Quantum simulation is capable of simulating certain dynamical systems in continuous time—Schrödinger’s equations being the most direct and well known—more efficiently than classical simulation. Any linear dynamical system can in fact be transformed into a system of Schrödinger’s equations via a method called Schrödingerisation (Jin et al. 2022. Quantum simulation of partial differential equations via Schrödingerisation. (https://arxiv.org/abs/2212.13969) and Jin et al. 2023. Phys. Rev. A 108, 032603. (doi:10.1103/PhysRevA.108.032603)). We show how Schrödingerisation allows quantum simulation to be directly used for the simulation of continuous-time versions of general (explicit) iterative schemes or discrete linear dynamical systems. In particular, we use this new method to solve linear systems of equations and for estimating the maximum eigenvector and eigenvalue of a matrix, respectively. This method is applicable using either discrete-variable quantum systems or on hybrid continuous-variable and discrete-variable quantum systems. This framework provides an interesting alternative to solve linear algebra problems using quantum simulation.
与经典模拟相比，量子模拟能够更高效地模拟某些连续时间的动态系统--薛定谔方程是最直接、最著名的动态系统。事实上，任何线性动态系统都可以通过一种称为薛定谔化（Schrödingerisation）的方法转化为薛定谔方程系统（Jin 等，2022 年）。通过薛定谔化实现偏微分方程的量子模拟。(https://arxiv.org/abs/2212.13969）和 Jin 等人，2023。Phys. Rev. A 108, 032603.(doi:10.1103/PhysRevA.108.032603)).我们展示了薛定谔化如何让量子模拟直接用于一般（显式）迭代方案或离散线性动态系统的连续时间版本的模拟。特别是，我们使用这种新方法分别求解线性方程组和估计矩阵的最大特征向量和特征值。这种方法既适用于离散变量量子系统，也适用于连续变量和离散变量混合量子系统。这一框架为利用量子模拟解决线性代数问题提供了一种有趣的选择。
{"title":"Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra","authors":"Shi Jin, Nana Liu","doi":"10.1098/rspa.2023.0370","DOIUrl":"https://doi.org/10.1098/rspa.2023.0370","url":null,"abstract":"Quantum simulation is capable of simulating certain dynamical systems in continuous time—Schrödinger’s equations being the most direct and well known—more efficiently than classical simulation. Any linear dynamical system can in fact be transformed into a system of Schrödinger’s equations via a method called Schrödingerisation (Jin et al. 2022. Quantum simulation of partial differential equations via Schrödingerisation. (https://arxiv.org/abs/2212.13969) and Jin et al. 2023. Phys. Rev. A 108, 032603. (doi:10.1103/PhysRevA.108.032603)). We show how Schrödingerisation allows quantum simulation to be directly used for the simulation of continuous-time versions of general (explicit) iterative schemes or discrete linear dynamical systems. In particular, we use this new method to solve linear systems of equations and for estimating the maximum eigenvector and eigenvalue of a matrix, respectively. This method is applicable using either discrete-variable quantum systems or on hybrid continuous-variable and discrete-variable quantum systems. This framework provides an interesting alternative to solve linear algebra problems using quantum simulation.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"32 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141398425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study presents a cluster-based Bayesian methodology for state estimation under realistic conditions including noisy data from sparse sensors. The proposed approach is interpretable and, building upon previous work on transition networks, explicitly accounts for experimental noise within the data-driven framework by means of data clustering. Experimental measurements are exploited, beyond model training, to quantify the degree of uncertainty (noise) for each trained state. Such noise levels are eventually associated with probability distributions that, when combined with Bayes’ theorem, allow us to perform real-time state estimation. The proposed methodology is tested on two cases of challenging flows generated by an accelerating elliptical plate and also a delta wing experiencing gusts. Results specifically indicate that the proposed approach is robust against the number of clusters, enabling state estimation with a significant order reduction, notably decreasing the computational cost while preserving estimation accuracy. Based on the present findings, the proposed data-driven approach can be employed for realistic state estimation in nonlinear systems where noise, sensor sparsity and nonlinearities represent a challenging scenario.
