The velocity of probability transport in quantum mechanics

In his study of the 'time of arrival' problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.

Mass Transport Perspective on an Accelerated Exclusion Process: Analysis of Augmented Current and Unit-Velocity Phases

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size ℓ⩽ℓ_{max}. With various choices of the interaction range, ℓ_{max}, we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.

Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations

The modelling of diffusive terms in particle methods is a delicate matter and several models were proposed in the literature to take such terms into account. The diffusion velocity method (DVM), originally designed for the diffusion of passive scalars, turns diffusive terms into convective ones by expressing them as a divergence involving a so-called diffusion velocity. In this paper, DVM is extended to the diffusion of vectorial quantities in the three-dimensional Navier–Stokes equations, in their incompressible, velocity–vorticity formulation. The integration of a large eddy simulation (LES) turbulence model is investigated and a DVM general formulation is proposed. Either with or without LES, a novel expression of the diffusion velocity is derived, which makes it easier to approximate and which highlights the analogy with the original formulation for scalar transport. From this statement, DVM is then analysed in one dimension, both analytically and numerically on test cases to point out its good behaviour.

Circulation and suspended particulate matter transport in a tidally dominated estuary: caravelas estuary, Bahia, Brazil

The circulation and transport of suspended particulate matter in the Caravelas Estuary are assessed. Nearly-synoptic hourly hydrographic, current (ADCP velocity and volume transport) and suspended particulate matter data were collected during a full semidiurnal spring tide, on the two transects Boca do Tomba and Barra Velha and on longitudinal sections at low and high tide. On the first transect the peak ebb currents (-1.5 ms-1) were almost twice as strong as those of the wider and shallow Barra Velha inlet (-0.80 ms-1) and the peak flood currents were 0.75 and 0.60 ms-1, respectively. Due to the strong tidal currents both inlets had weak vertical salinity stratification and were classified with the Stratification-circulation Diagram as Type 2a (partially mixed-weakly stratified) and Type 1a (well mixed). Volume transports were very close, ranging from -3,500 to 3,100 m³s-1 at the ebb and flood, respectively, with a residual -630 m³s-1. The concentration of the suspended particulate matter was closely related to the tidal variation and decreased landwards from 50 mg.L-1 at the estuary mouth, to 10 mg.L-1 at distances of 9 and 16 km for the low and high tide experiments, respectively. The total residual SPM transport was out of the estuary at rates of -18 tons per tidal cycle.

Hydrodynamics and suspended sediment transport in the Camboriú estuary - Brazil: pre jetty conditions

Estuarine hydrodynamics is a key factor in the definition of the filtering capacity of an estuary and results from the interaction of the processes that control the inlet morphodynamics and those that are acting in the mixing of the water in the estuary. The hydrodynamics and suspended sediment transport in the Camboriú estuary were assessed by two field campaigns conducted in 1998 that covered both neap and spring tide conditions. The period measured represents the estuarine hydrodynamics and sediment transport prior to the construction of the jetty in 2003 and provides important background information for the Camboriú estuary. Each field campaign covered two complete tidal cycles with hourly measurements of currents, salinity, suspended sediment concentration and water level. Results show that the Camboriú estuary is partially mixed with the vertical structure varying as a function of the tidal range and tidal phase. The dynamic estuarine structure can be balanced between the stabilizing effects generated by the vertical density gradient, which produces buoyancy and stratification flows, and the turbulent effects generated by the vertical velocity gradient that generates vertical mixing. The main sediment source for the water column are the bottom sediments, periodically resuspended by the tidal currents. The advective salt and suspended sediment transport was different between neap and spring tides, being more complex at spring tide. The river discharge term was important under both tidal conditions. The tidal correlation term was also important, being dominant in the suspended sediment transport during the spring tide. The gravitational circulation and Stokes drift played a secondary role in the estuarine transport processes.

