Proceedings of the Royal Society A最新文献

Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra 离散线性动力系统的量子模拟和线性代数中的简单迭代法

Proceedings of the Royal Society A Pub Date : 2024-06-01 DOI: 10.1098/rspa.2023.0370

Shi Jin, Nana Liu

{"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}

引用次数: 0

Cluster-based Bayesian approach for noisy and sparse data: application to flow-state estimation 基于聚类的贝叶斯方法用于噪声和稀疏数据：应用于流动状态估计

Proceedings of the Royal Society A Pub Date : 2024-06-01 DOI: 10.1098/rspa.2023.0608

F. Kaiser, G. Iacobello, D. Rival

{"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}

引用次数: 0

Modelling the dynamics of product adoption and abandonment 建立产品采用和放弃的动态模型

Proceedings of the Royal Society A Pub Date : 2024-06-01 DOI: 10.1098/rspa.2024.0034

Lingju Kong

{"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}

引用次数: 0

Localized pattern formation: semi-strong interaction asymptotic analysis for three components model 局部模式形成：三分量模型的半强相互作用渐近分析

Proceedings of the Royal Society A Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0591

Fahad Al Saadi, Chunyi Gai, Mark Nelson

引用次数: 0

Dynamics of elastic lattices with sliding constraints 具有滑动约束的弹性网格动力学

Proceedings of the Royal Society A Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0579

D. Bigoni, Sébastien Guenneau, A. Maurel, Kim Pham, L. Cabras, A. Piccolroaz

{"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}

引用次数: 0

Bifurcations of an elastic disc coated with an elastic inextensible rod 涂有不可拉伸弹性杆的弹性圆盘的分叉

Proceedings of the Royal Society A Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0491

M. Gaibotti, S. Mogilevskaya, A. Piccolroaz, D. Bigoni

引用次数: 0

A constitutive model for transversely isotropic dispersive materials 横向各向同性分散材料的构成模型

Proceedings of the Royal Society A Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0374

A. Amendola, J. de Castro Motta, G. Saccomandi, L. Vergori

引用次数: 0

General efficiency relation for dissipative molecular machines 耗散分子机器的一般效率关系

Proceedings of the Royal Society A Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0388

Milo M. Lin

{"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}

引用次数: 0

Kinematics and dynamics of non-developable origami 不可展开折纸的运动学和动力学

Proceedings of the Royal Society A Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0610

Yu Zou, F. Feng, Ke Liu, Pengyu Lv, Huiling Duan

引用次数: 0

Organ registration from partial surface data in augmented surgery from an optimal control perspective 从优化控制角度看增强手术中部分表面数据的器官配准

Proceedings of the Royal Society A Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0197

Stephane Cotin, Guillaume Mestdagh, Yannick Privat

引用次数: 0