Maximum crosswind integrated ground level concentration in two stability classes

bl 'kks/k i= esa fu"izHkkoh vkSj vfLFkj fLFkfr;ksa esa ØkWliou lekdfyr lkanz.k ysus ds fy, nks fn’kkvksa esa vfHkogu folj.k lehdj.k ¼ADE½ dks gy fd;k x;k gSA ykIykl :ikarj.k rduhd dk mi;ksx rFkk m/okZ/kj Å¡pkbZ ij vk/kkfjr iou xfr vkSj Hkaoj folj.k’khyrk dh leh{kk djrs gq, ;g gy fudkyk x;k gSA blds lkFk gh Hkw&Lrj vkSj vf/kdre lkanz.kksa dk Hkh vkdyu fd;k x;k gSA geus bl ekWMy esa iwokZuqekfur vkSj izsf{kr lkanz.k vk¡dM+ksa ds e/; rqyuk djus ds fy, dksiugsxu ¼MsuekdZ½ ls fy, x, vkuqHkfod vk¡dM+ksa dk mi;ksx fd;k gSA The advection diffusion equation (ADE) is solved in two directions to obtain the crosswind integrated concentration in neutral and unstable conditions. The solution is solved using Laplace transformation technique and considering the wind speed and eddy diffusivity depending on the vertical height. Also the ground level and maximum concentrations are estimated. We use in this model empirical data from Copenhagen (Denmark) to compare between predicted and observed concentration data.

Derivation of the Gaussian plume model in three dimensions

Gaussian plume model is a common model to study advection diffusion equation which is solved in three dimensions by using Laplace transformation considering constant eddy diffusivity and wind speed power law. Different schemes such as Irwin, Power Law, Briggs and Standard methods are used to obtain crosswind integrated concentration. Statistical measures are used in this paper to know which is the best scheme which agrees with the observed concentration data obtained from Copenhagen, Denmark. The results of model are compared with observed data.

Using dispersion modeling for ground level concentration

A short range model calculating ground-level concentration from elevated sources is estimated, which realized a Fickian-type formula. Taking the source and mixing height are functions of the wind velocity and eddy diffusivity profiles. The model estimated with an exact solution of the advection diffusion equation is compared with experimental ground level concentrations using meteorological data collected near the ground.

Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model

In this study, we give the numerical scheme to the stochastic nonlinear advection diffusion equation. This models is considered with white noise (or random process) having same intensity by changing frequencies. Furthermore, the stability and consistency of proposed scheme are also discussed. Moreover, it is concerned about the analytical solutions, the Riccati equation mapping method is adopted. The different families of single (shock and singular) and mixed (complex solitary-shock, shock-singular, and double-singular) form solutions are obtained with the different choices of free parameters. The graphical behavior of solutions is also depicted in 3D and corresponding contours.

On mixing enhancement by secondary baroclinic vorticity in a shock–bubble interaction

To investigate the intrinsic mechanism for mixing enhancement by variable-density (VD) behaviour, a canonical VD mixing extracted from a supersonic streamwise vortex protocol, a shock–bubble interaction (SBI), is numerically studied and compared with a counterpart of passive-scalar (PS) mixing. It is meaningful to observe that the maximum concentration decays much faster in a VD SBI than in a PS SBI regardless of the shock Mach number ( $Ma=1.22 - 4$ ). The quasi-Lamb–Oseen-type velocity distribution in the PS SBI is found by analysing the azimuthal velocity that stretches the bubble. Meanwhile, for the VD SBI, an additional stretching enhanced by the secondary baroclinic vorticity (SBV) production contributes to the faster-mixing decay. The underlying mechanism of the SBV-enhanced stretching is further revealed through the density and velocity difference between the light shocked bubble and the heavy ambient air. By combining the SBV-accelerated stretching model and the initial shock compression, a novel mixing time estimation for VD SBI is theoretically proposed by solving the advection–diffusion equation under a deformation field of an axisymmetric vortex with the additional SBV-induced azimuthal velocity. Based on the mixing time model, a mixing enhancement number, defined by the ratio of VD and PS mixing time further, reveals the contribution from the VD effect, which implies a better control of the density distribution for mixing enhancement in a supersonic streamwise vortex.

