Non-regular Shapes Research Articles

Automated design of 3D DNA origami with non-rasterized 2D curvature

Improving the precision and function of encapsulating three-dimensional (3D) DNA nanostructures via curved geometries could have transformative impacts on areas such as molecular transport, drug delivery, and nanofabrication. However, the addition of non-rasterized curvature escalates design complexity without algorithmic regularity, and these challenges have limited the ad hoc development and usage of previously unknown shapes. In this work, we develop and automate the application of a set of previously unknown design principles that now includes a multilayer design for closed and curved DNA nanostructures to resolve past obstacles in shape selection, yield, mechanical rigidity, and accessibility. We design, analyze, and experimentally demonstrate a set of diverse 3D curved nanoarchitectures, showing planar asymmetry and examining partial multilayer designs. Our automated design tool implements a combined algorithmic and numerical approximation strategy for scaffold routing and crossover placement, which may enable wider applications of general DNA nanostructure design for nonregular or oblique shapes.

A field evidence model: how to predict transport in heterogeneous aquifers at low investigation level

Abstract. Aquifer heterogeneity in combination with data scarcity is a major challenge for reliable solute transport prediction. Velocity fluctuations cause non-regular plume shapes with potentially long-tailing and/or fast-travelling mass fractions. High monitoring cost and a shortage of simple concepts have limited the incorporation of heterogeneity into many field transport models up to now. We present an easily applicable hierarchical conceptualization strategy for hydraulic conductivity to integrate aquifer heterogeneity into quantitative flow and transport modelling. The modular approach combines large-scale deterministic structures with random substructures. Depending on the modelling aim, the required structural complexity can be adapted. The same holds for the amount of monitoring data. The conductivity model is constructed step-wise following field evidence from observations, seeking a balance between model complexity and available field data. The starting point is a structure of deterministic blocks, derived from head profiles and pumping tests. Then, subscale heterogeneity in the form of random binary inclusions is introduced to each block. Structural parameters can be determined, for example, from flowmeter measurements or hydraulic profiling. As proof of concept, we implemented a predictive transport model for the heterogeneous MADE site. The proposed hierarchical aquifer structure reproduces the plume development of the MADE-1 transport experiment without calibration. Thus, classical advection–dispersion equation (ADE) models are able to describe highly skewed tracer plumes by incorporating deterministic contrasts and effects of connectivity in a stochastic way without using uni-modal heterogeneity models with high variances. The reliance of the conceptual model on few observations makes it appealing for a goal-oriented site-specific transport analysis of less well investigated heterogeneous sites.

Multi-directional Assessment of Respiratory and Cardiac Pulsatility of the Inferior Vena Cava From Ultrasound Imaging in Short Axis

The pulsatility of the inferior vena cava (IVC) reflects the volume status of patients. It can be investigated by ultrasounds (US), offering an important non-invasive tool supporting fluid management. However, the method has limitations attributable to many confounding factors, e.g., related to IVC movements and non-regular shapes. Short- or long-axis views have been used, both having advantages and limitations in counteracting such confounding factors, depending on the specific condition. The aim of this study is to investigate IVC pulsatility in the different directions on the transverse plane and to assess its variability. Moreover, different components of this pulsatility (induced by either respiratory or cardiac activity) are investigated. The method is tested on 10 healthy patients, with large variations across them of IVC section (mean diameters in the range 1 cm to 3 cm), shape and pulsatility (average caval index [CI] ranging from approximately 20% to 70%). The average coefficient of variation of the CI estimated on 10 different directions was 13% (21% and 20% for the respiratory and cardiac components, respectively), with a range that was approximately 50% of the mean CI across different directions (approximately the same for the 2 different components). The minimum and maximum CI were found close to the directions of maximum and minimum IVC diameter, respectively. The investigation of IVC dynamics in the entire cross-section is crucial to obtain a more repeatable and reliable characterization of IVC pulsatility. The calculation of a CI based on the “equivalent” diameter (proportional to the square root of the IVC cross-sectional area) is encouraged.

