Compatibility Conditions Research Articles

The 3D Euler equations with inflow, outflow and vorticity boundary conditions

The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of velocity when either the full value of the velocity is specified on inflow, or only the normal component is specified along with the vorticity (and an additional constraint). We derive compatibility conditions to obtain regularity in a Hölder space with prescribed arbitrary index, and allow multiply connected domains. Our results apply as well to impermeable boundaries, establishing higher regularity of solutions in Hölder spaces.

A two-stage hybrid flow-shop formulation for sterilization processes in hospitals

Sterile processing is a critical secondary process and a major cost factor in the processing, acquisition, and storage of costly medical devices. This article aims to improve the performance of sterile processing by developing, implementing, and evaluating a dispatching rule-based algorithm to reduce the time medical devices spend in the central sterile supply department using a two-stage hybrid flow-shop formulation. The algorithm combines dispatching rules with stage decomposition and compatibility conditions. A genetic algorithm is designed to benchmark the performance in addition to an analytic bound. Real-world data from a large German hospital were used to test the effectiveness of the heuristics. The case study demonstrated the practical implications of the approach, leading to a reduction in the time medical devices spend in the system and improved utilization of washer-disinfector machines and sterilizers. It also highlighted the importance of aligning machine capacity with demand and the potential trade-offs associated with batch processing decisions. Our approach can contribute to substantial operational cost savings and efficiency gains, offering significant benefits to decision makers at both the operational and tactical levels.

TOP2DFVT: An Efficient Matlab Implementation for Topology Optimization based on the Finite-Volume Theory.

The finite-volume theory has shown to be numerically efficient and stable for topology optimization of continuum elastic structures. The significant features of this numerical technique are the local satisfaction of equilibrium equations and the employment of compatibility conditions along edges in a surface-averaged sense. These are essential properties to adequately mitigate some numerical instabilities in the gradient version of topology optimization algorithms, such as checkerboard, mesh dependence, and local minima issues. Several computational tools have been proposed for topology optimization employing analysis domains discretized with essential features for finite-element approaches. However, this is the first contribution to offer a platform to generate optimized topologies by employing a Matlab code based on the finite-volume theory for compliance minimization problems. The Top2DFVT provides a platform to perform 2D topology optimization of structures in Matlab, from domain initialization for structured meshes to data post-processing. This contribution represents a significant advancement over earlier publications on topology optimization based on the finite-volume theory, which needed more efficient computational tools. Moreover, the Top2DFVT algorithm incorporates SIMP and RAMP material interpolation schemes alongside sensitivity and density filtering techniques, culminating in a notably enhanced optimization tool. The application of this algorithm to various illustrative cases confirms its efficacy and underscores its potential for advancing the field of structural optimization.

Theoretical research on load distribution of composite pre-tightened teeth connections embedded with soft layers

Abstract It has been proved by experiments that the soft layers can effectively adjust the load distribution ratio of composite pre-tightened tooth connection, but theoretical research on the composite pre-tightened tooth connection embedded with soft layers has not been carried out. Therefore, in this work, the load distribution theory of composite pre-tightened tooth connection embedded with soft layers is studied by spring stiffness method. First, based on deformation compatibility condition, the theoretical calculation formula of load distribution ratio of each tooth is derived by spring stiffness method. Then, load distribution ratio is obtained by experiments, and the theoretical calculation results are verified. Finally, through the derived formula, the load distribution ratio of the composite pre-tightened tooth connection embedded with soft layers is parameterized. Research shows that (1) The theoretical value is in good agreement with the experimental value, and the maximum error of calculation result of the load distribution of the joint is 8%; (2) Under the action of soft layers, each tooth of two-teeth and three-teeth joints are damaged at the same time, the ultimate bearing capacity is increased by 29.0 and 21.6%, respectively, compared with the traditional two-teeth and three-teeth joints; (3) The elastic modulus and thickness of soft layers have a significant impact on the load distribution ratio of each tooth.

