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We extend the vorticity-based modelling approach of Borden & Meiburg (Phys. Fluids, vol. 25 (10), 2013, 101301) to non-Boussinesq gravity currents and derive an analytical expression for the Froude number without the need for an energy closure or any assumptions about the pressure. The Froude-number expression we obtain reduces to the correct form in the Boussinesq limit and agrees closely with simulation data. Via detailed comparisons with simulation results, we furthermore assess the validity of three key assumptions underlying both our as well as earlier models: (i) steady-state flow in the moving reference frame; (ii) inviscid flow; and (iii) horizontal flow sufficiently far in front of and behind the current. The current approach does not require an assumption of zero velocity in the current.

AbstractWe investigate the bulldozing motion of a granular sandpile driven forwards by a vertical plate. The problem is set up in the laboratory by emplacing the pile on a table rotating underneath a stationary plate; the continual circulation of the bulldozed material allows the dynamics to be explored over relatively long times, and the variation of the velocity with radius permits one to explore the dependence on bulldozing speed within a single experiment. We measure the time-dependent surface shape of the dune for a range of rotation rates, initial volumes and radial positions, for four granular materials, ranging from glass spheres to irregularly shaped sand. The evolution of the dune can be separated into two phases: a rapid initial adjustment to a state of quasi-steady avalanching perpendicular to the blade, followed by a much slower phase of lateral spreading and radial migration. The quasi-steady avalanching sets up a well-defined perpendicular profile with a nearly constant slope. This profile can be scaled by the depth against the bulldozer to collapse data from different times, radial positions and experiments onto common ‘master curves’ that are characteristic of the granular material and depend on the local Froude number. The lateral profile of the dune along the face of the bulldozer varies more gradually with radial position, and evolves by slow lateral spreading. The spreading is asymmetrical, with the inward progress of the dune eventually arrested and its bulk migrating to larger radii. A one-dimensional depth-averaged model recovers the nearly linear perpendicular profile of the dune, but does not capture the finer nonlinear details of the master curves. A two-dimensional version of the model leads to an advection–diffusion equation that reproduces the lateral spreading and radial migration. Simulations using the discrete element method reproduce in more quantitative detail many of the experimental findings and furnish further insight into the flow dynamics.

The local redistribution of granular material by sublimation of the southern seasonal [Formula: see text] ice deposit is one of the most active surface shaping processes on Mars today. This unique geomorphic mechanism is hypothesised to be the cause of the dendritic, branching, spider-like araneiform terrain and associated fans and spots-features which are native to Mars and have no Earth analogues. However, there is a paucity of empirical data to test the validity of this hypothesis. Additionally, it is unclear whether some araneiform patterns began as radial and then grew outward, or whether troughs connected at mutual centres over time. Here we present the results of a suite of laboratory experiments undertaken to investigate if the interaction between a sublimating [Formula: see text] ice overburden containing central vents and a porous, mobile regolith will mobilise grains from beneath the ice in the form of a plume to generate araneiform patterns. We quantify the branching and area of the dendritic features that form. We provide the first observations of plume activity via [Formula: see text] sublimation and consequent erosion to form araneiform features. We show that [Formula: see text] sublimation can be a highly efficient agent of sediment transport under present day Martian atmospheric pressure and that morphometry is governed by the Shields parameter.

Understanding the initial and flow conditions of contemporary flows in Martian gullies, generally believed to be triggered and fluidized by CO 2 sublimation, is crucial for deciphering climate conditions needed to trigger and sustain them. We employ the RAMMS (RApid Mass Movement Simulation) debris flow and avalanche model to back calculate initial and flow conditions of recent flows in three gullies in Hale crater. We infer minimum release depths of 1.0-1.5 m and initial release volumes of 100-200 m 3 . Entrainment leads to final flow volumes that are ∼2.5-5.5 times larger than initially released, and entrainment is found necessary to match the observed flow deposits. Simulated mean cross-channel flow velocities decrease from 3-4 m/s to ∼1 m/s from release area to flow terminus, while flow depths generally decrease from 0.5-1 to 0.1-0.2 m. The mean cross-channel erosion depth and deposition thicknesses are ∼0.1-0.3 m. Back-calculated dry-Coulomb friction ranges from 0.1 to 0.25 and viscous-turbulent friction between 100 and 200 m/s 2 , which are values similar to those of granular debris flows on Earth. These results suggest that recent flows in gullies are fluidized to a similar degree as are granular debris flows on Earth. Using a novel model for mass flow fluidization by CO 2 sublimation we are able to show that under Martian atmospheric conditions very small volumetric fractions of CO 2 of ≪1% within mass flows may indeed yield sufficiently large gas fluxes to cause fluidization and enhance flow mobility., (©2019. The Authors.)

