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A quantum color image encryption algorithm based on geometric transformation and intensity channel diffusion was designed. Firstly, a plaintext image was transformed into a quantum state form using the quantum image representation based on HSI color space (QIRHSI) representation as a carrier. Next, a pseudo-random sequence was generated using the generalized logistic map, and the pixel positions permuted multiple two-point swap operations. Immediately afterward, the intensity values were changed by an intensity bit-plane cross-swap and XOR, XNOR operations. Finally, the intensity channel of the above image was diffused in combination with the pseudo-confusion sequence as produced by the quantum logistic map to perform a diffusion operation on the intensity bit-plane to obtain the ciphertext image. Numerical simulations and analyses show that the designed algorithm is implementable and robust, especially in terms of outstanding performance and less computational complexity than classical algorithms in terms of security perspective.

It is fundamental task to reveal the mechanism of the dispersion and the diffusion on solute transport in open channel flow. In this study, the dispersion and the diffusion coefficients were observed and compared with each other based on the tracer tests at a prototype channel in the Andong experimental site, South Korea. The channel has sinuosity of 1.2 and can control the flow rate. For each experimental condition, measurements of average velocity by wading and the turbulence intensity were performed with a fixed device. The dispersion and diffusion coefficients were calculated using a dissolved tracer (Rhodamine WT) and a surface particle tracer (GPS floater), respectively. For each channel section, based on the tracer experiments, the transverse dispersion coefficient and transverse diffusion coefficient were calculated. The observed diffusion and dispersion coefficients were laid on the reliable ranges. The relation between dispersion and diffusion was analyzed by comparing the transverse diffusion coefficient, calculated by the diffusion of surface particles, and the transverse dispersion coefficient, determined by the surface flow velocity, which was calculated using the vertical distribution equation. Based on the analysis, the results that the turbulent diffusion coefficient is proportional to the turbulence intensity, and the transverse turbulence intensity is proportional to the transverse flow velocity. Also, the transverse flow velocity is relative to the transverse dispersion coefficient. Thus, the correlation between dispersion and diffusion is confirmed by the experimental results, and a formula that could be converted based on the relation is proposed.

Townsend’s model of attached eddies for boundary layers is revisited within a quasi-linear approximation. The velocity field is decomposed into a mean profile and fluctuations. While the mean is obtained from the nonlinear equations, the fluctuations are modelled by replacing the nonlinear self-interaction terms with an eddy-viscosity-based turbulent diffusion and stochastic forcing. Under this particular approximation, the resulting fluctuation equations remain linear, enabling solutions to be superposed, the same theoretical idea used in the original attached eddy model. By leveraging this feature, the stochastic forcing is determined self-consistently by solving an optimisation problem which minimises the difference between the Reynolds shear stresses from the mean and fluctuation equations, subject to a constraint that the averaged Reynolds shear-stress spectrum is sufficiently smooth in the spatial wavenumber space. The proposed quasi-linear approximation is subsequently applied to channel flow for Reynolds number$Re_{\\unicode[STIX]{x1D70F}}$ranging from 500 to 20 000. The best result is obtained when the Reynolds stress is calculated by retaining only the two leading proper orthogonal decomposition modes, which further filters out the modelling artefact caused by the unphysical stochastic forcing. In this case, the resulting turbulence intensity profile and energy spectra exhibit the same qualitative behaviour as direct numerical simulation (DNS) data throughout the entire wall-normal domain, while reproducing the early theoretical predictions of the original attached eddy model within a controlled approximation to the Navier–Stokes equations. Finally, the proposed quasi-linear approximation reveals that the peak streamwise and spanwise turbulence intensities may deviate slightly from the logarithmic scaling with the Reynolds number for$Re_{\\unicode[STIX]{x1D70F}}\\gtrsim 10\\,000$, and the supporting evidence is presented using the existing DNS data.

Flash floods typically occur suddenly within hours of heavy rainfall. Accurate forecasting of flash floods in advance using the two-dimensional (2D) shallow water equations (SWEs) remains a challenge, due to the governing SWEs being difficult-to-solve partial differential equations (PDEs). Aiming at shortening the computational time and gaining more time for issuing early warnings of flash floods, constructing a new relationship between water storage and outflow in the rainfall–runoff process is attempted by assuming the catchment as a water storage system. Through numerical simulations of the diffusion wave (DW) approximation of SWEs, the water storage and discharge are found to be limited to envelope lines, and the discharge/water-depth process lines during water rising and falling showed a grid-shaped distribution. Furthermore, if a catchment is regarded as a semi-open water storage system, then there is a nonlinear relationship between the inside average water depth and the outlet water depth, namely, the water storage ratio curve, which resembles the shape of a plume. In the case of an open channel without considering spatial variability, the water storage ratio curve is limited to three values (i.e., the upper, the steady, and the lower limits), which are found to be independent of meteorological (rainfall intensity), vegetation (Manning's coefficient), and terrain (slope gradient) conditions. Meteorological, vegetation, and terrain conditions only affect the size of the plume without changing its shape. Rainfall, especially weak rain (i.e., when rainfall intensity is less than 5.0 mm h−1), significantly affects the fluctuations of the water storage ratio, which can be divided into three modes: Mode I (inverse S-shape type) during the rainfall beginning stage, Mode II (wave type) during the rainfall duration stage, and Mode III (checkmark type) during rainfall end stage. Results indicate that the determination of the nonlinear relationship of the water storage ratio curve under different geographical scenarios will provide new ideas for simulation and early warning of flash floods.