{"title":"Cluster-based Bayesian approach for noisy and sparse data: application to flow-state estimation","authors":"F. Kaiser, G. Iacobello, D. Rival","doi":"10.1098/rspa.2023.0608","DOIUrl":"https://doi.org/10.1098/rspa.2023.0608","url":null,"abstract":"This study presents a cluster-based Bayesian methodology for state estimation under realistic conditions including noisy data from sparse sensors. The proposed approach is interpretable and, building upon previous work on transition networks, explicitly accounts for experimental noise within the data-driven framework by means of data clustering. Experimental measurements are exploited, beyond model training, to quantify the degree of uncertainty (noise) for each trained state. Such noise levels are eventually associated with probability distributions that, when combined with Bayes’ theorem, allow us to perform real-time state estimation. The proposed methodology is tested on two cases of challenging flows generated by an accelerating elliptical plate and also a delta wing experiencing gusts. Results specifically indicate that the proposed approach is robust against the number of clusters, enabling state estimation with a significant order reduction, notably decreasing the computational cost while preserving estimation accuracy. Based on the present findings, the proposed data-driven approach can be employed for realistic state estimation in nonlinear systems where noise, sensor sparsity and nonlinearities represent a challenging scenario.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"13 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141409888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a new compartmental differential equation model to examine the dynamics of user adoption and abandonment within a product context. This model features a nonlinear adoption rate and encompasses two distinct abandonment dynamics: infectious abandonment stemming from interactions among current and past users, and non-infectious abandonment induced by mass media, advertisements or the emergence of new products. Our exploration encompasses discussions on the existence and stability of model equilibria, as well as the derivation of a critical threshold quantity that regulates the model dynamics. Additionally, we establish criteria for backward and forward bifurcations and various forms of Hopf bifurcation. Detailed scrutiny of an associated optimal control problem is undertaken, starting with the establishment of the existence of an optimal control pair, followed by the determination of the requisite system conditions for this control pair. Extensive numerical simulations are conducted to validate the theoretical findings. Finally, we showcase the model’s efficacy by fitting it to historical data on Facebook’s daily active users, employing the derived parameter values to predict future user counts.
{"title":"Modelling the dynamics of product adoption and abandonment","authors":"Lingju Kong","doi":"10.1098/rspa.2024.0034","DOIUrl":"https://doi.org/10.1098/rspa.2024.0034","url":null,"abstract":"We introduce a new compartmental differential equation model to examine the dynamics of user adoption and abandonment within a product context. This model features a nonlinear adoption rate and encompasses two distinct abandonment dynamics: infectious abandonment stemming from interactions among current and past users, and non-infectious abandonment induced by mass media, advertisements or the emergence of new products. Our exploration encompasses discussions on the existence and stability of model equilibria, as well as the derivation of a critical threshold quantity that regulates the model dynamics. Additionally, we establish criteria for backward and forward bifurcations and various forms of Hopf bifurcation. Detailed scrutiny of an associated optimal control problem is undertaken, starting with the establishment of the existence of an optimal control pair, followed by the determination of the requisite system conditions for this control pair. Extensive numerical simulations are conducted to validate the theoretical findings. Finally, we showcase the model’s efficacy by fitting it to historical data on Facebook’s daily active users, employing the derived parameter values to predict future user counts.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"2021 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141400212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate a three-component system involving the Belousov–Zhabotinsky reaction in water-in-oil microemulsions. Our goal is to investigate the connection between homoclinic snaking and semi-strength interaction in a three-variable reaction–diffusion system. A two-parameter bifurcation diagram of homogeneous, periodic and localized patterns is obtained numerically, and a natural asymptotic scaling for semi-strong interaction theory is found where an activator source term a=O(δ1) and b=O(δ1), with δ1≪1 being the diffusion ratio. Under this regime, singular perturbation techniques are used to construct localized steady-state patterns, and new types of non-local eigenvalue problems (NLEP) are derived to determine the stability of these patterns to O(1) time-scale instabilities. We extend the scope of the NLEP by considering a general scenario where both time-scaling parameters are non-zero. All analytical results are found to agree with numerics. Further numerical results are presented on the location of various types of breathing Hopf instability for localized patterns.
