On the use of the adjoint operator for source reconstruction in particle transport problems

Scalar flux in a uniform mean scalar gradient in homogeneous isotropic steady turbulence

The quasidiffusion (QD) method is an established and efficient iterative technique for solving particle transport problems. Each QD iteration consists of a high-order SN sweep, followed by a low-order QD calculation. QD has two defining characteristics: (1) its iterations converge rapidly for any spatial grid and (2) the converged scalar fluxes from the high-order SN sweep and the low-order QD calculation differ, by spatial truncation errors, from each other and from the scalar flux solution of the SN equations. In this paper, we show that by including a transport consistency factor in the low-order equation, the converged high-order and low-order scalar fluxes become equal to each other and to the converged SN scalar flux. However, the inclusion of the transport consistency factor has a negative impact on the convergence rate. We present numerical results that demonstrate the effect of the transport consistency factor on stability.

An arbitrary geometry finite element method for the adjoint neutron transport equation

Estimation of neutron sources driving prescribed power generations in subcritical systems using one-speed two-dimensional discrete ordinates formulations

An analytical version of the discrete‐ordinates method (the ADO method) is used with recently established analytical expressions for the rigid‐sphere scattering kernels in a study devoted to the flow of a binary gas mixture in a plane channel. In particular, concise and accurate solutions to basic flow problems in a plane channel driven by temperature, pressure, and concentration gradients and described by the linearized Boltzmann equation are established for the case of Maxwell boundary conditions for each of the two species. The velocity, heat‐flow, and shear‐stress profiles, as well as the mass‐ and heat‐flow rates, are established for each species of particles, and numerical results are reported for two binary mixtures (Ne‐Ar and He‐Xe).

Most of the existing DOA estimation algorithms are based on uniform array, whose estimation performance is limited by the shortcoming of small aperture of uniform array, and it is difficult to apply sparse array to DOA estimation of distributed sources. In order to solve the above problems, this paper introduces interqualitative array into DOA estimation of distributed sources, and proposes a DOA estimation algorithm for coherent distributed sources. Because the array element spacing is larger than half wavelength, the direct estimation will produce false peak. In order to eliminate the ambiguity, this paper proves that DOA estimation of two submatrices is performed separately, and its common value is unique, that is, the true incidence Angle. According to this proof, DOA estimation of two submatrices is carried out separately for the one-dimensional DOA estimation scenario of distributed sources, and the common part of the two sets of estimation results is taken as the final estimation result. The complexity analysis and performance verification of this method are also given. Simulation experiments show that the performance of the proposed method is better than that of the DSPE algorithm and TLS-ESPRIT algorithm under the same array number in the one-dimensional DOA estimation scenario.

Forest edges have significant impacts on flow dynamics and mass exchange across the forest–atmosphere interface. A better understanding of edge flows and scalar transport has implications for locating and interpreting eddy-covariance flux measurements over finite-size forests with edges. Here the large-eddy simulation module within the Weather Research and Forecasting model is deployed to study the influence of forest edges on flow dynamics and scalar transport for a range of vertical distributions of foliage and scalar sources/sinks. For plant canopies with a relatively dense trunk space, a strong in-canopy flow convergence develops near the leading edge, which dominates the flow dynamics and leads to distinct scalar concentration and flux patterns not only across edges but also across the forest–atmosphere interface for sources near the ground and lower part of the canopy. For plant canopies with a deep, sparse trunk space, a strong and long sub-canopy jet develops, leading to simpler features in flow dynamics and scalar transfer. A real case with scalar sources/sink distributions as simulated by a newly developed multiple-layer canopy module produces even more complex scalar concentration and flux patterns. The budget equations for scalars are also analyzed to quantify the contributions of different terms to scalar fluxes. Our results demonstrate that both the scalar source distributions and canopy structures should be considered when eddy-covariance flux measurements are made over finite-size forests with edges.