Turbulent characteristics in wall-wake flows downstream of wall-mounted and near-wall cylinders are investigated. The distributions of the defect of streamwise velocity, Reynolds shear stress and turbulence intensities exhibit a certain degree of self-preserving characteristic when they are scaled by their respective peak defect values. For the velocity defect distributions, the vertical distances are scaled by the half-width of peak defect velocity. However, for the distributions of the defects of the Reynolds shear stress and the turbulence intensities, the vertical distances are scaled by the half-width of Reynolds shear stress defect. The peak defects of all the quantities reduce with longitudinal distance signifying the recovery of the upstream distributions of the individual quantities. The third-order correlations reveal that for the wall-mounted cylinder, a streamwise acceleration associated with a downward flux of streamwise Reynolds normal stress (SRNS) in the inner-layer of wall-wake composes sweeps and a streamwise deceleration associated with an upward flux of SRNS in the outer-layer forms ejections. On the other hand, for the near-wall cylinder, a streamwise deceleration associated with a downward flux of SRNS in the inner-layer of wall-wake flow and the gap flow produces the inward interaction events, while the outer-layer characteristic is similar to that of wall-mounted cylinder. The turbulent kinetic energy (TKE) budget in the wake flow demonstrates strong negative pressure energy diffusion in addition to a strong TKE dissipation and diffusion and that in the gap flow exhibits a minor positive peak of pressure energy diffusion and a minor negative peak of TKE diffusion.

Temporal streams are vitally important for hydrology and riverine ecosystems. The identification of wet channel networks and spatial and temporal dynamics is essential for effective management, conservation, and restoration of water resources. This study investigated the temporal dynamics of stream networks in five watersheds under different climate conditions and levels of human interferences, using a systematic method recently developed for extracting wet channel networks based on light detection and ranging elevation and intensity data. In this paper, thresholds of canopy height for masking densely vegetated areas and the ‘time of forward diffusion’ parameter for filtering digital elevation model are found to be greatly influential and differing among sites. The inflection point of the exceedance probability distribution of elevation differences in each watershed is suggested to be used as the canopy height threshold. A lower value for the ‘time of forward diffusion’ is suggested for watersheds with artificial channels. The properties of decomposed and composite probability distribution functions of intensity and the extracted intensity thresholds are found to vary significantly among regions. Finally, the wet channel density and its variation with climate for five watersheds are found to be reasonable and reliable according to results reported previously in other regions.

The emergent activity of biological systems can often be represented as low-dimensional, Langevin-type stochastic differential equations. In certain systems, however, large and abrupt events occur and violate the assumptions of this approach. We address this situation here by providing a novel method that reconstructs a jump-diffusion stochastic process based solely on the statistics of the original data. Our method assumes that these data are stationary, that diffusive noise is additive, and that jumps are Poisson. We use threshold-crossing of the increments to detect jumps in the time series. This is followed by an iterative scheme that compensates for the presence of diffusive fluctuations that are falsely detected as jumps. Our approach is based on probabilistic calculations associated with these fluctuations and on the use of the Fokker–Planck and the differential Chapman–Kolmogorov equations. After some validation cases, we apply this method to recordings of membrane noise in pyramidal neurons of the electrosensory lateral line lobe of weakly electric fish. These recordings display large, jump-like depolarization events that occur at random times, the biophysics of which is unknown. We find that some pyramidal cells increase their jump rate and noise intensity as the membrane potential approaches spike threshold, while their drift function and jump amplitude distribution remain unchanged. As our method is fully data-driven, it provides a valuable means to further investigate the functional role of these jump-like events without relying on unconstrained biophysical models.

In theoretical and field primary production studies, much interest is currently focused on the influence of aperiodic vertical mixing generated at the surface by wind speed and/or heat flux. In the present work, a Lagrangian random walk model was used to study the interactions between periodic vertical tidal mixing and both photoadaptation and primary production of phytoplankton, in typical shallow coastal waters, such as the eastern English Channel. The model considers a depth-dependent diffusion coefficient fluctuating according to the high-low tidal cycles and neap-spring tidal cycles, water columns of different euphotic zone and mixed layer depths, and photoresponse time constants of natural phytoplankton populations collected in the eastern English Channel. Cells were allowed to light-shade adapt, according to the vertical mixing time scales, by altering their photosynthetic properties in response to variations in light. The simulation results indicate first that vertical tidal mixing could control photoadaptation processes at the scale of the high-low tidal cycles at spring tide, and at the scale of neap-spring tidal cycles in shallow coastal systems. Secondly, it appears that the decreasing vertical mixing intensity between spring and neap tide conditions is responsible for a significant increase in daily primary production rates, despite the occurrence of photoinhibition at neap tide. Therefore, primary production in coastal seas would be a function not only of light and nutrient concentrations, but also of photoadaptation processes in relation with vertical tidal mixing. In another way, the Lagrangian model suggests that the theory according to which cells are adapted to the mean light intensity of a water column in a turbulent regime is valid only from a populational point of view. From the model used, it appears also that our present knowledge on photosynthetic dynamic modeling is unsuited to generating pronounced vertical gradients of photosynthetic parameters in all water columns.