Ventilation efficiency assessment according to the variation of opening position in L-shaped rooms

Air change efficiency evaluates the ability of a system to achieve the change of the air contained in a confined interior space. It is conditioned by the geometry of the room, the different openings and the properties of the air among others. Rectangular rooms do not offer impediments when mixing the interior air; however, in rooms with non-regular shapes, stagnation phenomenon can occur in the corners. This paper proposes the study of the air change efficiency in an L-shaped room in which the position of the inlet and outlet openings is sequentially variated. This study is based on the execution of successive numerical simulations, validated by experimental studies. The results show that there are differences on the ventilation efficiency of up to 13.49% between the most dissimilar cases, which occur when one of the openings is located in a corner. If the other opening is placed nearby, the results are very poor; whereas if it is placed at the opposite corner, the efficiency value improves due to the circulation of the air through the room. When these openings are placed near the centre of the room, the efficiencies that are obtained are more similar and this analysis is less relevant.

Building irregularity issues and architectural design in seismic areas

When designing buildings in seismic areas, choices of the architectural designer heavily influences seismic structural performances. Namely, building morphology may lead to complex seismic responses as it occurs when building plan and elevation become irregular. Typical irregularities are due to architectural, functional and distribution constraints, thus leading to plan or vertical or combined plan/vertical irregularities. A frequent plan-wise irregularity arises when earthquake resistant structures, such as cores and shear walls, are concentrated on one side of the building plan, while vertical irregularity often arises from the presence of soft stories especially located at the ground level or, less frequently, at an intermediate level.In the last decades, some trends in architectural design, such as Deconstructivism and other contemporary theories, worked in pursuing architectural solutions based on the concept of “deconstruction” in place of “construction”, favoring non-rigid schemes, non-regular shapes and, more generally, avoiding geometric rules and classical canons of symmetry and regularity. In this paper the above issues are investigated with the goal of assessing effects of irregularity conditions, introduced by the architectural design, on the building seismic performances with the aim at not forbidding the designer ambitions but at making him aware of the effects of his architectural choices

Integration of Novel Shape Templates During Human Spatial Navigation Leads to Prototype Extraction

The ability to rapidly form stable representations of novel environments is crucial for successful navigation, yet the majority of studies involve environments composed of overlearned geometrical configurations, like rectangles. To address this gap in knowledge, participants underwent extensive pre-training with a non-regular shape and then navigated environments organized around this shape and other parametrically related novel non-regular shapes. Concurrent high-resolution fMRI indicated that, consistent with past studies on regular geometries, hippocampal neural activation patterns differentiated these environments, although with a bias toward the pre-exposed shape. Surprisingly, we found that hippocampal representations were most stable for the average geometric configuration of the novel environments, with subsequent map-drawing accuracy predictive of the stability of this average. Our findings challenge existing models of memory and navigation by suggesting unique mechanisms underlie the formation of novel spatial contexts, which may only become apparent under conditions that directly manipulate the influence of prior knowledge.

Computational study of the wind load on a free-form complex thin shell structure

The accelerated development of new materials, technologies and construction processes, in parallel with advances in computational algorithms and ever growing computational power, is leading to more daring and innovative architectural and structural designs. The search for non-regular building shapes and slender structures, as alternative to the traditional architectural forms that have been prevailing in the building sector, poses important engineering challenges in the assessment of the strength and mechanical stability of non-conventional structures and systems, namely against highly variable actions as wind and seismic forces. In case of complex structures, laboratory experiments are a widely used methodology for strength assessment and loading characterization. Nevertheless, powerful numerical tools providing reliable results are also available today and able to compete with the experimental approach. In this paper the wind action on a free-form complex thin shell is investigated through 3D-CFD simulation in terms of the pressure coefficients and global forces generated. All the modelling aspects and calibrating process are described. The results obtained showed that the CFD technique is effective in the study of the wind effects on complex-shaped structures.

