Gravity driven geophysical mass flows often consist of a heterogeneous fluid-solid mixture. The complex interplay between the components leads to phenomena such as lateral levee formation in avalanches, or a granular front and an excess fluid pore pressure in debris flows. These effects are very important for predicting runout and the forces on structures, yet they are only partially represented in simplified shallow flow theories, since rearrangement of the mixture composition perpendicular to the main flow direction is neglected. In realistic flows however, rheological properties and effective basal drag may depend strongly on the relative concentration of the components. We address this problem and present a depth-averaged model for shallow mixtures that explicitly allows for rearrangement in this direction. In particular we consider a fluid-solid mixture that experiences bulk horizontal motion, as well as internal sedimentation and resuspension of the particles, and therefore resembles the case of a debris flow. Starting from general mixture theory we derive bulk balance laws and an evolution equation for the particle concentration. Depth-integration yields a shallow mixture flow model in terms of bulk mass, depth-averaged particle concentration, the particle's vertical centre of mass and the depth-averaged velocity. This new equation in this model for the particle's vertical centre of mass is derived by taking the first moment, with respect to the vertical coordinate, of particle's mass conservation equation. Our approach does not make the Boussinesq approximation and results in additional terms coupling the momentum flux to the vertical centre of mass. The system is hyperbolic and reduces to the shallow water equations in the homogeneous limit of a pure fluid or perfect mixing. We highlight the effects of sedimentation on resuspension and finally present a simple friction feedback which qualitatively resembles a large-scale experimental debris flow data set acquired at the Illgraben, Switzerland.
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Laboratory experiments have shown that the steady flow of granular material down a rough inclined plane has a surface that is not parallel to the plane, but has a cur- vature across the slope with the height increasing toward the middle of the flow. We study this observation by postulating a new granular rheology, similar to that of a second order fluid. This model is applied to the experiments using a shal- low water approximation, given that the depth of the flow is much smaller than the width. The model predicts that a sec- ond normal stress difference allows cross-slope height vari- ations to develop in regions with considerable cross-slope velocity shear, consistent with the experiments. The model also predicts the development of lateral eddies, which are yet to be observed.
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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 which is consistent with our observations and discuss the challenges associated with the theoretical treatment of avalanche dynamics.
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Experiments are conducted to study the planing and skipping of a rectangular paddle on the surface of a shallow stream. The paddle is allowed to move freely up and down by attaching it to a pivoted arm. A steady planing state, in which the lift force from the water balances the weight on the paddle, is found to be stable for small stream velocities but to become unstable above a certain threshold velocity which depends upon the weight and the angle of attack. Above this threshold, the paddle oscillates in the water and can take off into a continual bouncing, or skipping, motion, with a well-defined amplitude and frequency. The transition is sometimes bistable so that both a steady planing state and a regular skipping state are possible for the same experimental parameters. Shallow-water theory is used to construct simple models that explain the qualitative features of the planing and skipping states in the experiments. It is found that a simple parameterisation of the lift force on the paddle proportional to the depth of entry is not sufficient to explain the observations, and it is concluded that the rise of water ahead of the paddle, in particular the way this varies over time, is responsible for causing the planing state to become unstable and for enabling a continual skipping state.
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abstract
The snow surface height was precisely measured, with a laser scanner, before and after the passage of two dry-mixed avalanches in Vallée de la Sionne during the winter of 2005-2006. The measurements were used to calculate the depth of the deposited snow along each entire avalanche path with a height resolution of 100 mm and a horizontal resolution of 500 mm. These data are much more accurate than any previous measurements from large avalanches and show that the deposit depth is strongly negatively correlated with the slope angle. That is, on steep slopes the deposit is shallow, and on gentle slopes the deposit is deep. The time evolution of the snow depth, showing the initial erosion and final deposition as the avalanche passed, was also observed at one position using a frequency-modulated continuous wave radar. Measurements at a nearby position gave flow speed profiles and showed that the avalanche tail consists of a steady state subcritical flow that lasts for about 100 s. Eventually, the tail slowly decelerates as the depth slightly decreases, and then it comes to rest. We show that the dependency between the slope angle and the deposition depth can be explained by both a cohesive friction model and the Pouliquen hstop model.