We derive here Lagrangian fluctuation–dissipation relations for advected scalars in wall-bounded flows. The relations equate the dissipation rate for either passive or active scalars to the variance of scalar inputs from the initial values, boundary values and internal sources, as those are sampled backward in time by stochastic Lagrangian trajectories. New probabilistic concepts are required to represent scalar boundary conditions at the walls: the boundary local-time density at points on the wall where scalar fluxes are imposed and the boundary first hitting time at points where scalar values are imposed. These concepts are illustrated both by analytical results for the problem of pure heat conduction and by numerical results from a database of channel-flow turbulence, which also demonstrate the scalar mixing properties of near-wall turbulence. As an application of the fluctuation–dissipation relation, we examine for wall-bounded flows the relation between anomalous scalar dissipation and Lagrangian spontaneous stochasticity, i.e. the persistent non-determinism of Lagrangian particle trajectories in the limit of vanishing viscosity and diffusivity. In Part I of this series, we showed that spontaneous stochasticity is the only possible mechanism for anomalous dissipation of passive or active scalars, away from walls. Here it is shown that this remains true when there are no scalar fluxes through walls. Simple examples show, on the other hand, that a distinct mechanism of non-vanishing scalar dissipation can be thin scalar boundary layers near the walls. Nevertheless, we prove for general wall-bounded flows that spontaneous stochasticity is another possible mechanism of anomalous scalar dissipation.

The problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel. It is shown that the minimum-variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly. It is shown that the channel can be blindly identified if and only if there is not more than one Gaussian source. This condition suggests that waveform-preserving blind estimation can be achieved over a wide range of signal processing applications, including those cases in which the source signals have identical nonGaussian distributions. The constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform-preserving blind signal estimation algorithms. Examples are presented to demonstrate the applications of the theoretical results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, the Symmetric Galerkin Boundary Element Method for Linear Elastic Fracture Mechanics is extended to non-linear cohesive cracks propagating through homogeneous linear elastic isotropic media. The cohesive model adopted is based on the concept of free energy density per unit undeformed area. The corresponding constitutive cohesive equations present a softening branch which induces a potential instability. Thus, a suitable solution algorithm capable of following the growth of the cohesive zone is needed, and in the present work the numerical simulation is controlled by an arc-length method combined with a Newton-Raphson algorithm for the iterative solution of nonlinear equations. The Boundary ElementMethod is very attractive for modeling cohesive crack problems as all nonlinearities are located on the boundaries of linear elastic domains. Moreover a Galerkin approximation scheme, applied to a suitable symmetric boundary integral equation formulation, ensures an easy and efficient treatment of cracks in homogeneous media and an excellent convergence behavior of the numerical solution. The cohesive zone model is applied to simulate a pure mode I crack propagation in concrete. Numerical results for three-point bending test are used to check the numerical results for mode I and are compared with some numerical results obtained by FEM analysis found in the literature.

In practical applications such as radar, sonar, and mobile communications, transmitted signals are often affected by the scattering and reflection phenomena, which causes the signal energy received by the antenna array to be distributed into a certain space. In this case, a distributed source model will be more applicable. In general, the distributed sources have been classified as coherently distributed (CD) source and incoherently distributed (ID) source, which prove to be suitable for the cases of slowly time-varying and rapidly time-varying channels, respectively.In this paper, we consider the two-dimensional direction of arrival (DOA) estimation of distributed sources (including CD source or ID source). Specifically, uniform circular array (UCA) is widely used because of its ability to measure full azimuth angle and high resolution. However, the existing estimation algorithms all require spectral peak searching and the eigenvalue decomposition, which can bring a large computational complexity. To solve this problem, a decoupled rapid two-dimensional DOA estimation algorithm is proposed based on vectoring differential phases considering the two cases of single CD source and ID source. Firstly, based on spatial frequency approximation model, it is proved that none of differential phases between the received signals of different sensors in the UCA is affected by angle spread parameters when there is only a single distributed source. Under the premise of such a property, the central DOAs can be decoupled through obtaining the differential phases. Next, we can obtain the phase angles of strictly upper triangular elements in the sample covariance matrix, which correspond to differential phases between different sensors. Finally, by vectoring these differential phases, the central azimuth and elevation DOAs are estimated in the closed form from a least-squared problem, where the spectral peak searching and eigenvalue decomposition can be avoided, hence the computational complexity is reduced greatly. Theoretical analysis and simulation results show that the proposed algorithm has higher estimation accuracy and does not require prior information about the distribution of angular signals. With both low computational complexity and low hardware complexity, the proposed algorithm is beneficial to the engineering practice of array direction finding in complex environment.

