Evolutionary Optimization of a Geometrically Refined Truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset

The Large Scale Bias of Dark Matter Halos: Numerical Calibration and Model Tests

We measure the clustering of dark matter halos in a large set of collisionless cosmological simulations of the flat LCDM cosmology. Halos are identified using the spherical overdensity algorithm, which finds the mass around isolated peaks in the density field such that the mean density is Delta times the background. We calibrate fitting functions for the large scale bias that are adaptable to any value of Delta we examine. We find a ~6% scatter about our best fit bias relation. Our fitting functions couple to the halo mass functions of Tinker et. al. (2008) such that bias of all dark matter is normalized to unity. We demonstrate that the bias of massive, rare halos is higher than that predicted in the modified ellipsoidal collapse model of Sheth, Mo, & Tormen (2001), and approaches the predictions of the spherical collapse model for the rarest halos. Halo bias results based on friends-of-friends halos identified with linking length 0.2 are systematically lower than for halos with the canonical Delta=200 overdensity by ~10%. In contrast to our previous results on the mass function, we find that the universal bias function evolves very weakly with redshift, if at all. We use our numerical results, both for the mass function and the bias relation, to test the peak-background split model for halo bias. We find that the peak-background split achieves a reasonable agreement with the numerical results, but ~20% residuals remain, both at high and low masses.Comment: 11 pages, submitted to ApJ, revised to include referee's coment

Topology Synthesis of Structures Using Parameter Relaxation and Geometric Refinement

Typically, structural topology optimization problems undergo relaxation of certain design parameters to allow the existence of intermediate variable optimum topologies. Relaxation permits the use of a variety of gradient-based search techniques and has been shown to guarantee the existence of optimal solutions and eliminate mesh dependencies. This Technical Publication (TP) will demonstrate the application of relaxation to a control point discretization of the design workspace for the structural topology optimization process. The control point parameterization with subdivision has been offered as an alternative to the traditional method of discretized finite element design domain. The principle of relaxation demonstrates the increased utility of the control point parameterization. One of the significant results of the relaxation process offered in this TP is that direct manufacturability of the optimized design will be maintained without the need for designer intervention or translation. In addition, it will be shown that relaxation of certain parameters may extend the range of problems that can be addressed; e.g., in permitting limited out-of-plane motion to be included in a path generation problem

Habitat Design Optimization and Analysis

Long-duration surface missions to the Moon and Mars will require habitats for the astronauts. The materials chosen for the habitat walls play a direct role in the protection against the harsh environments found on the surface. Choosing the best materials, their configuration, and the amount required is extremely difficult due to the immense size of the design region. Advanced optimization techniques are necessary for habitat wall design. Standard optimization techniques are not suitable for problems with such large search spaces; therefore, a habitat design optimization tool utilizing genetic algorithms has been developed. Genetic algorithms use a "survival of the fittest" philosophy, where the most fit individuals are more likely to survive and reproduce. This habitat design optimization tool is a multi-objective formulation of structural analysis, heat loss, radiation protection, and meteoroid protection. This paper presents the research and development of this tool

The pseudo-evolution of halo mass

A dark matter halo is commonly defined as a spherical overdensity of matter with respect to a reference density, such as the critical density or the mean matter density of the Universe. Such definitions can lead to a spurious pseudo-evolution of halo mass simply due to redshift evolution of the reference density, even if its physical density profile remains constant over time. We estimate the amount of such pseudo-evolution of mass between z=1 to 0 for halos identified in a large N-body simulation, and show that it accounts for almost the entire mass evolution of the majority of halos with M200 of about 1E12 solar masses and can be a significant fraction of the apparent mass growth even for cluster-sized halos. We estimate the magnitude of the pseudo-evolution assuming that halo density profiles remain static in physical coordinates, and show that this simple model predicts the pseudo-evolution of halos identified in numerical simulations to good accuracy, albeit with significant scatter. We discuss the impact of pseudo-evolution on the evolution of the halo mass function and show that the non-evolution of the low-mass end of the halo mass function is the result of a fortuitous cancellation between pseudo-evolution and the absorption of small halos into larger hosts. We also show that the evolution of the low mass end of the concentration-mass relation observed in simulations is almost entirely due to the pseudo-evolution of mass. Finally, we discuss the implications of our results for the interpretation of the evolution of various scaling relations between the observable properties of galaxies and galaxy clusters and their halo masses.Comment: 15 pages, 9 figures. Minor changes. Published Versio