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We present, analyse and discuss air pressure data from finite-volume chute flows of dry, fine snow in air. These experiments have the correct similarity criteria to model powder snow avalanches and they demonstrate transition from a dense to a suspended flow. We measured the dynamic air pressure at the flows' base, which features a marked negative pressure peak immediately behind the front. This feature is also seen in observations of natural powder snow avalanches measured in Russia, Japan and Switzerland, in direct numerical simulations of non-Boussinesq suspension flows and in ping-pong ball avalanches. This is evidence for large internal motions and suggests that there is a coherent vortex in the avalanche front, which can result in impact pressures many times larger than expected from the mean flow velocity. We analyse the external air pressures using three models and show how a flow's geometry and velocity can be found from this single air pressure measurement. We also measured flow heights and speeds using image analysis and we show that the speed is roughly independent of the slope angle and scales as the 1/4 power of release size, as predicted by similarity analysis for pseudo two-dimensional flows.
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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 congfiguration reminiscent of the Leidenfrost effect when a droplet of liquid lifted by its vapor is hovering above a hot surface.
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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.
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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 eIF4Eâs influence on cancer survival is modulated substantially by 4E-BPs, and that combined pathway analyses can estimate functional eIF4E.
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Pyroclastic flows from volcanoes, dust storms in the desert, and submarine turbidity currents are all gravity currents of particles in suspension occurring in nature. Powder snow avalanches are one such flow where the density difference between the suspended particles and the interstitial air is high and the particles carry a significant proportion of the flow's momentum. This means that the Boussinesq approximation, where density differences are considered negligible in inertia terms, is not valid. Aspects of such flows, such as their internal structure and the transition from a dense flow to a suspension current are not well understood. Repeatable laboratory experiments are necessary for a better understanding of the underlying physics. Up to now, an experiment has not been designed with the correct similarity criteria for modeling powder snow avalanches. We have addressed this by designing and analyzing the results from a new experimental model of powder snow avalanches that had three distinctive features. Fine, dry snow was used to form suspension currents in air. The high density ratio of powder snow avalanches was preserved so that the currents are non-Boussinesq. Our experiments started with a dense current that then self-ignited, undergoing the transition to a suspension current. The shape and position of the current was tracked with two video cameras, and the air flow measured with a high-frequency response pressure transducer mounted in the base. We show how the air pressure data closely match theory and reveal whether a current is primarily dense or suspended.
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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.
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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 start for the oscillating layer is similar to the corresponding variation of the tangent of the starting angle tanstart 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 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 , 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.
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Powder snow avalanches are natural hazards which affect the way populations live in mountainous areas. Field measurements from avalanches remain one of the most significant and useful sources of information about their dynamics and behaviour. In this paper we consider all the video data from the Vall\'ee de la Sionne test site from the years 2003 to 2005. General scaling laws are sought for the avalanche front velocity based on plume theories. Avalanche Froude numbers are found, comparing three different length scales: the cube root of the fracture volume, the avalanche height and the depth of entrained snow cover. We discuss the difficulties in defining the volume of a powder snow avalanche. Should we include just the head or also the turbulent wake that extends back to the starting zone? This relates to whether we use a compact model for the avalanche, such as the KSB model \citep{Ancey04,TuMceAn06} or a plume model \citep{Turner73}. Observations are made regarding the lateral spreading behaviour of the avalanches. We show that the slow lateral spreading can be explained by large internal velocities and anisotropic turbulence generated by the large scale motion in the avalanche head.
