A novel triple periodic minimal surface-like plate lattice and its data-driven optimization method for superior mechanical properties

Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM)technologies.In this work,a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes.The parametric model takes the basic unit of the triple periodic minimal surface(TPMS)lattice as a skeleton and adopts a set of generation parameters to determine the plate lattice structure with different topologies,which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity,and therefore is referred to as a TPMS-like plate lattice(TLPL).Furthermore,a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints.In this method,the genetic algorithm for the optimization is utilized for global search capability,and an artificial neural network(ANN)model for individual fitness estimation is integrated for high efficiency.A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting(SLM)fabricated samples.It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures.

Enhanced energy-absorbing and sound-absorbing capability of functionally graded and helicoidal lattice structures with triply periodic minimal surfaces

Lattice structures have drawn much attention in engineering applications due to their lightweight and multi-functional properties.In this work,a mathematical design approach for functionally graded(FG)and helicoidal lattice structures with triply periodic minimal surfaces is proposed.Four types of lattice structures including uniform,helicoidal,FG,and combined FG and helicoidal are fabricated by the additive manufacturing technology.The deformation behaviors,mechanical properties,energy absorption,and acoustic properties of lattice samples are thoroughly investigated.The load-bearing capability of helicoidal lattice samples is gradually improved in the plateau stage,leading to the plateau stress and total energy absorption improved by over 26.9%and 21.2%compared to the uniform sample,respectively.This phenomenon was attributed to the helicoidal design reduces the gap in unit cells and enhances fracture resistance.For acoustic properties,the design of helicoidal reduces the resonance frequency and improves the peak of absorption coefficient,while the FG design mainly influences the peak of absorption coefficient.Across broad range of frequency from 1000 to 6300 Hz,the maximum value of absorption coefficient is improved by18.6%-30%,and the number of points higher than 0.6 increased by 55.2%-61.7%by combining the FG and helicoidal designs.This study provides a novel strategy to simultaneously improve energy absorption and sound absorption properties by controlling the internal architecture of lattice structures.

Adaptive enhancement design of triply periodic minimal surface lattice structure based on non-uniform stress distribution

The Schwarz primitive triply periodic minimal surface(P-type TPMS)lattice structures are widely used.However,these lattice structures have weak load-bearing capacity compared with other cellular structures.In this paper,an adaptive enhancement design method based on the non-uniform stress distribution in structures with uniform thickness is proposed to design the P-type TPMS lattice structures with higher mechanical properties.Two types of structures are designed by adjusting the adaptive thickness distribution in the TPMS.One keeps the same relative density,and the other keeps the same of non-enhanced region thickness.Compared with the uniform lattice structure,the elastic modulus for the structure with the same relative density increases by more than 17%,and the yield strength increases by more than 10.2%.Three kinds of TPMS lattice structures are fabricated by laser powder bed fusion(L-PBF)with 316L stainless steel to verify the proposed enhanced design.The manufacture-induced geometric deviation between the as-design and as-printed models is measured by micro X-ray computed tomography(μ-CT)scans.The quasi-static compression experimental results of P-type TPMS lattice structures show that the reinforced structures have stronger elastic moduli,ultimate strengths,and energy absorption capabilities than the homogeneous P-TPMS lattice structure.

Channel Estimation for Reconfigurable Intelligent Surface Aided Multiuser Millimeter-Wave/THz Systems

It is assumed that reconfigurable intelligent surface(RIS)is a key technology to enable the potential of mmWave communications.The passivity of the RIS makes channel estimation difficult because the channel can only be measured at the transceiver and not at the RIS.In this paper,we propose a novel separate channel estimator via exploiting the cascaded sparsity in the continuously valued angular domain of the cascaded channel for the RIS-enabled millimeter-wave/Tera-Hz systems,i.e.,the two-stage estimation method where the cascaded channel is separated into the base station(BS)-RIS and the RIS-user(UE)ones.Specifically,we first reveal the cascaded sparsity,i.e.,the sparsity exists in the hybrid angular domains of BS-RIS and the RIS-UEs separated channels,to construct the specific sparsity structure for RIS enabled multi-user systems.Then,we formulate the channel estimation problem using atomic norm minimization(ANM)to enhance the proposed sparsity structure in the continuous angular domains,where a low-complexity channel estimator via Alternating Direction Method of Multipliers(ADMM)is proposed.Simulation findings demonstrate that the proposed channel estimator outperforms the current state-of-the-arts in terms of performance.