In-Space Radiator Shape Optimization using Genetic Algorithms

Future space exploration missions will require the development of more advanced in-space radiators. These radiators should be highly efficient and lightweight, deployable heat rejection systems. Typical radiators for in-space heat mitigation commonly comprise a substantial portion of the total vehicle mass. A small mass savings of even 5-10% can greatly improve vehicle performance. The objective of this paper is to present the development of detailed tools for the analysis and design of in-space radiators using evolutionary computation techniques. The optimality criterion is defined as a two-dimensional radiator with a shape demonstrating the smallest mass for the greatest overall heat transfer, thus the end result is a set of highly functional radiator designs. This cross-disciplinary work combines topology optimization and thermal analysis design by means of a genetic algorithm The proposed design tool consists of the following steps; design parameterization based on the exterior boundary of the radiator, objective function definition (mass minimization and heat loss maximization), objective function evaluation via finite element analysis (thermal radiation analysis) and optimization based on evolutionary algorithms. The radiator design problem is defined as follows: the input force is a driving temperature and the output reaction is heat loss. Appropriate modeling of the space environment is added to capture its effect on the radiator. The design parameters chosen for this radiator shape optimization problem fall into two classes, variable height along the width of the radiator and a spline curve defining the -material boundary of the radiator. The implementation of multiple design parameter schemes allows the user to have more confidence in the radiator optimization tool upon demonstration of convergence between the two design parameter schemes. This tool easily allows the user to manipulate the driving temperature regions thus permitting detailed design of in-space radiators for unique situations. Preliminary results indicate an optimized shape following that of the temperature distribution regions in the "cooler" portions of the radiator. The results closely follow the expected radiator shape

The overdensity and masses of the friends-of-friends halos and universality of the halo mass function

The friends-of-friends algorithm (hereafter, FOF) is a percolation algorithm which is routinely used to identify dark matter halos from N-body simulations. We use results from percolation theory to show that the boundary of FOF halos does not correspond to a single density threshold but to a range of densities close to a critical value that depends upon the linking length parameter, b. We show that for the commonly used choice of b = 0.2, this critical density is equal to 81.62 times the mean matter density. Consequently, halos identified by the FOF algorithm enclose an average overdensity which depends on their density profile (concentration) and therefore changes with halo mass contrary to the popular belief that the average overdensity is ~180. We derive an analytical expression for the overdensity as a function of the linking length parameter b and the concentration of the halo. Results of tests carried out using simulated and actual FOF halos identified in cosmological simulations show excellent agreement with our analytical prediction. We also find that the mass of the halo that the FOF algorithm selects crucially depends upon mass resolution. We find a percolation theory motivated formula that is able to accurately correct for the dependence on number of particles for the mock realizations of spherical and triaxial Navarro-Frenk-White halos. However, we show that this correction breaks down when applied to the real cosmological FOF halos due to presence of substructures. Given that abundance of substructure depends on redshift and cosmology, we expect that the resolution effects due to substructure on the FOF mass and halo mass function will also depend on redshift and cosmology and will be difficult to correct for in general. Finally, we discuss the implications of our results for the universality of the mass function.Comment: 19 pages, 17 figures, submitted to ApJ supplemen

Lunar Habitat Optimization Using Genetic Algorithms

Long-duration surface missions to the Moon and Mars will require bases to accommodate habitats for the astronauts. Transporting the materials and equipment required to build the necessary habitats is costly and difficult. The materials chosen for the habitat walls play a direct role in protection against each of the mentioned hazards. Choosing the best materials, their configuration, and the amount required is extremely difficult due to the immense size of the design region. Clearly, an optimization method is warranted for habitat wall design. Standard optimization techniques are not suitable for problems with such large search spaces; therefore, a habitat wall design tool utilizing genetic algorithms (GAs) has been developed. GAs use a "survival of the fittest" philosophy where the most fit individuals are more likely to survive and reproduce. This habitat design optimization tool is a multiobjective formulation of up-mass, heat loss, structural analysis, meteoroid impact protection, and radiation protection. This Technical Publication presents the research and development of this tool as well as a technique for finding the optimal GA search parameters

Photochemically re-bridging disulfide bonds and the discovery of a thiomaleimide mediated photodecarboxylation of C-terminal cysteines

Described in this work is a novel method for photochemically manipulating peptides and proteins via the installation of cysteine-selective photoactive tags. Thiomaleimides, generated simply by the addition of bromomaleimides to reduced disulfide bonds, undergo [2 + 2] photocycloadditions to reconnect the crosslink between the two cysteine residues. This methodology is demonstrated to enable photoactivation of a peptide by macrocyclisation, and reconnection of the heavy and light chains in an antibody fragment to form thiol stable conjugates. Finally we report on an intriguing thiomaleimide mediated photochemical decarboxylation of C-terminal cysteines, discovered during this study