N–Dimensional Orthogonal Tile Sizing Problem

AMS subject classification: 68Q22, 90C90

Necking and failure at low strains in a coarse-grained wrought Mg alloy

Tensile testing of rolled AZ31 alloy with a mean grain size of 80 μm reveals localization and failure prior to diffuse necking. Optical microscopy reveals that failure is caused by voids that have formed within twins. A simple localization criterion is proposed that captures the role of grain size in the effect. Such early failure is only predicted for coarse grain sizes, in line with observation.

Bulk geochemistry and grain-size composition of surface sediments from the SW Atlantic

Surface sediments from the South American continental margin surrounding tbe Argentine Basin were studied with respect to bulk geochemistry (Caeo) and C ) and grain-size composition (sand/silt/clay relation and terrigenous silt grain-size distribution). The grain-size distributions of the terrigenous silt fraction were unmixed into three end members (EMs), using an end-member modelling algorithm. Three unimodal EMs appear to satisfactorily explain the variations in the data set of the grain-size distributions ofterrigenous silt. The EMs are related to sediment supply by rivers, downslope transport, winnowing, dispersal and re-deposition by currents. The bulk geochemical composition was used to trace the distribution of prominent water masses within the vertical profile. The sediments of the eastern South American continental margin are generally divided into a coarse-grained and carbonate-depleted southwestern part, and a finer-grained and carbonate-rich northeastern part. The transition of both environments is located at the position of the Brazil Malvinas Confluence (BMC). The sediments below the confluence mixing zone of the Malvinas and Brazil Currents and its extensions are characterised by high concentrations of organic carbon, low carbonate contents and high proportions of the intennediate grain-size end member. Tracing these properties, the BMC emerges as a distinct north-south striking feature centered at 52-54°W crossing the continental margin diagonally. Adjacent to this prominent feature in the southwest, the direct detrital sediment discharge of the Rio de la Plata is clearly recognised by a downslope tongue of sand and high proportions of the coarsest EM. A similar coarse grain-size composition extends further south along the continental slope. However, it displays bener sorting due to intense winnowing by the vigorous Malvinas Current. Fine-grained sedimentary deposition zones are located at the southwestern deeper part of the Rio Grande Rise and the southern abyssal Brazil Basin, both within the AABW domain. Less conspicuous winnowing/accumulation panerns are indicated north of the La Plata within the NADW level according to the continental margin topography. We demonstrate that combined bulk geochemical and grain-size properties of surface sediments, unmixed with an end-member algorithm, provide a powerful tool to reconstruct the complex interplay of sedimentology and oceanography along a time slice.

Cyclic-oxidation behavior of Ti3SiC2-base material at 1100°c

The cyclic-oxidation behavior of Ti3SiC2-base material was studied at 1100°C in air. Scale spallation and weight loss were not observed in the present tests and the weight gain would just continue if the experiments were not interrupted. The present results demonstrated that the scale growth on Ti3SiC2-base material obeyed a parabolic rate law up to 20 cycles. It then changed to a linear rate with further increasing cycles. The scales formed on the Ti3SiC2base material were composed of an inward-growing, fine-grain mixture of Ti022 + SiO2 and an outward-growing, coarse-grain TiO2. Theoretical calculations show that the mismatch in thermal expansion coefficients between the inner scale and Ti3SiC2-base matrix is small. The outer TiO2 layer was under very low compressive stress, while the inner TiO2 + SiO2 layer was under tensile stress during cooling. Scale spaliation is, therefore, not expected and the scale formed on Ti3SiC2-base material is adherent and resistant to cyclic oxidation.