Triply periodic minimal surface(TPMS)porous structures:from multi-scale design,precise additive manufacturing to multidisciplinary applications

Inspired by natural porous architectures,numerous attempts have been made to generate porous structures.Owing to the smooth surfaces,highly interconnected porous architectures,and mathematical controllable geometry features,triply periodic minimal surface(TPMS)is emerging as an outstanding solution to constructing porous structures in recent years.However,many advantages of TPMS are not fully utilized in current research.Critical problems of the process from design,manufacturing to applications need further systematic and integrated discussions.In this work,a comprehensive overview of TPMS porous structures is provided.In order to generate the digital models of TPMS,the geometry design algorithms and performance control strategies are introduced according to diverse requirements.Based on that,precise additive manufacturing methods are summarized for fabricating physical TPMS products.Furthermore,actual multidisciplinary applications are presented to clarify the advantages and further potential of TPMS porous structures.Eventually,the existing problems and further research outlooks are discussed.

A NOTE ON CONICAL KHLER-RICCI FLOW ON MINIMAL ELLIPTIC KHLER SURFACES

We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Kahler-Ricci flow on a minimal elliptic Kahler surface converges in the sense of currents to a generalized conical Kahler-Einstein on its canonical model. Moreover, the convergence takes place smoothly outside the singular fibers and the chosen divisor.

DEGREE 3 ALGEBRAIC MINIMAL SURFACES IN THE 3-SPHERE

We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.

Innovative Design and Additive Manufacturing of Regenerative Cooling Thermal Protection System Based on the Triply Periodic Minimal Surface Porous Structure

The new regenerative cooling thermal protection system exhibits the multifunctional characteristics of load-carrying and heat exchange cooling,which are fundamental for the lightweight design and thermal protection of hypersonic vehicles.Triply periodic minimal surface(TPMS)is especially suitable for the structural design of the internal cavity of regenerative cooling structures owing to its excellent structural characteristics.In this study,test pieces were manufactured using Ti6Al4V lightweight material.We designed three types of porous test pieces,and the interior was filled with a TPMS lattice(Gyroid,Primitive,I-WP)with a porosity of 30%.All porous test pieces were manufactured via selective laser melting technology.A combination of experiments and finite element simulations were performed to study the selection of the internal cavity structure of the regenerative cooling thermal protection system.Hence,the relationship between the geometry and mechanical properties of a unit cell is established,and the deformation mechanism of the porous unit cell is clarified.Among the three types of porous test pieces,the weight of the test piece filled with the Gyroid unit cell was reduced by 8.21%,the average tensile strength was reduced by 17.7%compared to the solid test piece,while the average tensile strength of the Primitive and I-WP porous test pieces were decreased by 30.5%and 33.3%,respectively.Compared with the other two types of unit cells,Gyroid exhibited better mechanical conductivity characteristics.Its deformation process was characterised by stretching,shearing,and twisting,while the Primitive and I-WP unit cells underwent tensile deformation and tensile and shear deformation,respectively.The finite element predictions in the study agree well with the experimental results.The results can provide a basis for the design of regenerative cooling thermal protection system.

