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A Halbach array is a specialized arrangement of permanent magnets designed to generate a strong, uniform magnetic field in the designated region. This unique configuration has been widely utilized in various applications, including magnetic levitation (maglev) systems, electric motors, particle accelerators, and magnetic seals. The advantages of Halbach arrays include high efficiency, reduced weight, and precise directional control of the magnetic field. Halbach arrays are commonly categorized into two configurations: linear and cylindrical. A linear Halbach array produces a concentrated magnetic field on one face and is frequently employed in maglev trains and conveyor systems to ensure stable and efficient operation. In contrast, a cylindrical Halbach array consists of magnets arranged in a ring, generating a uniform magnetic field within the cylinder while suppressing the external field. This configuration is particularly advantageous in applications such as brushless electric motors and magnetic resonance imaging (MRI) systems. Traditionally, the design of electromagnetic systems incorporating Halbach arrays relied on engineers’ expertise and intuition due to the complexity of the permanent magnet configuration. However, advancements in numerical methods, particularly topology optimization, have introduced a systematic approach to optimizing the shape and distribution of permanent magnets within a given design domain. In the context of Halbach array design, topology optimization aims to maximize the total magnetic flux within a designated region while simultaneously determining the optimal material distribution to achieve a specified design objective. This approach enhances the performance and efficiency of Halbach arrays, providing a more precise and automated framework for their development. In this paper, we propose a Cardinal Basis Function (CBF)-based level-set method for designing a circular Halbach array capable of generating a uniform magnetic field within a designated region. The CBF-based level-set method offers significant computational advantages by reducing the computational cost and accelerating the convergence process. This approach enhances the efficiency of the optimization process, making it a promising technique for the systematic design of Halbach arrays. 

Abstract This paper introduces a new computational framework for modeling and designing morphable surface structures based on an integrated approach that leverages circle packing for surface representation, conformal mapping to link local and global kinematics, and topology optimization for actuator design. The framework utilizes a unique strategy for employing optimized compliant actuators as the basic building blocks of the morphable surface. These actuators, designed as circular elements capable of modifying their radius and curvature, are optimized using level set topology optimization, considering both kinematic performance and structural stiffness. Circle packing is employed to represent the surface geometry, while conformal mapping guides the kinematic analysis, ensuring alignment between local actuator motions and desired global surface transformations. The design process involves mapping optimized component designs back onto the circle packing representation, facilitating coordinated control, and achieving harmony between local and global geometries. This leads to efficient actuation and enables precise control over the surface morphology. The effectiveness of the proposed framework is demonstrated through two numerical examples, showcasing its capability to design complex, morphable surfaces with potential applications in fields requiring dynamic shape adaptation. 

Abstract This paper presents a new computational framework for the co-optimization and co-control of morphable surface structures using topology optimization and circle-packing algorithms. The proposed approach integrates the design of optimized compliant components and the system-level control of the overall surface morphology. By representing the surface shape using circle packing and leveraging conformal mapping, the framework enables smooth deformation between 2D and 3D shapes while maintaining local geometry and global morphology. The morphing surface design problem is recast as designing circular compliant actuators using level-set topology optimization with displacements and stiffness objectives. The optimized component designs are then mapped back onto the circle packing representation for coordinated control of the surface morphology. This integrated approach ensures compatibility between local and global geometries and enables efficient actuation of the morphable surface. The effectiveness of the proposed framework is demonstrated through numerical examples and physical prototypes, showcasing its ability to design and control complex morphable surfaces with applications in various fields. The co-optimization and co-control capabilities of the framework are verified, highlighting its potential for realizing advanced morphable structures with optimized geometries and coordinated actuation. This integrated approach goes beyond conventional methods by considering both local component geometry and global system morphology and enabling coordinated control of the morphable surface. The general nature of our approach makes it applicable to a wide range of problems involving the design and control of morphable structures with complex, adaptive geometries. 

This paper proposes a density-based topology optimization scheme to design a heat sink for the application of a 3D integrated SIC-based 75 kVA Intelligent Power Stage (IPS). The heat sink design considers the heat conduction and convection effects with forced air cooling. The objective function is to minimize the thermal compliance of the whole structure. A volume constraint is imposed to reduce the overall volume of the designed heat sink to make it conformal to the underlying power devices. Some numerical techniques like filtering and projection schemes are employed to render a crisp design. Some 2D benchmarks examples are first provided to demonstrate the effectiveness of the proposed method. Then a 3D heat sink, especially designed for the 3D IPS, is topologically optimized. The classic tree-like structure is reproduced to reinforce the convection effect. Some comparisons with the intuitive baseline designs are made through numerical simulation. The optimized heat sinks are shown to provide a more efficient cooling performance for the 3D integrated power converter assembly. 

Abstract Nanoparticle (NP) assembly has been extensively studied, and a library of NP superstructures has been synthesized. These intricate structures show unique collective optical, electronic, and magnetic properties. In this work, we report a bottom‐up approach for fabricating spherical gold nanoparticle (AuNP) assemblies that mimic colloidosomes. Co‐crystallization of lipoic acid‐end‐functionalized poly(ethylene oxide) (PEO) and AuNPs in solution via a self‐seeding method led to the formation of hollow spherical NP assemblies named nanoparticle crystalsomes (NPCs). Due to the spherical shape, the translational symmetry of PEO crystals is broken in NPCs, which can be attributed to the competition between NP close packing and polymer crystallization. This was confirmed by tuning the NPC morphology via varying the self‐seeding temperature, crystallization temperature, and PEO molecular weight. We envisage that this strategy paves the way to attaining exquisite morphological control of NP assemblies with broken translational symmetry.