Reduction of chaotic particle transport driven by drift waves in sheared flows

Investigations of chaotic particle transport by drift waves propagating in the edge plasma of tokamaks with poloidal zonal flow are described. For large aspect ratio tokamaks, the influence of radial electric field profiles on convective cells and transport barriers, created by the nonlinear interaction between the poloidal flow and resonant waves, is investigated. For equilibria with edge shear flow, particle transport is seen to be reduced when the electric field shear is reversed. The transport reduction is attributed to the robust invariant tori that occur in nontwist Hamiltonian systems. This mechanism is proposed as an explanation for the transport reduction in Tokamak Chauffage Alfven Bresilien [R. M. O. Galvao , Plasma Phys. Controlled Fusion 43, 1181 (2001)] for discharges with a biased electrode at the plasma edge.

Shear stress and sediment transport calculations for swash zone modelling

It is shown that the observed difference in sediment transporting efficiency by the swash uprush, compared with the downrush, could be mainly due to greater bed shear stress for a given velocity in the more abruptly accelerated uprush. The bed shear stress generated by an arbitrary free stream velocity time series is modelled in terms of usual wave boundary layer models plus a phase lead (phi(tau) of the bed shear stress compared with the free stream velocity at the peak frequency. With this approach, the total transport amounts in uprush and downrush can be modelled satisfactorily with the same sediment transport formula, without the need for different uprush and downrush coefficients. While the adaptation of sediment transport formulae from steady flow can thus lead to the right total amounts of sediment moved by this method, the timing of the instantaneous sediment transport rates are probably not accurately modelled due to the highly unsteady nature of the swash and the presence of pre-suspended sediment in the uprush. Nevertheless, the proposed method is a useful intermediate step before we have a complete understanding of sediment transport under very rapid accelerations and of the relative contribution of pre-suspended sediment to the onshore sediment transport in swash zones. (C) 2002 Published by Elsevier Science B.V.

Shear stress and sediment transport calculations for sheet flow under waves

A simple method is provided for calculating transport rates of not too fine (d(50) greater than or equal to 0.20 mm) sand under sheet flow conditions. The method consists of a Meyer-Peter-type transport formula operating on a time-varying Shields parameter, which accounts for both acceleration-asymmetry and boundary layer streaming. While velocity moment formulae, e.g.., = Constant x calibrated against U-tube measurements, fail spectacularly under some real waves (Ribberink, J.S., Dohmen-Janssen, C.M., Hanes, D.M., McLean, S.R., Vincent, C., 2000. Near-bed sand transport mechanisms under waves. Proc. 27th Int. Conf. Coastal Engineering, Sydney, ASCE, New York, pp. 3263-3276, Fig. 12), the new method predicts the real wave observations equally well. The reason that the velocity moment formulae fail under these waves is partly the presence of boundary layer streaming and partly the saw-tooth asymmetry, i.e., the front of the waves being steeper than the back. Waves with saw-tooth asymmetry may generate a net landward sediment transport even if = 0, because of the more abrupt acceleration under the steep front. More abrupt accelerations are associated with thinner boundary layers and greater pressure gradients for a given velocity magnitude. The two real wave effects are incorporated in a model of the form Q(s)(t) = Q(s)[theta(t)] rather than Q(S)(t) = Q(S)[u(infinity)(t)], i.e., by expressing the transport rate in terms of an instantaneous Shields parameter rather than in terms of the free stream velocity, and accounting for both streaming and accelerations in the 0(t) calculations. The instantaneous friction velocities u(*)(t) and subsequently theta(t) are calculated as follows. Firstly, a linear filter incorporating the grain roughness friction factor f(2.5) and a phase angle phi(tau) is applied to u(infinity)(t). This delivers u(*)(t) which is used to calculate an instantaneous grain roughness Shields parameter theta(2.5)(t). Secondly, a constant bed shear stress is added which corresponds to the streaming related bed shear stress -rho ($) over bar((u) over tilde(w) over tilde)(infinity) . The method can be applied to any u(infinity)(t) time series, but further experimental validation is recommended before application to conditions that differ strongly from the ones considered below. The method is not recommended for rippled beds or for sheet flow with typical prototype wave periods and d(50) < 0.20 turn. In such scenarios, time lags related to vertical sediment movement become important, and these are not considered by the present model. (C) 2002 Elsevier Science B.V. All rights reserved.

