's atmosphere

A positive corona discharge fed by a N2:CH4 mixture (98:2) at atmospheric pressure and ambient temperature has been studied as a laboratory mimic of the chemical processes occurring in the atmosphere of Titan, Saturn's largest moon. In-situ measurements of UV and IR transmission spectra within the discharge have shown that the main chemical product is C2H2, produced by dissociation of CH4, with small but significant traces of ethane and HCN, all species that have been detected in Titan's atmosphere. A small amount (0.2 %) CH4 was decomposed after 12 minutes of treatment requiring an average energy of 2.7 kWh/g. After 14 minutes the discharge was terminated due to the formation of a solid yellow deposit on the central wire electrode. Such a deposit is similar to that observed in other discharges and is believed to be an analogue of the aerosol and dust observed in Titan's atmosphere and is composed of chemcial species commonly knonw as 'tholins'. We have also explored the electrical properties of the discharge. The admixture of methane into nitrogen caused an increase in onset voltage of the discharge and consequently led to a reduction in the measured discharge current

Temperature-dependent resistance of a finite one-dimensional Josephson junction array

We study theoretically the temperature and array-length dependences of the resistance of a finite one-dimensional array of Josephson junctions. We use both analytic approximations and numerical simulations, and conclude that within the self-charging model, all finite arrays are resistive in the low-temperature limit. A heuristic analysis shows qualitative agreement with resistance obtained from Monte Carlo simulations, establishing a connection between resistance and the occurrence of vortices in the corresponding 1 +1D XY-model. We compare our results with recent experiments and conclude that while the self-charging model reproduces some of the experimental observations, it underestimates the superconducting tendencies in the experimental structures

Enhanced turbulence driven by mesoscale motions and flow-topography interaction in the Denmark Strait Overflow plume

The Denmark Strait Overflow (DSO) contributes roughly half to the total volume transport of the Nordic overflows. The overflow increases its volume by entraining ambient water as it descends into the subpolar North Atlantic, feeding into the deep branch of the Atlantic Meridional Overturning Circulation. In June 2012, a multiplatform experiment was carried out in the DSO plume on the continental slope off Greenland (180 km downstream of the sill in Denmark Strait), to observe the variability associated with the entrainment of ambient waters into the DSO plume. In this study, we report on two high-dissipation events captured by an autonomous underwater vehicle (AUV) by horizontal profiling in the interfacial layer between the DSO plume and the ambient water. Strong dissipation of turbulent kinetic energy of O( math formula) W kg−1 was associated with enhanced small-scale temperature variance at wavelengths between 0.05 and 500 m as deduced from a fast-response thermistor. Isotherm displacement slope spectra reveal a wave number-dependence characteristic of turbulence in the inertial-convective subrange ( math formula) at wavelengths between 0.14 and 100 m. The first event captured by the AUV was transient, and occurred near the edge of a bottom-intensified energetic eddy. Our observations imply that both horizontal advection of warm water and vertical mixing of it into the plume are eddy-driven and go hand in hand in entraining ambient water into the DSO plume. The second event was found to be a stationary feature on the upstream side of a topographic elevation located in the plume pathway. Flow-topography interaction is suggested to drive the intense mixing at this site

A computational analysis of the long-term regulation of arterial pressure

The asserted dominant role of the kidneys in the chronic regulation of blood pressure and in the etiology of hypertension has been debated since the 1970s. At the center of the theory is the observation that the acute relationships between arterial pressure and urine production—the acute pressure-diuresis and pressure-natriuresis curves—physiologically adapt to perturbations in pressure and/or changes in the rate of salt and volume intake. These adaptations, modulated by various interacting neurohumoral mechanisms, result in chronic relationships between water and salt excretion and pressure that are much steeper than the acute relationships. While the view that renal function is the dominant controller of arterial pressure has been supported by computer models of the cardiovascular system known as the “Guyton-Coleman model”, no unambiguous description of a computer model capturing chronic adaptation of acute renal function in blood pressure control has been presented. Here, such a model is developed with the goals of: 1. representing the relevant mechanisms in an identifiable mathematical model; 2. identifying model parameters using appropriate data; 3. validating model predictions in comparison to data; and 4. probing hypotheses regarding the long-term control of arterial pressure and the etiology of primary hypertension. The developed model reveals: long-term control of arterial blood pressure is primarily through the baroreflex arc and the renin-angiotensin system; and arterial stiffening provides a sufficient explanation for the etiology of primary hypertension associated with ageing. Furthermore, the model provides the first consistent explanation of the physiological response to chronic stimulation of the baroreflex