{"title":"Localized pattern formation: semi-strong interaction asymptotic analysis for three components model","authors":"Fahad Al Saadi, Chunyi Gai, Mark Nelson","doi":"10.1098/rspa.2023.0591","DOIUrl":"https://doi.org/10.1098/rspa.2023.0591","url":null,"abstract":"We investigate a three-component system involving the Belousov–Zhabotinsky reaction in water-in-oil microemulsions. Our goal is to investigate the connection between homoclinic snaking and semi-strength interaction in a three-variable reaction–diffusion system. A two-parameter bifurcation diagram of homogeneous, periodic and localized patterns is obtained numerically, and a natural asymptotic scaling for semi-strong interaction theory is found where an activator source term a=O(δ1) and b=O(δ1), with δ1≪1 being the diffusion ratio. Under this regime, singular perturbation techniques are used to construct localized steady-state patterns, and new types of non-local eigenvalue problems (NLEP) are derived to determine the stability of these patterns to O(1) time-scale instabilities. We extend the scope of the NLEP by considering a general scenario where both time-scaling parameters are non-zero. All analytical results are found to agree with numerics. Further numerical results are presented on the location of various types of breathing Hopf instability for localized patterns.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"120 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139453958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Bigoni, Sébastien Guenneau, A. Maurel, Kim Pham, L. Cabras, A. Piccolroaz
This study investigates the impact of sliders – constraints acting on elastic rods allowing for a transverse displacement jump while maintaining axial and rotational displacement continuity – on the dynamics of a periodic elastic grid, including the effects of axial preload. The grid is linearly elastic and subject to in-plane incremental deformation, involving normal and shear forces and bending moment. The periodicity of the infinite grid permits a Floquet–Bloch wave analysis and a rigorous dynamic homogenization, leading to an equivalent prestressed elastic solid. The investigation is complemented by ad hoc developed F.E. simulations and perturbations with a pulsating Green’s function. Results show that the sliders create band gaps, flat bands and Dirac cones in the dispersion diagrams and generate macro-instability even for tensile prestress. The latter corresponds to the loss of ellipticity at the parabolic boundary in the equivalent elastic solid and provides a rare example of an almost unexplored form of material instability. Therefore, our results offer design strategies for metamaterials and architected materials showing reversible material instabilities and filtering properties for mechanical signals.
{"title":"Dynamics of elastic lattices with sliding constraints","authors":"D. Bigoni, Sébastien Guenneau, A. Maurel, Kim Pham, L. Cabras, A. Piccolroaz","doi":"10.1098/rspa.2023.0579","DOIUrl":"https://doi.org/10.1098/rspa.2023.0579","url":null,"abstract":"This study investigates the impact of sliders – constraints acting on elastic rods allowing for a transverse displacement jump while maintaining axial and rotational displacement continuity – on the dynamics of a periodic elastic grid, including the effects of axial preload. The grid is linearly elastic and subject to in-plane incremental deformation, involving normal and shear forces and bending moment. The periodicity of the infinite grid permits a Floquet–Bloch wave analysis and a rigorous dynamic homogenization, leading to an equivalent prestressed elastic solid. The investigation is complemented by ad hoc developed F.E. simulations and perturbations with a pulsating Green’s function. Results show that the sliders create band gaps, flat bands and Dirac cones in the dispersion diagrams and generate macro-instability even for tensile prestress. The latter corresponds to the loss of ellipticity at the parabolic boundary in the equivalent elastic solid and provides a rare example of an almost unexplored form of material instability. Therefore, our results offer design strategies for metamaterials and architected materials showing reversible material instabilities and filtering properties for mechanical signals.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"124 49","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139537704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Amendola, J. de Castro Motta, G. Saccomandi, L. Vergori
Due to their intrinsic complexity, it is not easy to model the mechanical behaviour of biomaterials. Despite the challenges they faced, some researchers have presented mathematical models to describe some aspects of the mechanical response of soft tissues. Since most of the materials of biological interest are composites made of different constituents reinforced by collagen and/or elastin fibres, material dispersion and anisotropy are non-negligible. Within the theory of elasticity, several models for anisotropic materials have been developed. The same cannot be said for anisotropic dispersive materials. The models available in the literature that account for material dispersion are valid only for isotropic materials. This paper aims at introducing a very general model for anisotropic dispersion in transversely isotropic bodies within the theory of simple materials of differential type. Our model has the potential to represent a first step towards a better understanding of the mechanical response of fibre-reinforced soft materials.
{"title":"A constitutive model for transversely isotropic dispersive materials","authors":"A. Amendola, J. de Castro Motta, G. Saccomandi, L. Vergori","doi":"10.1098/rspa.2023.0374","DOIUrl":"https://doi.org/10.1098/rspa.2023.0374","url":null,"abstract":"Due to their intrinsic complexity, it is not easy to model the mechanical behaviour of biomaterials. Despite the challenges they faced, some researchers have presented mathematical models to describe some aspects of the mechanical response of soft tissues. Since most of the materials of biological interest are composites made of different constituents reinforced by collagen and/or elastin fibres, material dispersion and anisotropy are non-negligible. Within the theory of elasticity, several models for anisotropic materials have been developed. The same cannot be said for anisotropic dispersive materials. The models available in the literature that account for material dispersion are valid only for isotropic materials. This paper aims at introducing a very general model for anisotropic dispersion in transversely isotropic bodies within the theory of simple materials of differential type. Our model has the potential to represent a first step towards a better understanding of the mechanical response of fibre-reinforced soft materials.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"23 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139125831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Gaibotti, S. Mogilevskaya, A. Piccolroaz, D. Bigoni
An analytical solution is derived for the bifurcations of an elastic disc that is constrained on the boundary with an isoperimetric Cosserat coating. The latter is treated as an elastic circular rod, either perfectly or partially bonded (with a slip interface in the latter case) and is subjected to three different types of uniformly distributed radial loads (including hydrostatic pressure). The proposed solution technique employs complex potentials to treat the disc’s interior and incremental Lagrangian equations to describe the prestressed elastic rod modelling the coating. The bifurcations of the disc occur with modes characterized by different circumferential wavenumbers, ranging between ovalization and high-order waviness, as a function of the ratio between the elastic stiffness of the disc and the bending stiffness of its coating. The presented results find applications in various fields, such as coated fibres, mechanical rollers, and the growth and morphogenesis of plants and fruits.