Structure of polyamidoamide dendrimers up to limiting generations: A mesoscale description

The polyamidoamide (PAMAM) class of dendrimers was one of the first dendrimers synthesized by Tomalia and co-workers at Dow. Since its discovery the PAMAMs have stimulated many discussions on the structure and dynamics of such hyperbranched polymers. Many questions remain open because the huge conformation disorder combined with very similar local symmetries have made it difficult to characterize experimentally at the atomistic level the structure and dynamics of PAMAM dendrimers. The higher generation dendrimers have also been difficult to characterize computationally because of the large size (294852 atoms for generation 11) and the huge number of conformations. To help provide a practical means of atomistic computational studies, we have developed an atomistically informed coarse-grained description for the PAMAM dendrimer. We find that a two-bead per monomer representation retains the accuracy of atomistic simulations for predicting size and conformational complexity, while reducing the degrees of freedom by tenfold. This mesoscale description has allowed us to study the structural properties of PAMAM dendrimer up to generation 11 for time scale of up to several nanoseconds. The gross properties such as the radius of gyration compare very well with those from full atomistic simulation and with available small angle x-ray experiment and small angle neutron scattering data. The radial monomer density shows very similar behavior with those obtained from the fully atomistic simulation. Our approach to deriving the coarse-grain model is general and straightforward to apply to other classes of dendrimers.

RETHROTTLE: Execution Throttling in the REDEFINE SoC Architecture

REDEFINE is a reconfigurable SoC architecture that provides a unique platform for high performance and low power computing by exploiting the synergistic interaction between coarse grain dynamic dataflow model of computation (to expose abundant parallelism in applications) and runtime composition of efficient compute structures (on the reconfigurable computation resources). We propose and study the throttling of execution in REDEFINE to maximize the architecture efficiency. A feature specific fast hybrid (mixed level) simulation framework for early in design phase study is developed and implemented to make the huge design space exploration practical. We do performance modeling in terms of selection of important performance criteria, ranking of the explored throttling schemes and investigate effectiveness of the design space exploration using statistical hypothesis testing. We find throttling schemes which give appreciable (24.8%) overall performance gain in the architecture and 37% resource usage gain in the throttling unit simultaneously.

Tensile flow behaviour of 2.25Cr-1Mo ferritic steel base metal and simulated heat affected zone structures of 2.25Cr-1Mo weld joint

Tensile tests in the temperature range 298 to 873 K have been performed on 2.25Cr-1Mo base metal and simulated heat affected zone (HAZ) structures of its weld joint, namely coarse grain bainite, fine grain bainite and intercritical structure. Tensile flow behaviour of all the microstructural conditions could be adequately described by the Hollomon equation (sigma = K-1 epsilon(n1)) at higher (> 623 K) temperatures. Deviation from the Hollomon equation was observed at low strains and lower (< 623 K) temperatures. The Ludwigson modification of Hollomon's equation, sigma = K-1 epsilon(n1) + exp (K-2 + n(2) epsilon), was found to describe the flow curve. In general, the flow parameters n(1), K-1, n(2) and K-2 were found to decrease with increase in temperature except in the intermediate temperature range (423 to 623 K). Peaks/plateaus were observed in their variation with temperature in the intermediate temperature range coinciding with the occurrence of serrated flow in the load-elongation curve. The n(1) Value increased and the K-1 value decreased with the type of microstructure in the order: coarse grain bainite, fine grain bainite, base metal and intercritical structure. The variation of nl with microstructure has been rationalized on the basis of mean free path (MFP) of dislocations which is directly related to the inter-particle spacing. Larger MFP of dislocations lead to higher strain hardening exponents n(1).

Computer simulation of liquid crystals

In this article we review the current status in the modelling of both thermotropic and lyotropic Liquid crystal. We discuss various coarse-graining schemes as well as simulation techniques such as Monte Carlo (MC) and Molecular dynamics (MD) simulations.In the area of MC simulations we discuss in detail the algorithm for simulating hard objects such as spherocylinders of various aspect ratios where excluded volume interaction enters in the simulation through overlap test. We use this technique to study the phase diagram, of a special class of thermotropic liquid crystals namely banana liquid crystals. Next we discuss a coarse-grain model of surfactant molecules and study the self-assembly of the surfactant oligomers using MD simulations. Finally we discuss an atomistically informed coarse-grained description of the lipid molecules used to study the gel to liquid crystalline phase transition in the lipid bilayer system.