Carbon dioxide is Mars' primary atmospheric constituent and is an active driver of Martian surface evolution. CO 2 ice sublimation mechanisms have been proposed for a host of features that form in the contemporary Martian climate. However, there has been very little experimental work or quantitative modelling to test the validity of these hypotheses. Here we present the results of the first laboratory experiments undertaken to investigate if the interaction between sublimating CO 2 ice blocks and a warm, porous, mobile regolith can generate features similar in morphology to those forming on Martian dunes today. We find that CO 2 sublimation can mobilise grains to form (i) pits and (ii) furrows. We have documented new detached pits at the termini of linear gullies on Martian dunes. Based on their geomorphic similarity to the features observed in our laboratory experiments, and on scaling arguments, we propose a new hypothesis that detached pits are formed by the impact of granular jets generated by sublimating CO 2 . We also study the erosion patterns formed underneath a sublimating block of CO 2 ice and demonstrate that these resemble furrow patterns on Mars, suggesting similar formation mechanisms.

Accurately predicting future tropical cyclone risk requires understanding the fundamental controls on tropical cyclone dynamics. Here we present an annually-resolved 450-year reconstruction of western Caribbean tropical cyclone activity developed using a new coupled carbon and oxygen isotope ratio technique in an exceptionally well-dated stalagmite from Belize. Western Caribbean tropical cyclone activity peaked at 1650 A.D., coincident with maximum Little Ice Age cooling, and decreased gradually until the end of the record in 1983. Considered with other reconstructions, the new record suggests that the mean track of Cape Verde tropical cyclones shifted gradually north-eastward from the western Caribbean toward the North American east coast over the last 450 years. Since ~1870 A.D., these shifts were largely driven by anthropogenic greenhouse gas and sulphate aerosol emissions. Our results strongly suggest that future emission scenarios will result in more frequent tropical cyclone impacts on the financial and population centres of the northeastern United States.

Flows of hard granular materials depend strongly on the interparticle friction coefficient μ_{p} and on the inertial number I, which characterizes proximity to the jamming transition where flow stops. Guided by numerical simulations, we derive the phase diagram of dense inertial flow of spherical particles, finding three regimes for 10^{-4}≲I≲10^{-1}: frictionless, frictional sliding, and rolling. These are distinguished by the dominant means of energy dissipation, changing from collisional to sliding friction, and back to collisional, as μ_{p} increases from zero at constant I. The three regimes differ in their kinetics and rheology; in particular, the velocity fluctuations and the stress ratio both display nonmonotonic behavior with μ_{p}, corresponding to transitions between the three regimes of flow. We rationalize the phase boundaries between these regimes, show that energy balance yields scaling relations between microscopic properties in each of them, and derive the strain scale at which particles lose memory of their velocity. For the frictional sliding regime most relevant experimentally, we find for I≥10^{-2.5} that the growth of the macroscopic friction μ(I) with I is induced by an increase of collisional dissipation. This implies in that range that μ(I)-μ(0)∼I^{1-2b}, where b≈0.2 is an exponent that characterizes both the dimensionless velocity fluctuations L∼I^{-b} and the density of sliding contacts χ∼I^{b}.

The mechanisms responsible for millennial scale climate change within glacial time intervals are equivocal. Here we show that all eight known radiometrically-dated Tambora-sized or larger NH eruptions over the interval 30 to 80 ka BP are associated with abrupt Greenland cooling (>95% confidence). Additionally, previous research reported a strong statistical correlation between the timing of Southern Hemisphere volcanism and Dansgaard-Oeschger (DO) events (>99% confidence), but did not identify a causative mechanism. Volcanic aerosol-induced asymmetrical hemispheric cooling over the last few hundred years restructured atmospheric circulation in a similar fashion as that associated with Last Glacial millennial-scale shifts (albeit on a smaller scale). We hypothesise that following both recent and Last Glacial NH eruptions, volcanogenic sulphate injections into the stratosphere cooled the NH preferentially, inducing a hemispheric temperature asymmetry that shifted atmospheric circulation cells southward. This resulted in Greenland cooling, Antarctic warming, and a southward shifted ITCZ. However, during the Last Glacial, the initial eruption-induced climate response was prolonged by NH glacier and sea ice expansion, increased NH albedo, AMOC weakening, more NH cooling, and a consequent positive feedback. Conversely, preferential SH cooling following large SH eruptions shifted atmospheric circulation to the north, resulting in the characteristic features of DO events.