{"title":"Bifurcations of an elastic disc coated with an elastic inextensible rod","authors":"M. Gaibotti, S. Mogilevskaya, A. Piccolroaz, D. Bigoni","doi":"10.1098/rspa.2023.0491","DOIUrl":"https://doi.org/10.1098/rspa.2023.0491","url":null,"abstract":"An analytical solution is derived for the bifurcations of an elastic disc that is constrained on the boundary with an isoperimetric Cosserat coating. The latter is treated as an elastic circular rod, either perfectly or partially bonded (with a slip interface in the latter case) and is subjected to three different types of uniformly distributed radial loads (including hydrostatic pressure). The proposed solution technique employs complex potentials to treat the disc’s interior and incremental Lagrangian equations to describe the prestressed elastic rod modelling the coating. The bifurcations of the disc occur with modes characterized by different circumferential wavenumbers, ranging between ovalization and high-order waviness, as a function of the ratio between the elastic stiffness of the disc and the bending stiffness of its coating. The presented results find applications in various fields, such as coated fibres, mechanical rollers, and the growth and morphogenesis of plants and fruits.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"118 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139126135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Living systems use chemical fuel to process information, assemble structures and maintain fluxes. Many of these processes are dissipative: energy is consumed purely to maintain non-equilibrium steady-state outputs. How efficiently the input energy is transduced toward the output dissipation as opposed to being lost during intermediate steps, and whether the efficiency is constrained by general principles or specific fine-tuning, are open questions. Here, applying a recent mapping from non-equilibrium systems to battery-resistor circuits, an analytic expression for the efficiency of any dissipative molecular machine driven by a chemical potential difference is derived. This expression disentangles the chemical potential from the machine’s details, whose effect on the efficiency is fully specified by a constant called the load resistance. The efficiency passes through an inflection point separating totally inefficient machines from efficient machines if the balance between chemical potential difference and load resistance exceeds thermal noise. This explains all-or-none dynein stepping with increasing ATP concentration observed in single-molecule experiments. These results indicate that energy transduction in living systems is efficient not because of idiosyncratic optimization of biomolecules, but rather because the concentration of chemical fuel is kept above a threshold level.
生命系统使用化学燃料来处理信息、组装结构和维持通量。其中许多过程都是耗散性的：能量消耗纯粹是为了维持非平衡稳态输出。输入能量如何有效地转化为输出耗散，而不是在中间步骤中损失掉，以及这种效率是受一般原理的制约还是受特定微调的制约，这些都是有待解决的问题。在此，应用最近从非平衡系统到电池-电阻电路的映射，得出了由化学势差驱动的任何耗散分子机器效率的解析表达式。该表达式将化学势与机器的细节分离开来，而细节对效率的影响完全由一个称为负载电阻的常数来确定。如果化学势差和负载电阻之间的平衡超过热噪声，则效率会通过一个拐点，将完全低效的机器与高效的机器区分开来。这就解释了在单分子实验中观察到的随着 ATP 浓度的增加，动力蛋白步进全有或全无的现象。这些结果表明，生命系统中的能量转换之所以高效，不是因为生物分子的特异性优化，而是因为化学燃料的浓度保持在阈值水平之上。
{"title":"General efficiency relation for dissipative molecular machines","authors":"Milo M. Lin","doi":"10.1098/rspa.2023.0388","DOIUrl":"https://doi.org/10.1098/rspa.2023.0388","url":null,"abstract":"Living systems use chemical fuel to process information, assemble structures and maintain fluxes. Many of these processes are dissipative: energy is consumed purely to maintain non-equilibrium steady-state outputs. How efficiently the input energy is transduced toward the output dissipation as opposed to being lost during intermediate steps, and whether the efficiency is constrained by general principles or specific fine-tuning, are open questions. Here, applying a recent mapping from non-equilibrium systems to battery-resistor circuits, an analytic expression for the efficiency of any dissipative molecular machine driven by a chemical potential difference is derived. This expression disentangles the chemical potential from the machine’s details, whose effect on the efficiency is fully specified by a constant called the load resistance. The efficiency passes through an inflection point separating totally inefficient machines from efficient machines if the balance between chemical potential difference and load resistance exceeds thermal noise. This explains all-or-none dynein stepping with increasing ATP concentration observed in single-molecule experiments. These results indicate that energy transduction in living systems is efficient not because of idiosyncratic optimization of biomolecules, but rather because the concentration of chemical fuel is kept above a threshold level.