Lagrangian approach to origami vertex analysis: kinematics.

The use of origami in engineering has significantly expanded in recent years, spanning deployable structures across scales, folding robotics and mechanical metamaterials. However, finding foldable paths can be a formidable task as the kinematics are determined by a nonlinear system of equations, often with several degrees of freedom. In this article, we leverage a Lagrangian approach to derive reduced-order compatibility conditions for rigid-facet origami vertices with reflection and rotational symmetries. Then, using the reduced-order conditions, we derive exact, multi-degree of freedom solutions for degree 6 and degree 8 vertices with prescribed symmetries. The exact kinematic solutions allow us to efficiently investigate the topology of allowable kinematics, including the consideration of a self-contact constraint, and then visually interpret the role of geometric design parameters on these admissible fold paths by monitoring the change in the kinematic topology. We then introduce a procedure to construct lower-symmetry kinematic solutions by breaking symmetry of higher-order kinematic solutions in a systematic way that preserves compatibility. The multi-degree of freedom solutions discovered here should assist with building intuition of the kinematic feasibility of higher-degree origami vertices and also facilitate the development of new algorithmic procedures for origami-engineering design.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Families of exact similaritons with flexible modulations in N-coupled homogeneous and inhomogeneous systems

In this paper, a family of exact solutions to N-coupled nonlinear Schrödinger (N-CNLS) equations including bright and dark solitons, Akhmediev breathers, Kuznetsov-Ma breathers, and rogue waves are derived with the aid of a generic nonlinear wave assumption. As an application of the solutions, we present a scheme to realize amplitude coding in an identical waveguide system. Furthermore, by a general self-similar transformation method, exact controllable similaritons of N-coupled inhomogeneous NLS (N-CINLS) equations are constructed under relaxed compatibility conditions. Flexible modulations of similaritons are investigated in a typical inhomogeneous system. Based on the general self-similar transformation, we further study various and novel modulations of composite similariton of 2-CINLS regimes. The various similaritons presented here may be expected to find application in the control and transmission of nonlinear waves in realizable complex systems including those based on optical fibers and Bose-Einstein condensates.

Free Vibration of Graphene Nanoplatelet-Reinforced Porous Double-Curved Shells of Revolution with a General Radius of Curvature Based on a Semi-Analytical Method

Based on domain decomposition, a semi-analytical method (SAM) is applied to analyze the free vibration of double-curved shells of revolution with a general curvature radius made from graphene nanoplatelet (GPL)-reinforced porous composites. The mechanical properties of the GPL-reinforced composition are assessed with the Halpin–Tsai model. The double-curvature shell of revolution is broken down into segments along its axis in accordance with first-order shear deformation theory (FSDT) and the multi-segment partitioning technique, to derive the shell’s functional energy. At the same time, interfacial potential is used to ensure the continuity of the contact surface between neighboring segments. By applying the least-squares weighted residual method (LWRM) and modified variational principle (MVP) to relax and achieve interface compatibility conditions, a theoretical framework for analyzing vibrations is developed. The displacements and rotations are described through Fourier series and Chebyshev polynomials, accordingly, converting a two-dimensional issue into a suite of decoupled one-dimensional problems. The obtained solutions are contrasted with those achieved using the finite element method (FEM) and other existing results, and the current formulation’s validity and precision are confirmed. Example cases are presented to demonstrate the free vibration of GPL-reinforced porous composite double-curved paraboloidal, elliptical, and hyperbolical shells of revolution. The findings demonstrate that the natural frequency of the shell is related to pore coefficients, porosity, the mass fraction of the GPLs, and the distribution patterns of the GPLs.