We studied the drag and lift forces acting on an inclined plate while it is dragged on the surface of a granular media, both in experiment and in numerical simulation. In particular, we investigated the influence of the horizontal velocity of the plate and its angle of attack. We show that a steady wedge of grains is moved in front of the plow and that the lift and drag forces are proportional to the weight of this wedge. These constants of proportionality vary with the angle of attack but not (or only weakly) on the velocity. We found a universal effective friction law that accounts for the dependence on all the above-mentioned parameters. The stress and velocity fields are calculated from the numerical simulations and show the existence of a shear band under the wedge and that the pressure is nonhydrostatic. The strongest gradients in stress and shear occur at the base of the plow where the dissipation rate is therefore highest.

Many processes in geophysical and industrial settings involve the flow of granular materials down a slope. In order to investigate the granular dynamics, we report a series of laboratory experiments conducted by releasing grains at a steady rate from a localized source on a rough inclined plane. Different types of dense granular flow are observed by varying the flow rate at the source and the slope of the inclined plane. The two cases of steady flow confined by levees and the flow of avalanches down the plane are examined. The width of the steady flow increases linearly with the prescribed flow rate, which does not appreciably affect the characteristic depth or surface velocity of the bulk flow. When the flow rate is just below that required for sustaining the steady flow, avalanches are triggered at regular intervals. The avalanches maintain their shape, size, and speed down the inclined plane. We propose a simple model of steady flow that is consistent with our observations and discuss the challenges associated with the theoretical treatment of avalanche dynamics.

Background: Inhibitors of the kinase mTOR, such as rapamycin and everolimus, have been used as cancer therapeutics with limited success since some tumours are resistant. Efforts to establish predictive markers to allow selection of patients with tumours likely to respond have centred on determining phosphorylation states of mTOR or its targets 4E-BP1 and S6K in cancer cells. In an alternative approach we estimated eIF4E activity, a key effector of mTOR function, and tested the hypothesis that eIF4E activity predicts sensitivity to mTOR inhibition in cell lines and in breast tumours., Results: We found a greater than three fold difference in sensitivity of representative colon, lung and breast cell lines to rapamycin. Using an assay to quantify influences of eIF4E on the translational efficiency specified by structured 5'UTRs, we showed that this estimate of eIF4E activity was a significant predictor of rapamycin sensitivity, with higher eIF4E activities indicative of enhanced sensitivity. Surprisingly, non-transformed cell lines were not less sensitive to rapamycin and did not have lower eIF4E activities than cancer lines, suggesting the mTOR/4E-BP1/eIF4E axis is deregulated in these non-transformed cells. In the context of clinical breast cancers, we estimated eIF4E activity by analysing expression of eIF4E and its functional regulators within tumour cells and combining these scores to reflect inhibitory and activating influences on eIF4E. Estimates of eIF4E activity in cancer biopsies taken at diagnosis did not predict sensitivity to 11-14 days of pre-operative everolimus treatment, as assessed by change in tumour cell proliferation from diagnosis to surgical excision. However, higher pre-treatment eIF4E activity was significantly associated with dramatic post-treatment changes in expression of eIF4E and 4E-binding proteins, suggesting that eIF4E is further deregulated in these tumours in response to mTOR inhibition., Conclusions: Estimates of eIF4E activity predict sensitivity to mTOR inhibition in cell lines but breast tumours with high estimated eIF4E activity gain changes in eIF4E regulation in order to enhance resistance.

Dense granular flows are often unstable and form inhomogeneous structures. Although significant advances have been recently made in understanding simple flows, instabilities of such flows are often not understood. We present experimental and numerical results that show the formation of longitudinal stripes that arise from instability of the uniform flowing state of granular media on a rough inclined plane. The form of the stripes depends critically on the mean density of the flow with a robust form of stripes at high density that consists of fast sliding pluglike regions (stripes) on top of highly agitated boiling material--a configuration reminiscent of the Leidenfrost effect when a droplet of liquid lifted by its vapor is hovering above a hot surface.

Granular surfaces subjected to forces due to rolling wheels develop ripples above a critical speed. The resulting pattern, known as washboard or corrugated road, is common on dry unpaved roads. We investigated this phenomenon theoretically and experimentally using laboratory-scale apparatus and beds of dry sand. A thick layer of sand on a circular track was forced by a rolling wheel on an arm whose weight and moment of inertia could be varied. We compared the ripples made by the rolling wheel to those made using a simple inclined plow blade. We investigated the dependence of the critical speed on various parameters and described a scaling argument that leads to a dimensionless ratio, analogous to the hydrodynamic Froude number, which controls the instability. This represents the crossover between conservative dynamic forces and dissipative static forces. Above onset wheel-driven ripples move in the direction of motion of the wheel, but plow-driven ripples move in the reverse direction for a narrow range of Froude numbers.

