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Monte Carlo ray-tracing schemes have been developed for the evaluation of radiative heat transfer for problems, in which the participating medium is represented by discrete point masses, such as the flow field and scalar fields in PDF Monte Carlo methods frequently used in combustion modeling. Photon ray tracing in such cases requires that an optical thickness is assigned to each of the point masses. Two approaches are dis-cussed, the point particle model (PPM), in which the shape of particle is not specified, and the spherical particle model (SPM) in which particles are assumed to be spheres with specified radiation properties across their volumes. Another issue for ray tracing in particle fields is the influence region of a ray. Two ways of modeling a ray are proposed. In the first, each ray is treated as a standard volume-less line. In the other approach, the ray is assigned a small solid angle, and is thus treated as a cone with a decaying influence function away from its centerline. Based on these models, three different inter-action schemes between rays and particles are proposed, i.e., line-SPM, cone-PPM and cone-SPM methods, and are compared employing several test problems. DOI: 10.1115/1.2345431

SummaryCULLIN4-RING ubiquitin ligases (CRL4s) as well as their targets are fundamental regulators functioning in many key developmental and stress responses in eukaryotes. In tomato (Solanum lycopersicum), molecular cloning has revealed that the underlying genes of natural spontaneous mutations high pigment 1 (hp1), high pigment 2 (hp2) and uniform ripening (u) encode UV-DAMAGED DNA BINDING PROTEIN 1 (DDB1), DE-ETIOLATED 1 (DET1) and GOLDEN 2-LIKE (GLK2), respectively. However, the molecular basis of the opposite actions of tomato GLK2 vs CUL4-DDB1-DET1 complex on regulating plastid level and fruit quality remains unknown.Here, we provide molecular evidence showing that the tomato GLK2 protein is a substrate of the CUL4-DDB1-DET1 ubiquitin ligase complex for the proteasome degradation.SlGLK2 is degraded by the ubiquitin-proteasome system, which is mainly determined by two lysine residues (K11 and K253). SlGLK2 associates with the CUL4-DDB1-DET1 E3 complex in plant cells. Genetically impairing CUL4, DDB1 or DET1 results in a retardation of SlGLK2 degradation by the 26S proteasome.These findings are relevant to the potential of nutrient accumulation in tomato fruit by mediating the plastid level and contribute to a deeper understanding of an important regulatory loop, linking protein turnover to gene regulation.