Alternating sums of binomial coefficients with unit fraction arithmetic sequence coefficients

Expressions for finite sums involving the binomial coefficients with unit fraction coefficients whose denominators form an arithmetic sequence are determined.

Critical slip and time dependence in sea ice friction

Recent research into sea ice friction has focussed on ways to provide a model which maintains much of the clarity and simplicity of Amonton's law, yet also accounts for memory effects. One promising avenue of research has been to adapt the rate- and state- dependent models which are prevalent in rock friction. In such models it is assumed that there is some fixed critical slip displacement, which is effectively a measure of the displacement over which memory effects might be considered important. Here we show experimentally that a fixed critical slip displacement is not a valid assumption in ice friction, whereas a constant critical slip time appears to hold across a range of parameters and scales. As a simple rule of thumb, memory effects persist to a significant level for 10 s. We then discuss the implications of this finding for modelling sea ice friction and for our understanding of friction in general.

A rate and state friction law for saline ice

Sea ice friction models are necessary to predict the nature of interactions between sea ice floes. These interactions are of interest on a range of scales, for example, to predict loads on engineering structures in icy waters or to understand the basin-scale motion of sea ice. Many models use Amonton's friction law due to its simplicity. More advanced models allow for hydrodynamic lubrication and refreezing of asperities; however, modeling these processes leads to greatly increased complexity. In this paper we propose, by analogy with rock physics, that a rate- and state-dependent friction law allows us to incorporate memory (and thus the effects of lubrication and bonding) into ice friction models without a great increase in complexity. We support this proposal with experimental data on both the laboratory (∼0.1 m) and ice tank (∼1 m) scale. These experiments show that the effects of static contact under normal load can be incorporated into a friction model. We find the parameters for a first-order rate and state model to be A = 0.310, B = 0.382, and μ0 = 0.872. Such a model then allows us to make predictions about the nature of memory effects in moving ice-ice contacts.

Ice internal friction: Standard theoretical perspectives on friction codified, adapted for the unusual rheology of ice, and unified

Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials. We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.

A multithickness sea ice model accounting for sliding friction

A multithickness sea ice model explicitly accounting for the ridging and sliding friction contributions to sea ice stress is developed. Both ridging and sliding contributions depend on the deformation type through functions adopted from the Ukita and Moritz kinematic model of floe interaction. In contrast to most previous work, the ice strength of a uniform ice sheet of constant ice thickness is taken to be proportional to the ice thickness raised to the 3/2 power, as is revealed in discrete element simulations by Hopkins. The new multithickness sea ice model for sea ice stress has been implemented into the Los Alamos “CICE” sea ice model code and is shown to improve agreement between model predictions and observed spatial distribution of sea ice thickness in the Arctic.

Sensitivity of a hydraulic model to changes in channel erosion during extreme flooding

Recent research into flood modelling has primarily concentrated on the simulation of inundation flow without considering the influences of channel morphology. River channels are often represented by a simplified geometry that is implicitly assumed to remain unchanged during flood simulations. However, field evidence demonstrates that significant morphological changes can occur during floods to mobilise the boundary sediments. Despite this, the effect of channel morphology on model results has been largely unexplored. To address this issue, the impact of channel cross-section geometry and channel long-profile variability on flood dynamics is examined using an ensemble of a 1D-2D hydraulic model (LISFLOOD-FP) of the 1:2102 year recurrence interval floods in Cockermouth, UK, within an uncertainty framework. A series of hypothetical scenarios of channel morphology were constructed based on a simple velocity based model of critical entrainment. A Monte-Carlo simulation framework was used to quantify the effects of channel morphology together with variations in the channel and floodplain roughness coefficients, grain size characteristics, and critical shear stress on measures of flood inundation. The results showed that the bed elevation modifications generated by the simplistic equations reflected a good approximation of the observed patterns of spatial erosion despite its overestimation of erosion depths. The effect of uncertainty on channel long-profile variability only affected the local flood dynamics and did not significantly affect the friction sensitivity and flood inundation mapping. The results imply that hydraulic models generally do not need to account for within event morphodynamic changes of the type and magnitude modelled, as these have a negligible impact that is smaller than other uncertainties, e.g. boundary conditions. Instead morphodynamic change needs to happen over a series of events to become large enough to change the hydrodynamics of floods in supply limited gravel-bed rivers like the one used in this research.

Friction in mid-latitude cyclones: an Ekman-PV mechanism

The mechanism by which the atmospheric boundary layer reduces the intensity of mid-latitude cyclones is investigated. It is demonstrated that two alternative theories, Ekman pumping and the baroclinic potential vorticity (PV) mechanism, in fact act in union to maximize the spin-down. Ekman pumping aids the ventilation of PV from the boundary layer, and shapes the resulting PV anomaly into one of increased static stability. PV inversion techniques are used to demonstrate how this anomaly reduces the coupling between the upper- and lower-levels within the cyclone, reducing the growth rate.

Determination of the embedded thermo-optical expansion coefficients of PbTe and ZnSe thin film infrared multilayers

This paper reports the first derived thermo-optical properties for vacuum deposited infrared thin films embedded in multilayers. These properties were extracted from the temperature-dependence of manufactured narrow bandpass filters across the 4-17 µm mid-infrared wavelength region. Using a repository of spaceflight multi-cavity bandpass filters, the thermo-optical expansion coefficients of PbTe and ZnSe were determined across an elevated temperature range 20-160 ºC. Embedded ZnSe films showed thermo-optical properties similar to reported bulk values, whilst the embedded PbTe films of lower optical density, deviate from reference literature sources. Detailed knowledge of derived coefficients is essential to the multilayer design of temperature-invariant narrow bandpass filters for use in non-cooled infrared detection systems. We further present manufacture of the first reported temperature-invariant multi-cavity narrow bandpass filter utilizing PbS chalcogenide layer material.

Intensities and self-broadening coefficients of the strongest water vapour lines in the 2.7 and 6.25μm absorption bands

Intensities and self-broadening coefficients are presented for about 460 of the strongest water vapour lines in the spectral regions 1400–1840 cm−1 and 3440–3970 cm−1 at room temperature, obtained from rather unique measurements using a 5-mm-path-length cell. The retrieved spectral line parameters are compared with those in the HITRAN database ver. 2008 and 2012 and with recent ab-initio calculations. Both the retrieved intensities and half-widths are on average in reasonable agreement with those in HITRAN-2012. Maximum systematic differences do not exceed 4% for intensities (1600 cm−1 band) and 7% for self-broadening coefficients (3600 cm−1 band). For many lines however significant disagreements were detected with the HITRAN-2012 data, exceeding the average uncertainty of the retrieval. In addition, water vapour line parameters for 5300 cm−1 (1.9 μm) band reported by us in 2005 were also compared with HITRAN-2012, and show average differences of 4–5% for both intensities and half-widths.