A Novel Two-Stage Design Framework for Two-Dimensional Spatial Packing of Interconnected Components

Packing and routing separately are each challenging NP-hard problems. Therefore, solving the coupled packing and routing problem simultaneously will require disruptive methods to better address pressing-related challenges, such as system volume reduction, interconnect length reduction, ensuring non-intersection, and physics (thermal, hydraulic, or electromagnetic) considerations. Here we present a novel two-stage sequential design framework to perform simultaneous physics-based packing and routing optimization. Stage 1 generates interference-free initial layouts that are fed to stage 2 as starting points to perform continuous physics-based optimization. Three distinct strategies for stage 1 have been introduced recently, (1) the force-directed layout method (FDLM), (2) an extension of the shortest path algorithms (SPAs), and (3) a unique geometric topology (UGT) generation algorithm. In stage 2, a gradient-based topology optimization method is used to simultaneously optimize both component locations and interconnect routing paths. In addition to geometric considerations, this method supports optimization based on system behavior by including physics-based objectives and constraints. The proposed framework is demonstrated using three case studies. First, the layout generation methods developed for stage 1 are compared with respect to system performance metrics obtained from stage 2. Second, a multi-objective optimization problem using the epsilon-constraint method is solved to obtain Pareto optimal solutions. Third, an extension to multi-loop systems is demonstrated. In summary, the design automation framework integrates several elements together as a step toward a more comprehensive solution of 3D packing and routing problems with both geometric and physics considerations.

A Novel Two-Stage Design Framework for 2D Spatial Packing of Interconnected Components

Packing and routing problems separately are each challenging NP-hard problems. Therefore, solving the coupled packing and routing problem simultaneously will require disruptive methods to better address pressing related challenges, such as system volume reduction, interconnect length reduction, ensuring non-intersection, and physics (heat, fluid pressure or electromagnetic) considerations. Here we present a novel two-stage sequential design framework to perform simultaneous physics-based packing and routing optimization. Stage 1 is comprised of generating interference-free initial layouts that are fed to stage 2 as starting points to perform continuous physics-based optimization. Three distinct strategies for stage 1 have been introduced recently, 1) the force-directed layout method (FDLM), 2) an extension of the shortest path algorithms (SPAs) and 3) a unique geometric topology (UGT) generation algorithm. In stage 2, a gradient-based topology optimization method is used to simultaneously optimize both component locations and routing paths of component interconnects. In addition to geometric considerations, this method supports optimization based on system behavior by including physics-based objectives and constraints (e.g., modeled using 1D lumped parameter and 2D finite element physics models). The three layout generation methods developed for stage 1 are compared here with respect to system performance metrics obtained from stage 2. In summary, the design automation framework presented here integrates several elements together as a step toward a more comprehensive solution of 3D packing and routing problems with both geometric and physics considerations.

Dielectric and Magnetic Properties of Nanocomposites Based on Opal Matrixes, Phosphates and Vanadates of Metals

Opal matrix is a regular 3D-packing of spherical particles of amorphous SiO2, forming an ordered system of voids. Opal matrixes with spherical particles of SiO2 diameter d ≈ 260 nm (Δd ≈ 2 %) were synthesized. The frequency dependences of the conductivity, real and imaginary components of the dielectric and magnetic conductivity of nanocomposites containing crystallites 16–65 nm in size of magnetic materials ‒ double phosphates (LiNiPO4, LiCoPO4) and vanadates (GdVO4 and DyVO4) were measured. The dielectric losses of nanocomposites remain low (at a level of ~ 0.06) in the frequency range 107–1010 Hz for nanocomposites with DyVO4 and LiCoPO4. The dielectric loss increases both in the direction of low frequencies (< 106 Hz) and in the direction of THz frequencies.

3D Packing Defects in Lipid Membrane as a Function of Membrane Order

Lipid membrane packing defects are considered as essential parameter that regulates specific membrane binding of several peripheral proteins. In absence of direct experimental characterization, lipid packing defects and their role in the binding of peripheral proteins are generally investigated through computational studies, which have been immensely successful in unraveling the key steps of the membrane-binding process. However, packing defects are calculated using 2-dimensional projections and the crucial information on their depths is generally overlooked. Here we present a simple yet computationally efficient algorithm, which identifies these defects in 3-dimensions. We employ the algorithm to understand the nature of packing defects in flat bilayer membranes exhibiting liquid-ordered (Lo), liquid-disordered (Ld) and co-existing Lo/Ld phases. Our results indicate the presence of shallower and smaller defects in the Lo phase membranes as compared to the defects in Ld and mixed Lo/Ld phase membranes. Such analyses can elucidate the molecular scale mechanisms that drive the preferential localization of certain proteins to either of the liquid phases or their interface. Moreover, on the methodology front, our analyses suggest that the projection based 2-dimensional calculation of packing defects might result in inaccurate quantification of their sizes - a very important feature for membrane association of protein motifs, thus advocating the importance of the 3-dimensional calculations.