The effect of porosity on the mechanical properties of 3D-printed triplyperiodic minimal surface (TPMS) bioscaffold

Prevailing tissue degeneration caused by musculoskeletal maladies poses a great demand on bioscaffolds,which are artificial,biocompatible structures implanted into human bodies with appropriate mechanical properties.Recent advances in additive manufacturing,i.e.,3D printing,facilitated the fabrication of bioscaffolds with unprecedented geometrical complexity and size flexibility and allowed for the fabrication of topologies that would not have been achieved otherwise.In our work,we explored the effect of porosity on themechanical properties of a periodic cellular structure.The structure was derived from the mathematically created triply periodic minimal surface(TPMS),namely the Sheet-Diamond topology.First,we employed a series of software including MathMod,Meshmixer,Netfabb and Cura to design the model.Then,we utilized additive manufacturing technology to fabricate the cellular structures with designated scale.Finally,we performed compressive testing to deduce the mechanical properties of each cellular structure.Results showed that,in comparison with the highporosity group,the yield strength of the low-porosity group was 3 times higher,and the modulus was 2.5 times larger.Our experiments revealed a specific relationship between porosity and Young’s modulus of PLA-made Sheet-Diamond TPMS structure.Moreover,it was observed that the high-and low-porosity structures failed through distinctive mechanisms,with the former breaking down via buckling and the latter via micro-fracturing.

Control mesh representation of a class of minimal surfaces

Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right helicoid and catenoid as special examples. We firstly construct the Bézier-like basis called AHT Bézier basis in the space spanned by {1, t, sint, cost, sinht, cosht}, t∈[0,α], α∈[0,5π/2]. Then we propose the control mesh representation of the generalized helicoid using the AHT Bézier basis. This kind of representation enables generating the minimal surfaces using the de Casteljau-like algorithm in CAD/CAGD mod- elling systems.

Robust construction of minimal surface from general initial mesh

We analyze three commonly used energy functions in solving Plateau-Mesh Prob- lem, that is, Dirichlet, area, and the discrete mean curvature（DMC）. They all possess unique advantages compared to others, but their drawbacks restrict their usages individually. Our algo- rithm combines the three steps together to make full use of their features. At first the Dirichlet energy is optimized for faster approximation with better topology. Then the area energy is used to come close to the constrained domain. Finally the DMC energy is engaged to achieve a better converging step. Results show that our method can work under a rather noisy initial mesh, which is even topologically different from the final result.

Computing Open-Loop Optimal Control of the q-Profile in Ramp-Up Tokamak Plasmas Using the Minimal-Surface Theory

The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op-timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID （proportional-integral-derivative） controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.

ON THE AREAS OF THE MINIMAL TRIANGLES IN VEECH SURFACES

Smillie and Weiss proved that the set of the areas of the minimal triangles of Veech surfaces with area 1 can be arranged as a strictly decreasing sequence{an}.And each an in the sequence corresponds to finitely many affine equivalent classes of Veech surfaces with area 1.In this article,we give an algorithm for calculating the area of the minimal triangles in a Veech surface and prove that the first element of{an}which corresponds to non arithmetic Veech surfaces is(5-√5)/20,which is uniquely realized by the area of the minimal triangles of the normalized golden L-shaped translation surface up to affine equivalence.

Minimal Surfaces and Gauss Curvature of Conoid in Fins-ler Spaces with (<i>α</i>, <i>β</i>)-Metrics

In this paper, minimal submanifolds in Finsler spaces with (α, β)-metrics are studied. Especially, helicoids are also minimal in (α, β)-Minkowski spaces. Then the minimal surfaces of conoid in Finsler spaces with (α, β)-metrics are given. Last, the Gauss curvature of the conoid in the 3-dimension Randers-Minkowski space is studied.