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"68 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139537020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Non-developable origami is a unique type of origami structures that cannot be unfolded into a flat sheet without stretching. In this work, we study the kinematics and dynamics of such origami, theoretically, numerically and experimentally, considering rigid panels and stretchable creases. Unlike developable origami, we find that non-developable origami exhibits distinct folding angle relationships, leading to several separate branches in its kinematic configuration space with snap-through and locking behaviours. By modelling the creases as stretchable torsional springs, we derive a dynamic model to analyse the deployment of non-developable origami structures, from single-vertex origami to origami chains. Our dynamic model unveils the snap-through behaviour between the two kinematics branches of the single-vertex non-developable origami structure, which is further validated by experiments with excellent agreement. We believe that our kinematic and dynamic framework of non-developable origami will greatly expand the current design space of origami structures and guide the design of novel origami actuators.
{"title":"Kinematics and dynamics of non-developable origami","authors":"Yu Zou, F. Feng, Ke Liu, Pengyu Lv, Huiling Duan","doi":"10.1098/rspa.2023.0610","DOIUrl":"https://doi.org/10.1098/rspa.2023.0610","url":null,"abstract":"Non-developable origami is a unique type of origami structures that cannot be unfolded into a flat sheet without stretching. In this work, we study the kinematics and dynamics of such origami, theoretically, numerically and experimentally, considering rigid panels and stretchable creases. Unlike developable origami, we find that non-developable origami exhibits distinct folding angle relationships, leading to several separate branches in its kinematic configuration space with snap-through and locking behaviours. By modelling the creases as stretchable torsional springs, we derive a dynamic model to analyse the deployment of non-developable origami structures, from single-vertex origami to origami chains. Our dynamic model unveils the snap-through behaviour between the two kinematics branches of the single-vertex non-developable origami structure, which is further validated by experiments with excellent agreement. We believe that our kinematic and dynamic framework of non-developable origami will greatly expand the current design space of origami structures and guide the design of novel origami actuators.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"12 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139537248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We address the problem of organ registration in augmented surgery, where the deformation of the patient’s organ is reconstructed in real-time from a partial observation of its surface. Physics-based registration methods rely on adding artificial forces to drive the registration, which may result in implausible displacement fields. In this paper, we look at this inverse problem through the lens of optimal control, in an attempt to reconstruct a physically consistent surface load. The resulting optimization problem features an elastic model, a least-squares data attachment term based on orthogonal projections, and an admissible set of surface loads defined prior to reconstruction in the mechanical model. After a discussion about the existence of solutions, we analyse the necessary optimality conditions and use them to derive a suitable optimization algorithm. We implement an adjoint method and we test our approach on multiple examples, including the so-called Sparse Data Challenge. We obtain very promising results, that illustrate the feasibility of our approach with linear and nonlinear models.
{"title":"Organ registration from partial surface data in augmented surgery from an optimal control perspective","authors":"Stephane Cotin, Guillaume Mestdagh, Yannick Privat","doi":"10.1098/rspa.2023.0197","DOIUrl":"https://doi.org/10.1098/rspa.2023.0197","url":null,"abstract":"We address the problem of organ registration in augmented surgery, where the deformation of the patient’s organ is reconstructed in real-time from a partial observation of its surface. Physics-based registration methods rely on adding artificial forces to drive the registration, which may result in implausible displacement fields. In this paper, we look at this inverse problem through the lens of optimal control, in an attempt to reconstruct a physically consistent surface load. The resulting optimization problem features an elastic model, a least-squares data attachment term based on orthogonal projections, and an admissible set of surface loads defined prior to reconstruction in the mechanical model. After a discussion about the existence of solutions, we analyse the necessary optimality conditions and use them to derive a suitable optimization algorithm. We implement an adjoint method and we test our approach on multiple examples, including the so-called Sparse Data Challenge. We obtain very promising results, that illustrate the feasibility of our approach with linear and nonlinear models.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"27 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139456066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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