Search

Main purpose of this paper is to formulate canonical quantum continuity equations for white noise operators and to find their explicit unique solutions. By applying the continuity equations for white noise functionals and canonical topological isomorphisms between the spaces of white noise operators and the spaces of two-variable white noise functionals, we formulate canonical quantum continuity equations for white noise operators, and then we induce time dependent quantum evolution systems which are equivalent to the quantum continuity equations. Then we find explicit forms, in terms of the quantum analogues of generalized Fourier-Mehler transforms, of the unique solutions of the quantum continuity equations by solving the quantum evolution systems for white noise operators. [ABSTRACT FROM AUTHOR]

Based on the quantum white noise theory, we formulate new types of anticipating quantum stochastic integrals by combining the Hitsuda–Skorokhod quantum stochastic integrals and the interactions between the integrands and the integrators. For our purpose, we prove various versions of analytic characterization theorems of symbols of white noise operators as more general cases. Also, several types of quantum (stochastic) gradients are formulated as continuous linear operators which are related to the quantum white noise derivatives and reflecting the interactions with the external noises. Finally, we formulate further systematical study of anticipating quantum stochastic integrals. [ABSTRACT FROM AUTHOR]

Riparian vegetation plays a fundamental role in alluvial channel evolution by modifying flow and sedimentation dynamics. To elucidate the roles of sediment supply, flow‐dependent transport capacity, and morphodynamic feedbacks on the evolution of emergent vegetation patches over a single hydrograph, we conducted two experiments with different reach‐scale sediment supplies: a high‐supply experiment (HSE) and low‐supply experiment (LSE). We measured flow velocities, bedload transport, and topographic changes around a full‐scale patch of live emergent willows in an outdoor laboratory flume. Erosion occurred in the patch‐adjacent channel areas irrespective of the sediment supply, whereas deposition within the patch interior was suppressed in the LSE and enhanced in the HSE. The magnitude of patch deposition in each experiment was controlled by the local sediment supply to the patch and local sediment mobility during each discharge in the hydrograph. The local sediment supply was affected by bed morphodynamics at the patch head, which modulated the reach‐scale sediment supply by redistributing the bedload in the channel. Sediment mobility within the patch was flow‐dependent and a function of velocity and turbulent kinetic energy. For different discharges, the velocity in the patch changed proportionally with the freestream velocity; however, the turbulent kinetic energy was more sensitive, being elevated compared with the freestream during high flows and inhibited at low flows. Therefore, deposition and erosion within vegetation patches are not simply functions of the reach‐scale sediment supply or patch flow characteristics, as is often assumed, but additionally depend on the local sediment supply to the patch interior. Plain Language Summary: Riparian vegetation in rivers and deltas is considered a primary cause of sediment deposition and channel stabilization. However, in the laboratory, we identified the physical mechanisms influencing sediment deposition and erosion and their change over a natural flow regime to illustrate that the same full‐sized willow patch can either enhance or reduce sediment deposition within the patch interior relative to the same channel without vegetation. The amount of sediment deposited in the vegetation patch depended on the velocity and turbulent kinetic energy of the water, which changed as the flow decreased. Additionally, the presence of a single vegetation patch fundamentally changed the character of the channel from depositional to erosional near the patch, indicating that more erosion occurred in adjacent channels than deposition within the patch. Deposition and erosion of the bed were also influenced by the amount of sediment supplied to the channel from upstream. This reach‐scale sediment supply was modified by a sediment mound that formed at the upstream end of the patch during high sediment supply to the channel. The mound redistributed the sediment transport within the channel and vegetation patch, revealing another physical mechanism influencing the spatial and temporal variability of bedload transport in vegetated channels. Key Points: Relative to the open depositional channel located upstream, a single vegetation patch caused channel erosion that lowered the median bed elevations by up to 640%The same vegetation patch can both inhibit and enhance interior sediment deposition depending on the flow‐dependent transport capacity and local sediment supplyMorphodynamic bed changes modulated the reach‐scale sediment supply in and around the patch by spatially redistributing bedload within the channel [ABSTRACT FROM AUTHOR]