Effect of growth condition on structure and optical properties of hybrid Ag-CuO nanomaterials

This study aimed to use hydrothermal-microwave process to synthesize hybrid Ag-CuO nanomaterials. The effects of different irradiation time ranging 5–20min, and reaction temperatures ranging 120–180°C on the structure and optical properties of the samples were studied. The X-ray diffraction assessments indicated that the synthesized nanomaterials had Ag and CuO phases. The elemental analyses confirmed the presence of Ag, Cu, and O in the samples. Transmission electron microscopy images revealed non-regular and impacted shapes of Ag and CuO. Increasing the reaction temperature and irradiation time increased the absorption intensity of the samples. Furthermore, increasing the irradiation time induced a shift in the absorption edge towards larger wavelengths (red shift), while increasing the reaction temperature shifted it towards smaller wavelengths (blue shift).

3D simulation of short fatigue crack propagation by finite element crystal plasticity and remeshing

An iterative method to simulate 3D fatigue crack propagation in crystalline materials is proposed and demonstrated on simple test cases. The method relies on the computation of a damage indicator based on plastic activity around the crack tip. By post-processing this quantity after a given loading sequence, local crack direction and growth rate are estimated along the crack path. Dedicated remeshing routines allow the crack to propagate in 3D and the iterative process can continue with the updated crack geometry. Two examples in a BCC single crystal featuring different slip systems demonstrate the crack propagation simulations under cyclic loading over distances comparable to the crystal size and with non-regular crack shapes such as zig-zag crack paths. The effect of transferring plastic fields between propagation steps is also analysed.

Temperature variation aware multi-scale delay, power and thermal analysis at RT and gate level

Thermal effects are rapidly gaining importance in nanometer CMOS technologies. Increased power density, coupled with spatio-temporal variability of chip workloads, causes on-die temperature non-uniformities. The assumption of a uniform temperature for the delay and power analysis of a large CMOS circuit produces inaccurate results. For this reason, significant design margins are taken to ensure safe operation. To improve design quality, we need precise localization of hotspots at detailed spatial resolution which is very computationally intensive. Consequently, thermal analysis needs to be done at multiple levels of granularity using a versatile thermal floorplan. We propose MiMAPT, an approach for analyzing delay, power and temperature in digital circuits. MiMAPT integrates seamlessly into major industrial Front-end and Back-end chip design flows. It accounts for temperature non-uniformities and self-heating while performing analysis. Thermal analysis is done at register-transfer (RT) and then gate-level considering non-regular shapes of on-die units with multiple scales of resolution and speed. To demonstrate the capability of MiMAPT in temperature variation aware delay/power estimation, a widely used IP block is chosen and four different chips are implemented using 65nm and 40nm (LVT, HVT) technology nodes. Different temperature patterns are then applied to the design. Accuracy improvements of up to 28% for static power and 16% for minimum clock period are reported in comparison with uniform averaged temperature assumption. Evaluating the ability of MiMAPT in multi-scale thermal analysis, a speed-up of 98× is reported compared to fine-grained method, while keeping false negatives at zero and the error of temperature estimation below 0.05°C.

Dealing with Nonregular Shapes Packing

This paper addresses the irregular strip packing problem, a particular two-dimensional cutting and packing problem in which convex/nonconvex shapes (polygons) have to be packed onto a single rectangular object. We propose an approach that prescribes the integration of a metaheuristic engine (i.e., genetic algorithm) and a placement rule (i.e., greedy bottom-left). Moreover, a shrinking algorithm is encapsulated into the metaheuristic engine to improve good quality solutions. To accomplish this task, we propose a no-fit polygon based heuristic that shifts polygons closer to each other. Computational experiments performed on standard benchmark problems, as well as practical case studies developed in the ambit of a large textile industry, are also reported and discussed here in order to testify the potentialities of proposed approach.