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A simple theoretical model, the Kulikovskiy-Sveshnikova-Beghin (KSB) model, is outlined describing the motion of a particle cloud moving down an incline. This model includes both the entrainment of surrounding ambient fluid and the entrainment of particles from the slope and is equally valid for Boussinesq and non-Boussinesq flows. However, this model can predict physically impossible densities when there is significant particle entrainment. Modifications to the model are proposed which eliminate this problem by including the entrained snow volume. With the modified model, physically realistic mean densities are predicted which have a significant impact on the Richardson number-dependent ambient entrainment. The improvements are illustrated by comparing analytical solutions to the original and the modified KSB equations for the case of a particle cloud traveling on a slope of constant angle, with constant ambient fluid and particle entrainment. Solving the modified model numerically, predictions are compared with data from several large powder snow avalanches at the Swiss Vall\'ee de la Sionne avalanche test site. The modified KSB model appears to capture the dynamics of the avalanche front well, however problems remain with relating the theoretical geometry to a real avalanche geometry. The success of this model in capturing the front dynamics shows that, with careful assumptions that reflect the physics, it is possible to describe aspects of complex flows such as powder snow avalanches with simple models.
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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.
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Quantitative time-dependent laboratory measurements are made of the irreversible mixing caused by the development, saturation and turbulent breakdown of Kelvin-Helmholtz (KH) billows in an initially stable two-layer stratified shear flow of miscible fluids. The measurements are obtained using a light attenuation technique. Irreversible mixing is found to be strongly dependent on the life-cycle of the flow, in particular the characteristics of large-scale, quasi-two-dimensional billow merging events, which stir the flow and then trigger mixing during turbulent transition.
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Despite their clear danger to humans, snow avalanches are hard to document. They occur in inaccessible and dangerous locations, often at times of bad weather. Observation instruments frequently malfunction in the harsh conditions or are destroyed. Measurements of powder snow avalanches are particularly difficult, as these occur less frequently and are usually very large. To understand the air flow in front of and inside powder snow avalanches, we have designed an air pressure sensor to survive the harsh conditions. It consists of a differential pressure transducer, with a high-frequency response, built into a specially designed housing unit. We mounted this 10 m from the ground on a measurement mast in the Vallée de la Sionne avalanche test site in Switzerland. Data from five powder snow avalanches over the winter of 2004 were recorded. Three of these were natural releases, and two were artificially triggered with explosives. We present an analysis of the sensor response and an interpretation of the signals in terms of simple flow fields. We show how these data can be used to deduce information about the speed, size, and location of the avalanches using a dipole approximation. Our sensor has two major limitations: The length of the internal tubing produces low-frequency resonances, and there is only one transducer, so a complete flow model is needed to deduce the three velocity components and pressure. We discuss these limitations and give a design for a new sensor to overcome them.
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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 \sqrt{2} 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.
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The velocity profile and basal shear force were measured for snow flowing down a chute 34 m long and 2.5 m wide. The flows were approximately steady by the end of the chute where measurements were taken and the angle was 32 degrees. Measurements of the basal shear stress confirm approximate dynamic balance. The velocity profile was measured using opto-electronic sensors and showed a large slip velocity at the base, a shear layer of around 50 mm and an overlying plug-like flow of about 350 mm. The velocity profile is compatible with both a Herschel-Bulkley rheological model, which combines a constant critical stress with a power law dependence on the mean shear rate, and a Cross model where the effective viscosity varies between two limits. Estimates of the Reynolds number suggest that the flow is not turbulent. The measurements are used to estimate the distribution of energy dissipation and to show that its concentration near the base may locally melt the snow, and thus serve as an explanation for icy melt surfaces observed at the base of flowing avalanche tracks.
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Notes and suggestions on filming avalanches.
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In wind transport of snow horizontal momentum is extracted from the mean wind flow and transfered to the snow grains. Upon colliding with the surface the grains can bounce and eject further grains in a process known as splashing. How efficiently the horizontal momentum is converted to vertical momentum in the splash process is the determining factor for mass transport rates. This paper discusses wind tunnel experiments performed to calculate the splash function for snow particles. The data is used to develop a new splash function. Particular care is taken to include correlations in the data such as between ejection velocity and ejection angle. The new splash function includes these correlations and its parameters are related to physical properties of the bed and snow.