Coherent structures in open channel flows with bed load transport over an hydraulically rough bed

Dissertação para obtenção do Grau de Mestre em Engenharia Civil – Perfil de Estruturas

Imaging and quantifying salt-tracer transport in a riparian groundwater system by means of 3D ERT monitoring

Determining groundwater flow paths of infiltrated river water is necessary for studying biochemical processes in the riparian zone, but their characterization is complicated by strong temporal and spatial heterogeneity. We investigated to what extent repeat 3D surface electrical resistance tomography (ERT) can be used to monitor transport of a salt-tracer plume under close to natural gradient conditions. The aim is to estimate groundwater flow velocities and pathways at a site located within a riparian groundwater system adjacent to the perialpine Thur River in northeastern Switzerland. Our ERT time-lapse images provide constraints on the plume's shape, flow direction, and velocity. These images allow the movement of the plume to be followed for 35 m. Although the hydraulic gradient is only 1.43 parts per thousand, the ERT time-lapse images demonstrate that the plume's center of mass and its front propagate with velocities of 2x10(-4) m/s and 5x10(-4) m/s, respectively. These velocities are compatible with groundwater resistivity monitoring data in two observation wells 5 m from the injection well. Five additional sensors in the 5-30 m distance range did not detect the plume. Comparison of the ERT time-lapse images with a groundwater transport model and time-lapse inversions of synthetic ERT data indicate that the movement of the plume can be described for the first 6 h after injection by a uniform transport model. Subsurface heterogeneity causes a change of the plume's direction and velocity at later times. Our results demonstrate the effectiveness of using time-lapse 3D surface ERT to monitor flow pathways in a challenging perialpine environment over larger scales than is practically possible with crosshole 3D ERT.

Acoustic transport of charge and spins in GaAs-based heterostructures

Report for the scientific sojourn carried out at the Paul Drude Institut für Festkörperelektronik of the Stanford University, USA, from 2010 to 2012. The objective of this project is the transport and control of electronic charge and spin along GaAs-based semiconductor heterostructures. The electronic transport has been achieved by taking advantage of the piezolectric field induced by surface acoustic waves in non-centrosymmetric materials like GaAs. This piezolectric field separates photogenerated electrons and holes at different positions along the acoustic wave, where they acummulate and are transported at the same velocity as the wave. Two different kinds of structures have been studied: quantum wells grown along the (110) direction, both intrinsic and n-doped, as well as GaAs nanowires. The analysis of the charge acoustic transport was performed by micro-photoluminescence, whereas the detection of the spin transport was done either by analyzing the polarization state of the emitted photoluminescence or by Kerr reflectometry. Our results in GaAs quantum wells show that charge and spin transport is clearly observed at the non-doped structures,obtaining spin lifetimes of the order of several nanoseconds, whereas no acoutically induced spin transport was detected for the n-doped quantum wells. In the GaAs nanowires, we were able of transporting successfully both electrons and holes along the nanowire axis, but no conservation of the spin polarization has been observed until now. The photoluminescence emitted by these structures after acoustic transport, however, shows anti-bunching characteristics, making this system a very good candidate for its use as single photon emitters.

Inferring transport characteristics in a fractured rock aquifer by combining single-hole ground-penetrating radar reflection monitoring and tracer test data