Analytical models for predicting the moment‒rotation relationships of steel hub joints with bolted steel side plates in single-layer wood reticulated domes

A very popular and efficient pattern of joints adopted for wood reticulated domes is steel hub joints featuring end-bearing and bolt-connected wood members (EBBC joints). This type of joint shows clear semi-rigidity, which affects the rigidity and overall stability of the structures. This study developed analytical models for predicting the moment‒rotation curves of EBBC joints, considering the effect of axial compression. Specifically, two models termed the WR and WEP models, were developed assuming rigid and elastic-plastic constitutive behaviour, respectively, of the wood in the compression zone of the joint. A tri-linear model for the lateral force-slip relationship of bolt connections was derived. A formula for calculating the deformation modulus and predicting the shear failure of wood members under local compression was proposed and verified. The moment–rotation relationship of the joint was established with equilibrium and compatibility conditions. The accuracy of the analytical models was verified by comparison with a series of experimental results as well as the parametric study results obtained using a refined finite element model. It was revealed that both the WR and the WEP models can predict the moment–rotation relationships accurately for joints without axial compression, whereas for the case of non-negligible axial compression loads, the WEP model offers more accurate predictions. The analytical WEP model proposed in the current paper provides a versatile tool for general design practice to predict moment–rotation curves for traditional or novel EBBC joints.

A novel time-varying mesh stiffness model for orthogonal face gear drives considering EHL

PurposeThis study aims to research the time-varying mesh stiffness (TVMS) model for orthogonal face gear drives considering elastohydrodynamic lubrication (EHL) and provide a theoretical basis for understanding the dynamic characteristics of face gear drives.Design/methodology/approachConsidering EHL, a novel model is proposed to calculate the TVMS of orthogonal face gears using the deformation compatibility condition. First, the tooth surface equations of orthogonal face gears are derived according to the tooth surface generation principle. Then, the oil film thickness on the tooth surface of face gears is obtained by solving the governing equations of EHL. Furthermore, the proposed model is used to calculate the TVMS of face gears along the mesh cycle and is verified. Finally, the effects of module, tooth number of shaper cutter and pressure angle on mesh stiffness are analyzed.FindingsThe results indicate that when the contact ratio is greater than 1 and less than or equal to 2, the TVMS of face gears exhibits a phenomenon of double-single tooth alternating meshing where sudden changes occur. As the module increases, the overall mesh stiffness of face gears increases, and the magnitude of the sudden change at the moment of single-double tooth alternating meshing gradually increases. As the tooth number of shaper cutter and pressure angle increase, so does the TVMS of face gears. When the effect of oil film is considered, the calculated TVMS of face gears slightly increases overall and the increase in average oil film thickness leads to a rise in the TVMS. This study provides a theoretical basis for understanding the dynamic characteristics of face gear drives.Originality/valueThis study’s originality and value lie in its comprehensive approach, which includes conducting analysis based on loaded tooth contact, considering the influence of elastohydrodynamic lubrication, proposing a novel analytical–finite–element model, calculating TVMS of face gears, verifying the proposed model and analyzing the effects of typical structural parameters and oil film thickness.

QUASI-HEREDITARY SKEW GROUP ALGEBRAS

Abstract Given an algebra and a finite group acting on it via automorphisms, a natural object of study is the associated skew group algebra. In this article, we study the relationship between quasi-hereditary structures on the original algebra and on the corresponding skew group algebra. Assuming a natural compatibility condition on the partial order, we show that the skew group algebra is quasi-hereditary if and only if the original algebra is. Moreover, we show that in this setting an exact Borel subalgebra of the original algebra which is invariant as a set under the group action gives rise to an exact Borel subalgebra of the skew group algebra and that under this construction, properties such as normality and regularity of the exact Borel subalgebra are preserved.

Intrinsically Stable Charged Domain Walls in Molecular Ferroelectric Thin Films

AbstractCharged domain walls in ferroelectrics hold great promise for applications in ferroelectric random‐access memory (FeRAM), with advantages such as low energy consumption, high density, and non‐destructive operation. Due to the mechanical compatibility condition, the neutral domain walls are dominant in traditional ferroelectric thin films. Herein, using phase‐field simulations, the formation of intrinsically stable charged domain walls (CDWs) in the molecular ferroelectric films is demonstrated, which can be mainly attributed to the small mechanical stiffness. The switching kinetics are further investigated for the CDWs, showing a lower switching barrier as compared to the neutral counterparts. Moreover, it is indicated that increasing the compressive misfit strain can lead to prolonged switching time, with a significantly increased switching energy barrier. These findings pave the way for the potential applications of metal‐free organic ferroelectric materials in FeRAM devices.