Contact pressure of porous Al2O3 probed by nanoindentations

Contact pressure of porous Al2O3 probed by nanoindentation was investigated by dimensional analysis with special attention paid to scaling effects in the mechanical behavior. It was found that, for sample containing small grains and interconnected pores, the contact pressure is manifest dominated by bonding strength of the porous alumina. Whereas the samples with coarse grain and various porous structures exhibit higher contact pressures and smaller residual deformations, which can be attributed to the mechanical response of the solid-phase under current limited peak loads.

Protein structure refinement algorithms

Protein structure prediction has remained a major challenge in structural biology for more than half a century. Accelerated and cost efficient sequencing technologies have allowed researchers to sequence new organisms and discover new protein sequences. Novel protein structure prediction technologies will allow researchers to study the structure of proteins and to determine their roles in the underlying biology processes and develop novel therapeutics.

Difficulty of the problem stems from two folds: (a) describing the energy landscape that corresponds to the protein structure, commonly referred to as force field problem; and (b) sampling of the energy landscape, trying to find the lowest energy configuration that is hypothesized to be the native state of the structure in solution. The two problems are interweaved and they have to be solved simultaneously. This thesis is composed of three major contributions. In the first chapter we describe a novel high-resolution protein structure refinement algorithm called GRID. In the second chapter we present REMCGRID, an algorithm for generation of low energy decoy sets. In the third chapter, we present a machine learning approach to ranking decoys by incorporating coarse-grain features of protein structures.

A fully-nonlocal energy-based formulation and high-performance realization of the quasicontinuum method

The quasicontinuum (QC) method was introduced to coarse-grain crystalline atomic ensembles in order to bridge the scales from individual atoms to the micro- and mesoscales. Though many QC formulations have been proposed with varying characteristics and capabilities, a crucial cornerstone of all QC techniques is the concept of summation rules, which attempt to efficiently approximate the total Hamiltonian of a crystalline atomic ensemble by a weighted sum over a small subset of atoms. In this work we propose a novel, fully-nonlocal, energy-based formulation of the QC method with support for legacy and new summation rules through a general energy-sampling scheme. Our formulation does not conceptually differentiate between atomistic and coarse-grained regions and thus allows for seamless bridging without domain-coupling interfaces. Within this structure, we introduce a new class of summation rules which leverage the affine kinematics of this QC formulation to most accurately integrate thermodynamic quantities of interest. By comparing this new class of summation rules to commonly-employed rules through analysis of energy and spurious force errors, we find that the new rules produce no residual or spurious force artifacts in the large-element limit under arbitrary affine deformation, while allowing us to seamlessly bridge to full atomistics. We verify that the new summation rules exhibit significantly smaller force artifacts and energy approximation errors than all comparable previous summation rules through a comprehensive suite of examples with spatially non-uniform QC discretizations in two and three dimensions. Due to the unique structure of these summation rules, we also use the new formulation to study scenarios with large regions of free surface, a class of problems previously out of reach of the QC method. Lastly, we present the key components of a high-performance, distributed-memory realization of the new method, including a novel algorithm for supporting unparalleled levels of deformation. Overall, this new formulation and implementation allows us to efficiently perform simulations containing an unprecedented number of degrees of freedom with low approximation error.

Modelling Lipid Competition Dynamics in Heterogeneous Protocell Populations

Recent experimental work in the field of synthetic protocell biology has shown that prebiotic vesicles are able to 'steal' lipids from each other. This phenomenon is driven purely by asymmetries in the physical state or composition of the vesicle membranes, and, when lipid resource is limited, translates directly into competition amongst the vesicles. Such a scenario is interesting from an origins of life perspective because a rudimentary form of cell-level selection emerges. To sharpen intuition about possible mechanisms underlying this behaviour, experimental work must be complemented with theoretical modelling. The aim of this paper is to provide a coarse-grain mathematical model of protocell lipid competition. Our model is capable of reproducing, often quantitatively, results from core experimental papers that reported distinct types vesicle competition. Additionally, we make some predictions untested in the lab, and develop a general numerical method for quickly solving the equilibrium point of a model vesicle population.