Increased eukaryotic translation initiation factor 4E (eIF4E) expression occurs in many cancers, and makes fundamental contributions to carcinogenesis by stimulating the expression of cancer-related genes at post-transcriptional levels. This key role is highlighted by the facts that eIF4E levels can predict prognosis, and that eIF4E is an established therapeutic target. However, eIF4E activity is a complex function of expression levels and phosphorylation statuses of eIF4E and eIF4E-binding proteins (4E-BPs). Our hypothesis was that the combined analyses of these pathway components would allow insights into eIF4E activity and its influence on cancer. We have determined expression levels of eIF4E, 4E-BP1, 4E-BP2 and phosphorylated 4E-BP1 within 424 breast tumours, and have carried out analyses to combine these and relate the product to patient survival, in order to estimate eIF4E activity. We show that this analysis gives greater prognostic insights than that of eIF4E alone. We show that eIF4E and 4E-BP expression are positively associated, and that 4E-BP2 has a stronger influence on cancer behaviour than 4E-BP1. Finally, we examine eIF4E, estimated eIF4E activity, and phosphorylated 4E-BP1 as potential predictive biomarkers for eIF4E-targeted therapies, and show that each determines selection of different patient groups. We conclude that eIF4E's influence on cancer survival is modulated substantially by 4E-BPs, and that combined pathway analyses can estimate functional eIF4E.

We report laboratory experiments on rippled granular surfaces formed under rolling wheels. Ripples appear above a critical speed and drift slowly in the driving direction. Ripples coarsen as they saturate and exhibit ripple creation and destruction events. All of these effects are captured qualitatively by 2D soft-particle simulations in which a disk rolls over smaller disks in a periodic box. The simulations show that compaction and segregation are inessential to the ripple phenomenon. We describe a simplified scaling model which gives some insight into the mechanism of the instability.

The onset and dynamics of flow in shallow horizontally oscillating granular layers are studied as a function of the depth of the layer and imposed acceleration. Measurements of the flow velocity made from the top and side are presented in the frame of reference of the container. As is also found for avalanches of inclined layers, the thresholds for starting and stopping of flow are slightly different. The variation with depth of the starting acceleration Gamma{start} for the oscillating layer is similar to the corresponding variation of the tangent of the starting angle tan(theta{start}) for avalanches in the same container at low frequencies, but deviates as the frequency is increased. However, the threshold behavior depends significantly on the measurement protocol. Just above Gamma{start} , the motion decays with time as the material reorganizes over a minute or so, causing the apparent threshold to increase. Furthermore, the rms velocity as a function of acceleration rises more sharply above the starting threshold if the first minute or so of excitation is discarded. Once excited, the rheology of the material is found to vary in time during the cycle in surprising ways. If the maximum inertial force (proportional to the container acceleration amplitude) is slightly higher than that required to produce flow, the flow velocity grows as soon as the inertial force exceeds zero in each cycle, but jamming occurs long before the inertial force returns to zero. At higher Gamma , the motion is fluidlike over the entire cycle. However, the fraction of the cycle during which the layer is mobile is typically far higher than what one would predict from static considerations or the behavior of the inclined layer. Finally, we consider the flow profiles as a function of both the transverse distance across the cell at the free surface and also as a function of the vertical coordinate in the boundary layer near the sidewall. These profiles have time-dependent shapes and are therefore significantly different from profiles previously measured for avalanche flows.

Secondary structures within the 5' untranslated regions of messenger RNAs can have profound effects on the efficiency of translation of their messages and thereby on gene expression. Consequently they can act as important regulatory motifs in both physiological and pathological settings. Current approaches to predicting the secondary structure of these RNA sequences find the structure with the global-minimum free energy. However, since RNA folds progressively from the 5' end when synthesised or released from the translational machinery, this may not be the most probable structure. We discuss secondary structure prediction based on local-minimisation of free energy with thermodynamic fluctuations as nucleotides are added to the 3' end and show that these can result in different secondary structures. We also discuss approaches for studying the extent of the translational inhibition specified by structures within the 5' untranslated region.

The structure of gravity currents and plumes, in an unbounded ambient, on a slope of arbitrary angle is analysed. Inviscid, rotational flow solutions in a wedge are used to study the flow near the front of a current, and used to show that the Froude number is radical2 and the angle of the front to the slope is 60 degrees. This extends the result of von Kármán (1940) to arbitrary slope angles and large internal current velocities. The predictions of the theory are briefly compared with experiments and used to explain the large negative (relative to ambient) pressures involved in avalanches.