Cascade Cyclization of N-Cyanamide Alkenes for the Divergent Synthesis of Azido-, Nitro-, and Alkenyl-Containing Pyrroloquinazolinones.

Radical cascade cyclizations of N-cyanamide alkenes have been developed for the divergent synthesis of pyrroloquinazolinones bearing azido, alkenyl, and nitro groups by controlling the reaction conditions. The reaction temperature and the loading of the base play important roles in the different reaction pathways. These reactions are characterized by wide functional group compatibility and mild conditions.

A Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves

We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance as a detuning parameter is varied. The system can be finite- or infinite-dimensional (and quasilinear) and have a non-constant symplectic structure. We allow the origin to be a ‘trivial’ eigenvalue arising from a translational symmetry or, in an infinite-dimensional setting, to lie in the continuous spectrum of the linearised Hamiltonian vector field provided a compatibility condition on its range is satisfied. As an application, we show how Kirchgässner’s spatial dynamics approach can be used to construct doubly periodic travelling waves on the surface of a three-dimensional body of water (of finite or infinite depth) beneath a thin ice sheet (‘hydroelastic waves’). The hydrodynamic problem is formulated as a reversible Hamiltonian system in which an arbitrary horizontal spatial direction is the time-like variable, and the infinite-dimensional phase space consists of wave profiles which are periodic (with fixed period) in a second, different horizontal direction. Applying our Lyapunov centre theorem at a point in parameter space associated with a 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance yields a periodic solution of the spatial Hamiltonian system corresponding to a doubly periodic hydroelastic wave.

On the nature of Bregman functions

Let C⊂Rn be convex, compact, with nonempty interior and h be Legendre with domain C, continuous on C. We prove that h is Bregman if and only if it is strictly convex on C and C is a polytope. This provides insights on sequential convergence of many Bregman divergence based algorithm: abstract compatibility conditions between Bregman and Euclidean topology may equivalently be replaced by explicit conditions on h and C. This also emphasizes that a general convergence theory for these methods (beyond polyhedral domains) would require more refinements than Bregman's conditions.

The aeroelastic stability characteristics of a ring-stiffened conical three-layered sandwich shell with an FG auxetic honeycomb core utilizing zig-zag shell theory

This paper is devoted to the supersonic flutter analysis of a ring-stiffened conical three-layered sandwich shell consisting of an auxetic honeycomb (AH) core fabricated from functionally graded material (FGM). The face sheets are manufactured of FGM as well in which the volume fraction of the ceramic increases from zero at the inner surface to one at the outer surface based on a power-law function. The sandwich shell is mathematically modeled based on the Murakami's zig-zag shell theory and the aerodynamic pressure is modeled utilizing piston theory. The derivation of governing equations along with compatibility and boundary conditions are performed using Hamilton's principle and are solved through a semi-analytical solution consisting of an exact solution in the circumferential direction followed by an approximate solution in the meridional direction. The flutter boundaries are attained to investigate the variations of the natural frequencies and damping ratios to find the critical aerodynamic pressure (CAP). The impacts of several factors on the CAP are examined such as the power-law index, geometric characteristics of the cells in the FGAH, thickness of the honeycomb core, location of the ring, and boundary conditions. It is observed that an optimal location can be found for the ring support somewhere between the middle length and large radius of a conical shell that provides the best aeroelastic stability.