Investigations of solute transport in fractured rock aquifers often rely on tracer test data acquired at a limited number of observation points. Such data do not, by themselves, allow detailed assessments of the spreading of the injected tracer plume. To better understand the transport behavior in a granitic aquifer, we combine tracer test data with single-hole ground-penetrating radar (GPR) reflection monitoring data. Five successful tracer tests were performed under various experimental conditions between two boreholes 6 m apart. For each experiment, saline tracer was injected into a previously identified packed-off transmissive fracture while repeatedly acquiring single-hole GPR reflection profiles together with electrical conductivity logs in the pumping borehole. By analyzing depth-migrated GPR difference images together with tracer breakthrough curves and associated simplified flow and transport modeling, we estimate (1) the number, the connectivity, and the geometry of fractures that contribute to tracer transport, (2) the velocity and the mass of tracer that was carried along each flow path, and (3) the effective transport parameters of the identified flow paths. We find a qualitative agreement when comparing the time evolution of GPR reflectivity strengths at strategic locations in the formation with those arising from simulated transport. The discrepancies are on the same order as those between observed and simulated breakthrough curves at the outflow locations. The rather subtle and repeatable GPR signals provide useful and complementary information to tracer test data acquired at the outflow locations and may help us to characterize transport phenomena in fractured rock aquifers.

Runoff and sediment transport in a degraded area

Gully erosion occurs by the combined action of splash, sheetwash and rill-wash (interrill and rill erosion). These erosion processes have a great capacity for both sediment production and sediment transport. The objectives of this experiment were to evaluate hydrological and sediment transport in a degraded area, severely dissected by gullies; to assess the hydraulic flow characteristics and their aggregate transport capacity; and to measure the initial splash erosion rate. In the study area in Guarapuava, State of Paraná, Brazil (lat 25º 24' S; long 51º24' W; 1034 m asl), the soil was classified as Cambissolo Húmico alumínico, with the following particle-size composition: sand 0.116 kg kg-1; silt 0.180 kg kg-1; and clay 0.704 kg kg-1. The approach of this research was based on microcatchments formed in the ground, to study the hydrological response and sediment transport. A total of eight rill systems were simulated with dry and wet soil. An average rainfall of 33.7 ± 4.0 mm was produced for 35 to 54 min by a rainfall simulator. The equipment was installed, and a trough was placed at the end of the rill to collect sediments and water. During the simulation, the following variables were measured: time to runoff, time to ponding, time of recession, flow velocity, depth, ratio of the initial splash and grain size. The rainsplash of dry topsoil was more than twice as high as under moist conditions (5 g m-2 min-1 and 2 g m-2 min-1, respectively). The characteristics of the flow hydraulics indicate transition from laminar to turbulent flow [Re (Reynolds number) 1000-2000]. In addition, it was observed that a flow velocity of 0.12 m s-1 was the threshold for turbulent flow (Re > 2000), especially at the end of the rainfall simulation. The rill flow tended to be subcritical [Fr (Froude Number) < 1.0]. The variation in hydrological attributes (infiltration and runoff) was lower, while the sediment yield was variable. The erosion in the rill systems was characterized as limited transport, although the degraded area generated an average of 394 g m-2 of sediment in each simulation.

Dispersionless transport in a washboard potential

We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over long intervals of time. The associated distribution of the particle positions moves at an essentially constant velocity and is far from Gaussian-like. This new regime is complementary to, and entirely different from, well-known nonlinear response and large dispersion regimes observed for other values of the external force.

Single-hole GPR reflection imaging of solute transport in a granitic aquifer

Identifying transport pathways in fractured rock is extremely challenging as flow is often organized in a few fractures that occupy a very small portion of the rock volume. We demonstrate that saline tracer experiments combined with single-hole ground penetrating radar (GPR) reflection imaging can be used to monitor saline tracer movement within mm-aperture fractures. A dipole tracer test was performed in a granitic aquifer by injecting a saline solution in a known fracture, while repeatedly acquiring single-hole GPR sections in the pumping borehole located 6 m away. The final depth-migrated difference sections make it possible to identify consistent temporal changes over a 30 m depth interval at locations corresponding to fractures previously imaged in GPR sections acquired under natural flow and tracer-free conditions. The experiment allows determining the dominant flow paths of the injected tracer and the velocity (0.4-0.7 m/min) of the tracer front. Citation: Dorn, C., N. Linde, T. Le Borgne, O. Bour, and L. Baron (2011), Single-hole GPR reflection imaging of solute transport in a granitic aquifer, Geophys. Res. Lett., 38, L08401, doi: 10.1029/2011GL047152.