Whereas wrack dynamics on tidally influenced beaches have been studied to some detail, essentially nothing is known about how drift lines in tide-free coastal systems vary in space and time. We provide evidence for high spatial and temporal dynamics of beach-cast wrack on a sand beach in the Western Baltic Sea. Over the course of one year, the amount of weekly deposited macrophyte wrack fluctuated from zero to 3000 g·m-1 shoreline. Wrack mostly accumulated just above the waterline. Part of the beach-cast wrack is frequently re-suspended into coastal water upon extreme high water level events, or wrack patches are translocated landwards by wind-driven changes in water level or along the shoreline by winds. Consequently, the deposited wrack does accumulate, but a steady-state of ca 400 g·m-1 builds up within 2 - 3 weeks. Eelgrass wrack buried in sand decomposed almost twice as fast as on top of the sand or re-suspended in water. Fragmentation of leaves promoted decomposition only when wrack remained on the sand surface. The spatial and temporal distribution of this valuable source of organic matter is unpredictable and depends on wind and wind-driven waves.

In the context of the advancement of the “dual carbon” goals, research on the carbon source—carbon sink balance of the urban agglomeration around Poyang Lake has very important practical significance. However, due to socio-economic differences in industrial layout and uneven population distribution, there are significant spatial differences in carbon sources and sinks. Based on this, the author will conduct an in-depth analysis of the general situation of the urban agglomeration around Poyang Lake in this paper, and propose corresponding carbon source and carbon sink spatial optimization strategies for the urban agglomeration in combination with the influencing factors of the spatial distribution of carbon source and carbon sink in the urban agglomeration around Poyang Lake, hoping to provide some reference and assistance to readers.

Light utilization is the vital first step of photosynthesis for photoautotrophic organisms. Boosting the growth and yield of photosynthetic organisms is critical in sustainable food and biofuel production in a photobioreactor. In this contribution, we improved the light quality of cyanobacteria by the addition of aggregation-induced emission luminogens (AIEgens), which could absorb the ultraviolet/blue light and emit the green/yellow light into the culture medium, thus effectively converted the light to a more usable range. Our designed AIEgens formed highly bright luminogenic aggregates in the exposure medium and dispersed around the cells, which effectively modified the wavelength and spatial distribution of the light source. The photosynthesis parameters of AIEgen-treated cyanobacteria, including the maximum photosynthetic quantum yield, the effective photochemical quantum yield of photosystem II, and the relative electron transport rate, were significantly improved with the application of our AIEgens. Specifically, after 14 days of incubation, we demonstrated that the AIEgens boosted the cell density of cyanobacteria by 5-fold and the lipid contents by 5- to 6-fold. Furthermore, cyanobacteria continued to grow under UV light irradiation in the presence of AIEgens, highlighting the important role of AIEgens in light conversion to improve light quality. Our study demonstrated the potential application of AIEgens in a photosynthetic biofactory without genetic modification of photosynthetic organisms.

An interferometry based wavefront sensing scheme applicable to low-coherent light sources is proposed and demonstrated. Using a pair of cascaded Sagnac interferometers, spatial frequency multiplexed interference of three sheared copies of the wavefront is recorded. The independent vector gradients obtained are used to reconstruct the wavefront. We overcome the spatio-temporal coherence limitations of the light source through the choice of spatial and spectral distribution of the light source. A Gaussian spectral distribution enables the measurement of the phase gradient corresponding to the central wavelength. Introduction of aperture for controlling the spatial distribution of the extended light source, we revive the spatial coherence of the optical field at the detector plane. We revive the spatial coherence of the field for the set value of lateral shear to maintain the visibility of the interference at the detectable level. Validating the scheme through measurement of changes in wavefront as a function of a collimation lens position, we apply it to reconstruct the wavefront of a light beam passing through a pseudo random phase plate, an atmospheric turbulence simulator.