Palladium‐Catalyzed Denitrogenative Coupling of Aryldiazonium Salts with Terminal Alkynes for the Assembly of Internal Alkynes

AbstractAn N‐heterocyclic carbene palladium (NHC‐palladium)‐catalyzed denitrogenative coupling of aryldiazonium salts with terminal alkynes in ionic liquids has been accomplished. This catalytic strategy provides an effective and green synthetic protocol for the assembly of structurally diverse internal alkynes with excellent functional group compatibility and mild conditions. In the presence of 1 mol % of IMes‐Pd‐Im‐Cl2 as the catalyst, a wide range of terminal alkynes and aryldiazonium salts could be excellently tolerated. Basic ionic liquid plays a crucial role in this catalytic system, which not only acts as the green solvent, but also provides basic environment for the carbon‐carbon bond formation process. Notably, this catalytic system could be recycled up to six times and reused without significant loss of catalytic activity.

Initial Boundary Value Problem for the Coupled Kundu Equations on the Half-Line

In this article, the coupled Kundu equations are analyzed using the Fokas unified method on the half-line. We resolve a Riemann–Hilbert (RH) problem in order to illustrate the representation of the potential function in the coupled Kundu equations. The jump matrix is obtained from the spectral matrix, which is determined according to the initial value data and the boundary value data. The findings indicate that these spectral functions exhibit interdependence rather than being mutually independent, and adhere to a global relation while being connected by a compatibility condition.

MKdV Equation on Time Scales: Darboux Transformation and N-Soliton Solutions

In this paper, the spectral problem of the mKdV equation satisfying the compatibility condition on time scales is directly constructed. By using the zero-curvature equation on time scales, the mKdV equation on time scales is obtained. When x∈R and t∈R, the equation degenerates to the classical mKdV equation. Then, the single-soliton, two-soliton, and N-soliton solutions of the mKdV equation under the zero boundary condition on time scales are presented via employing the Darboux transformation (DT). Particularly, we obtain the corresponding single-soliton solutions expressed using the Cayley exponential function on four different time scales (R, Z, q-discrete, C).

Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity

Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymptotic description in the limit of a large number of cells. Starting from a bar and hinge model for the elastic energy of a generic four parallelogram panel origami pattern, we derive a complete set of geometric compatibility conditions identifying the pattern’s soft modes in this limit. The compatibility equations form a system of partial differential equations constraining the actuation of the origami’s creases (a scalar angle field) and the relative rotations of its unit cells (a pair of skew tensor fields). We show that every solution of the compatibility equations is the limit of a sequence of soft modes — origami deformations with finite bending energy and negligible stretching. Using these sequences, we derive a plate-like theory for parallelogram origami patterns with an explicit coarse-grained quadratic energy depending on the gradient of the crease-actuation and the relative rotations of the cells. Finally, we illustrate our theory in the context of two well-known origami designs: the Miura and Eggbox patterns. Though these patterns are distinguished in their anticlastic and synclastic bending responses, they show a universal twisting response. General soft modes captured by our theory involve a rich nonlinear interplay between actuation, bending and twisting, determined by the underlying crease geometry.

Continuous optimization method of micro geometry for unparallel beveloid gears

To enhance the bearing capacity and minimize the loaded transmission error for unparallel beveloid gears, a continuous optimization method of micro geometry is proposed. Considering that the conjugate characteristic of tooth surfaces is destroyed by misalignments and modification, an unload contact analysis model is first developed. This includes a contact tooth sequence determination model and an unloaded transmission error calculation model for multi-tooth contact. To determine contact due to deformation, a potential contact point matching model of non-contact tooth surfaces is introduced. Further, a numerical loaded contact analysis model based on the influence coefficient method for unparallel beveloid gear is developed. For multi-tooth contact of modified tooth surfaces, the transmission error compatibility condition is introduced. Based on the loaded contact model, a continuous optimization model for the comprehensive performance of contact pressures and loaded transmission error within a meshing cycle is established. To improve optimization efficiency, a calculation strategy for continuous optimization is developed. The feasibility of the proposed method is validated using a numerical example.