A Practical Low-Power Nonregular Interconnect Design With Manufacturing for Design Approach

Wire shaping for delay/power minimization has been extensively studied. Due to the perceived high design and manufacturing costs for using nonregular wire shapes, wire shaping is generally considered to be impractical. In this paper, we present a practical wire shaping method to reduce power consumption of interconnect. Nonregular wire shapes are directly implemented on silicon wafer instead of in GDSII during design. We present novel enhancements to existing optical proximity correction (OPC) technology to accurately print nonregular wire shapes. Experimental results show that the post-OPC mask complexities of uniform wire and nonregular wire are comparable. With minimal impact on the design and manufacturing flows and minimal additional design and manufacturing costs, we demonstrate that wire shaping can help to obtain substantial reduction of interconnect dynamic power without affecting timing closure. Our wire shaping methodology is an excellent example of Manufacturing for Design.

Lacunarity as a novel measure of cancer cells behavior

An important goal in many branches of science, especially in molecular biology and medicine is the quantitative analysis of the structures and their morphology. The morphology can be analyzed in many ways, in particular by the fractal analysis. Apart from the fractal dimension, an important part of the fractal analysis is the lacunarity measurement which, roughly speaking, characterizes the distribution of gaps in the fractal: a fractal with high lacunarity has large gaps. In this paper, we present an extension of the lacunarity measure to objects with nonregular shapes that enables us to provide a successful discrimination of cancer cell lines. The cell lines differ in the shape of vacuole (the gaps in their body) which is perfectly suited for the lacunarity analysis.

Digitization of non-regular shapes in arbitrary dimensions

The preservation of topological properties during digitization is a hard problem in 3 and higher dimensions. Only for the very restricted class of r-regular shapes it is known that the connectivity and inclusion properties of shape components do not change. In a previous paper it was shown for the 2D case, how a much wider class of shapes, for which the morphological open–close and the close–open-operator with an r-disc lead to the same result, can be digitized correctly in this sense by using an additional repairing step. This paper extends this to the arbitrary dimensions and analyses the difficulties which occur in 3 or higher dimensional spaces. The repairing step is easy to compute, parallelizable and does not change as much hyper-voxels as a preprocessing regularization step. The results are applicable for arbitrary, even irregular, sampling grids in arbitrary dimensions.

Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners

Flushing of the inter-electrode gap is of critical importance in the performance of electrical discharge sinking operations. When the provision of flushing holes in the tool or the workpiece is impractical, effective flushing is best realized by inducing a relative motion between the electrodes. This paper relates to a novel application inspired by the kinematics of a Reuleaux Triangle that facilitates flushing through synchronous orbiting of a rotating curvilinear tool. This innovative scheme enables the machining of regular as well as non-regular polygonal shapes with sharp corners. Experimental results from implementing this concept on a 4-axis CNC EDM machine tool are presented.

Form-finding of complex tensegrity structures: application to cell cytoskeleton modelling

The ability to model the mechanical behaviour of the cell cytoskeleton as realistically as possible is a key point in understanding numerous biological mechanisms. Tensegrity systems have already demonstrated their pertinence for this purpose. However, the structures considered until now are based only on models with simplified geometry and topology compared to the true complexity of cytoskeleton architecture. The aim of this Note is to propose a form-finding method for generating nonregular tensegrity shapes of higher diversity and complexity. The process relies on the use of the dynamic relaxation method. Further improvements have made it possible to control the computed morphologies and to modify them to approach experimentally observed configurations. Various examples illustrate the use of the method and the results obtained for different cell typologies. To cite this article: H. Baudriller et al., C. R. Mecanique 334 (2006).

Complex and Non-Regular Shapes: Their Evolution in Greek Textbooks (1749–1971)

Current research suggests that problem solving concerning complex and non-regular shapes can enhance the acquisition of the concept of area. Despite the fact that this topic was always present in Greek mathematical textbooks it disappeared in the modern ones. In this paper we deal with the way the specific topic has been presented for a long period (since 1749 until 1971). We describe the methods that known Greek scholars proposed for the calculation of the area of complex and non-regular shapes and how the content of the relevant problems varies through these three centuries according to the social circumstances that affected the philosophy of the educational system.