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Opto-electronic sensors using infrared LEDs and photo-transistors have been used for measuring velocities in snow avalanches for more than ten years in America, Europe and Japan. Though they have been extensively used, how they should be designed and how the data should be processed has received little discussion. This paper discusses how these sensors can be applied to measure two-dimensional velocities. The effects of acceleration and structure in the underlying field of reflectance are carefully accounted for. An algorithm is proposed for calculating the continuous velocity vector of an avalanche and a sketch of the mathematical analysis given. The paper concludes by suggesting design criteria for such sensors.
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Velocities inside avalanches have been calculated for many years by calculating the cross-correlation between opto-electronic sensors using a method pioneered by \inlinecite{nishimura87:internal} and \inlinecite{dent98:velocity}. Their approach has been widely adopted but there has been little discussion of the optimal design of such instruments and the best analysis techniques. This paper discuses some of the different sources of error that arise and how these can be mitigated. A statistical framework that describes such instruments is developed and used to quantify the errors.
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An algorithm for calculating the motion of avalanches from films based on changepoint determination is described. The method is designed for the detection of moving objects against a static background and works for partially transparent objects and objects with spatially and temporarily varying colour components. The method can be applied to mono-spectral or multi-spectral signals and works well even with low quality video pictures and uncontrolled illumination. The method is particularly suitable for tracking granular flows and other scientific experiments.
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This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections defined by the Schmidt decomposition by making projections at the earliest possible time. The algorithm unconditionally predicts the possible events in closed quantum systems and ascribes probabilities to these events. A simple random Hamiltonian model is described and the results of applying the algorithm to this model using computer programs are discussed and compared with approximate analytic calculations.
This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm uses a maximum information principle to select from among the consistent sets formed by projections defined by the Schmidt decomposition. The algorithm unconditionally predicts the possible events in closed quantum systems and ascribes probabilities to these events. A simple spin model is described and a complete classification of all exactly consistent sets of histories formed from Schmidt projections in the model is proved. This result is used to show that for this example the algorithm selects a physically realistic set. Other tentative suggestions in the literature for set selection algorithms using ideas from information theory are discussed.
The consistent histories formulation of the quantum theory of a closed system with pure initial state defines an infinite number of incompatible consistent sets, each of which gives a possible description of the physics. We investigate the possibility of using the properties of the Schmidt decomposition to define an algorithm which selects a single, physically natural, consistent set. We explain the problems which arise, set out some possible algorithms, and explain their properties with the aid of simple models. Though the discussion is framed in the language of the consistent histories approach, it is intended to highlight the difficulty in making any interpretation of quantum theory based on decoherence into a mathematically precise theory.
This dissertation investigates questions arising in the consistent histories formulation of the quantum mechanics of closed systems. Various criteria for approximate consistency are analysed. The connection between the Dowker-Halliwell criterion and sphere packing problems is shown and used to prove several new bounds on the violation of probability sum rules. The quantum Zeno effect is also analysed within the consistent histories formalism and used to demonstrate some of the difficulties involved in discussing approximate consistency. The complications associated with null histories and infinite sets are briefly discussed.
The possibility of using the properties of the Schmidt decomposition to define an algorithm which selects a single, physically natural, consistent set for pure initial density matrices is investigated. The problems that arise are explained, and different possible algorithms discussed. Their properties are analysed with the aid of simple models. A set of computer programs is described which apply the algorithms to more complicated examples.
Another algorithm is proposed that selects the consistent set (formed using Schmidt projections) with the highest Shannon information. This is applied to a simple model and shown to produce physically sensible histories. The theory is capable of unconditional probabilistic prediction for closed quantum systems, and is strong enough to be falsifiable. Ideas on applying the theory to more complicated examples are discussed.
The consistent histories formalism is discussed using path-projected states. These are used to analyse various criteria for approximate consistency. The connection between the Dowker-Halliwell criterion and sphere packing problems is shown and used to prove several new bounds on the violation of probability sum rules. The quantum Zeno effect is also analysed within the consistent histories formalism and used to demonstrate some of the difficulties involved in discussing approximate consistency. The complications associated with null histories and infinite sets are briefly discussed.
abstract
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