Delay Minimization for Intelligent Reflecting Surface Assisted Federated Learning

Federated learning(FL), which allows multiple mobile devices to cooperatively train a machine learning model without sharing their data with the central server, has received widespread attention.However, the process of FL involves frequent communications between the server and mobile devices,which incurs a long latency. Intelligent reflecting surface(IRS) provides a promising technology to address this issue, thanks to its capacity to reconfigure the wireless propagation environment. In this paper, we exploit the advantage of IRS to reduce the latency of FL. Specifically, we formulate a latency minimization problem for the IRS assisted FL system, by optimizing the communication resource allocations including the devices’ transmit-powers, the uploading time, the downloading time, the multi-user decomposition matrix and the phase shift matrix of IRS. To solve this non-convex problem, we propose an efficient algorithm which is based on the Block Coordinate Descent(BCD) and the penalty difference of convex(DC) algorithm to compute the solution. Numerical results are provided to validate the efficiency of our proposed algorithm and demonstrate the benefit of deploying IRS for reducing the latency of FL. In particular, the results show that our algorithm can outperform the baseline of Majorization-Minimization(MM) algorithm with the fixed transmit-power by up to 30%.

A narrative review of ocular surface disease considerations in the management of glaucoma

s from those searches were screened for relevance to our review topics.Publications were included if the subjects included glaucoma patients,and if ocular surface outcomes were described.Non-English papers were excluded.Key Content and Findings:Topical glaucoma medications frequently cause adverse effects on the ocular surface,both through direct action of the medications themselves as well as through toxicity from their associated preservatives.Optimization of the ocular surface may improve medication compliance rates.Traditional surgical treatments for glaucoma,such as trabeculectomy,can exacerbate OSD by disrupting the ocular surface but can also reduce the need for chronic medications.Optimization of ocular surface health is imperative in reducing trabeculectomy complication rates,while also potentially reducing the need for trabeculectomy in patients that are able to achieve intraocular pressure control through improved drop tolerability.The introduction of MIGS represents a promising alternative to existing therapies and has been shown to alleviate the overall medication burden.It would be reasonable to assume that decreasing the medication burden could reduce OSD prevalence and severity.However,more research is needed to directly assess the extent of improvement seen after MIGS.Conclusions:A comprehensive understanding of the importance of OSD in medical and surgical management of glaucoma is essential in optimizing patient care and improving outcomes.

A Simple Proof of ACC for Minimal Log Discrepancies for Surfaces

Following Shokurov's idea,we give a simple proof of the ACC conjecture for minimal log discrepancies for surfaces.

Geometrical design of blade's surface and boundary control of Navier-Stokes equations

In this article a new principle of geometric design for blade's surface of an impeller is provided.This is an optimal control problem for the boundary geometric shape of flow and the control variable is the surface of the blade.We give a minimal functional depending on the geometry of the blade's surface and such that the flow's loss achieves minimum.The existence of the solution of the optimal control problem is proved and the Euler-Lagrange equations for the surface of the blade are derived.In addition,under a new curvilinear coordinate system,the flow domain between the two blades becomes a fixed hexahedron,and the surface as a mapping from a bounded domain in R2 into R3,is explicitly appearing in the objective functional.The Navier-Stokes equations,which include the mapping in their coefficients,can be computed by using operator splitting algorithm.Furthermore,derivatives of the solution of Navier-Stokes equations with respect to the mapping satisfy linearized Navier-Stokes equations which can be solved by using operator splitting algorithms too.Hence,a conjugate gradient method can be used to solve the optimal control problem.

Jacobian-free Newton-Krylov subspace method with wavelet-based preconditioner for analysis of transient elastohydrodynamic lubrication problems with surface asperities

This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free Newtongeneralized minimal residual(GMRES) from the Krylov subspace method(KSM). The acceleration of the GMRES iteration is accomplished by a wavelet-based preconditioner.The profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of bearings.The analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest.

On Translation Hypersurfaces with Constant Mean Curvature in (n+1)-Dimensional Spaces

The translation hypersurfaces with nonzero constant mean curvature in (n+1) dimensional spaces are studied. It is the generalization of the classical Scherk theorem. The classification of translation hypersurfaces with nonzero constant mean curvature in Euclidean and Lorentz spaces is completely given.