Monte Carlo Inversion of DInSAR Data for Dislocation Modeling: Application to the 1997 Umbria-Marche Seismic Sequence (Central Italy)

— The study of surface deformation due to seismic activity is often made using dislocations with uniform slip and simple geometries. A better modeling of coseismic and postseismic surface displacements can be obtained by using dislocations with variable slip and nonregular shapes. This is consistent with the asperity model of fault surfaces, assuming a friction distribution on faults made of locked zones with much higher friction than surrounding zones. In this paper we consider the 1997–1998 Colfiorito seismic sequence. The coseismic surface displacements in the Colfiorito zone are used in order to infer the slip distribution on the fault surface at different stages of the sequence. The displacement field has been modeled varying the slip distribution on the fault, and comparing the deformation observed by SAR and GPS techniques with model results. The slip distribution is calculated by Monte Carlo simulations on a normal fault with the dip angle equal to 40°. A good approximation is obtained by using square asperity units of 1.5×1.5 km2. In the first stage, we employed a simplified model with uniform slip, in which each asperity unit is allowed to slip a constant amount or not to slip at all, and in the second stage, we evaluate the slip distribution in the dislocation area determined by the Monte Carlo inversion: in this case we allow unit cells to undergo different values of slip in order to refine the initial dislocation model. The results show that the 1997 seismic events of the sequence can be modeled by irregular dislocations, obtaining a good fit to the DInSAR and GPS observations. The model also confirms the results of previous studies by a different methodology, defining the distribution of asperities on the fault plane using the fault geometry, the geodetic data and the seismic moment of the 1997–1998 Colfiorito seismic sequence. Furthermore, the analysis of 1997 aftershocks in the seismogenic region shows a strong correlation between most events and the asperity distribution, which can be considered as an independent test of the validity of the model.

Optimized secondary concentrators for a partitioned central receiver system

We present secondary concentrators with non-regular shapes for increasing the concentration of radiation from a given field of heliostats, well suited for partitioning the receiver into several units, arranged side by side. For a general heliostat field with a non-axisymmetric directional distribution of the radiation at the entrance aperture of the secondary concentrator, concentrators with non-regular shape can significantly increase the concentration as compared to their symmetric analogs. Our optimizations indicate best results for concentrators based on rectangular entrance and exit apertures. The concentration may be increased by a factor of 2.3 at an optical efficiency of 90%. If the shape of the exit aperture is required to be close to circular, concentrators based on non-regular hexagonal apertures may reach concentration higher than their symmetric analogs by a factor of 1.3. For the given radiation, concentrators with polygonal apertures perform significantly better than concentrators with smooth elliptic apertures.

Solving linear diffusion‐reaction networks in porous catalyst particles using BEM

AbstractMultiple diffusion reactions are frequently encountered in the modeling of heterogeneous catalytic reactors. Obtaining an accurate estimate of the yield and selectivity in such reactions is crucial for an optimal design of reactors. Due to the inadequacy of analytical techniques in handling nonuniform catalyst shapes and mixed boundary conditions, numerical techniques are often employed to compute these design parameters. Among other numerical techniques, the boundary element method (BEM) is a superior method to solve linear diffusion reaction problems. The integral nature of the BEM formulation allows for boundary‐only discretization of the particle, thus reducing the computer execution time and the data preparation effort. A boundary element algorithm is developed to solve a network of linear diffusion reactions in porous catalyst particles in two dimensions. For this purpose, a matrix of fundamental solutions is defined and derived. The developed algorithm is applied to complex reaction networks to obtain the yield of intermediates for nonregular catalyst shapes and nonuniform boundary conditions. The method can be used as a design tool to study particle scale modeling in detail and can be incorporated into an overall reactor model.