Different solutions of the diffusion equation and its applications

In this report, we solved the advection–diffusion equation under pollutants deposition on the ground surface, taking wind speed and vertical diffusion depend on the vertical height. Also, we estimated a simple diffusion model from point source in an urban atmosphere and the conservative material with downwind was evaluated. Then, we calculated the extreme ground-level concentration as a function of stack height and plume rise in two cases. Comparison between the proposed models and the emission from the Egyptian Atomic Research Reactor at Inshas had been done. Lastly, we discussed the results in this report.

Influence of Shear Displacement on Fluid Flow and Solute Transport in a 3D Rough Fracture

Fractured rocks in the subsurface are ubiquitous, and the dynamics of mass transfer in fractured rocks plays an important role in understanding the problem in engineering geology and environmental geology. In this study, the influence of shear displacement on fluid flow and solute transport in a 3D rough fracture was investigated. A 3D self-affine rough fracture was generated using the modified successive random addition (SRA) technology, and three sheared fractures with different shear displacements were constructed based on the mechanistic model. A direct numerical model based on the Navier-Stokes equation and the advection-diffusion equation was developed to solve the fluid flow and the solute transport. The results showed that shear displacement had a significant influence not only on the fluid flow but also on the solute transport. A global measure of the spatial variability of the flow velocity showed that the heterogeneity became weaker with decreasing shear displacement. All measured BTCs deviated from the Gaussian profile and exhibited the typical anomalous behaviors, such as the long tail and the early arrival. Although the best-fitted results of the advection-dispersion equation (ADE) model and mobile-immobile model (MIM) were generally consistent with those of the BTCs, the MIM was more capable than the ADE model for characterizing the shear-induced anomalous behavior of the BTCs. It was found that the mass exchange process between the immobile and mobile domains was enhanced in the sheared fractures while the fraction of the advection-dominant mobile domain decreased as the shear displacement increased. Furthermore, the deviation of the Taylor dispersion coefficient from the fitted dispersion coefficient by the ADE model and MIM in the sheared fractures was confirmed due to the influence of shear displacement.

RADT-14. TOWARDS IMAGE-GUIDED MODELING OF PATIENT-SPECIFIC RHENIUM-186 NANOLIPOSOME DISTRIBUTION VIA CONVECTION-ENHANCED DELIVERY FOR GLIOBLASTOMA MULTIFORME

Convection-enhanced delivery (CED) of Rhenium-186 nanoliposomes (RNL) is a promising approach to provide precise delivery of large, localized doses of radiation with the goal of extending overall survival for patients with recurrent GBM. A central component of successful CED, is achieving optimal catheter placement for delivery of the therapy. While surgical planning software exists for this purpose, current approaches are designed for small molecules and therefore are not appropriate for larger particles like RNL. To address this concern, we have developed a mathematical model to predict the distribution of RNL via CED on a patient-specific basis. The model is defined on the 3D brain domain which consists of 1) pressure and flow fields generated by accounting for catheter infusion, flow through brain, and fluid loss into capillaries, and 2) the transport of RNL governed by an advection-diffusion equation. We utilize pre-operative MRI to assign patient-specific tissue geometry and properties (e.g., diffusivity, conductivity), and calibrate the model with SPECT measurements within 24 h post the RNL delivery. This model is implemented on one patient enrolled in NCT01906385. The accuracy of model calibration and prediction is evaluated by the Dice score and concordance correlation coefficient (CCC) between modeled and measured distributions of RNL. Our model calibration achieves Dice scores of 0.80, 0.81, 0.69 and CCC of 0.92, 0.93, 0.73 for RNL distributions at the mid-delivery, end of delivery, and 24 h after the delivery, respectively. Long-term model prediction achieves Dice scores of 0.69 and 0.52 at 144 h and 196 h after the delivery, respectively, and CCC of 0.57 and 0.31. Preliminary results demonstrate a proof-of-concept for a patient-specific model to predict the spatiotemporally-resolved distribution of nanoparticles. Ongoing efforts focus on improving our model by accounting backflow and angle of catheter placement, and applying to more patients. Funding: NIH R01CA235800, CPRIT RR160005.