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In this contribution we introduce a novel space-time formulation for non-linear elasticity, able to calculate large deformations and displacements with high efficiency using structured and unstructured meshes in the space-time cylinder without changing the required regularity and thus, enabling the use of Lagrangian shape functions including tetrahedron and hypertetrahedron or tesseract elements. The common and indiscriminate treatment of spatial and temporal directions allows us to remove one of the major bottlenecks in parallel computations: The design of time-stepping schemes, which can neither been parallelized efficiently in time nor allow for local refinements as no information transfer backwards in time is possible. Moreover, stability of time-stepping schemes depend on the accumulation of local approximation errors in each time-step, in contrast to space-time formulation, characterized by enhanced stability and robustness. Eventually, we will demonstrate superiority in the convergence against classical time-stepping schemes using various examples including highly sensitive systems in the context of non-linear elasticity.

This letter presents a method to estimate the space-dependent transport coefficients (diffusion, convection, reaction, and source/sink) for a generic scalar transport model, e.g., heat or mass. As the problem is solved in the frequency domain, the complex valued state as a function of the spatial variable is estimated using Gaussian process regression. The resulting probability density function of the state, together with a semi-discretization of the model, and a linear parameterization of the coefficients are used to determine the maximum likelihood solution for these space-dependent coefficients. The proposed method is illustrated by simulations.

Introduction: On-scene detection of acute coronary occlusion (ACO) during ongoing ventricular fibrillation (VF) may facilitate patient-tailored triage and treatment during cardiac arrest. Experimental studies have demonstrated the diagnostic potential of the amplitude spectrum area (AMSA) of the VF-waveform to detect myocardial infarction (MI). In follow-up, we performed this clinical pilot study on VF-waveform based discriminative models to diagnose acute MI due to ACO in real-world VF-patients. Methods: In our registry of VF-patients transported to a tertiary hospital (Nijmegen, The Netherlands), we studied patients with high-quality VF-registrations. We calculated VF-characteristics prior to the first shock, and first-to-second shock changes (Δ-characteristics). Primary aim was to assess the discriminative ability of the AMSA to detect patients with ACO. Secondarily, we investigated the discriminative value of adding ΔAMSA-measures using machine learning algorithms. Model performances were assessed using C-statistics. Results: In total, there were 67 VF-patients with and 34 without an ACO, and baseline characteristics did not differ significantly. Based on the AMSA prior to the first defibrillation attempt, discrimination between ACO and non-ACO was possible, with a C-statistic of 0.66 (0.56–0.75). The discriminative model using AMSA + ΔAMSA yielded a C-statistic of 0.80 (0.69–0.88). Conclusion: These clinical pilot data confirm previous experimental findings that early detection of MI using VF-waveform analysis seems feasible, and add insights on the diagnostic impact of accounting for first-to-second shock changes in VF-characteristics. Confirmative studies in larger cohorts and with a variety of VF-algorithms are warranted to further investigate the potential of this innovative approach.

This article proposes a distributed voltage control strategy for multiterminal high-voltage dc (MTdc) systems with fair power sharing among converters. A mathematical model for representing the dynamics of converters in MTdc systems is proposed. A distributed cooperative voltage control scheme is developed in which each converter only needs to communicate with the neighboring converters to regulate the voltage of the pilot bus of MTdc systems. The associated graph to the communication topology of the network is assumed to be a general time-varying graph. The proposed adaptive nonlinear protocol is scale-free and does not need any information about the communication graph and the number of agents and operates properly for time-varying graph. These features enhance the resilience of the proposed method against communication systems failures, multiplicative noise in communication network, and degradations. The performance of the proposed controller is demonstrated though the simulation of CIGRE MTdc test system.

We study input-to-state stability of bilinear control systems with possibly unbounded control operators. Natural sufficient conditions for integral input-to-state stability are given. The obtained results are applied to a bilinearly controlled Fokker-Planck equation., 17 pages, the manuscript has been thoroughly revised and streamlined. Furthermore, the main result could be significantly improved

This note deals with Bounded-Input-Bounded-Output (BIBO) stability for semilinear infinite-dimensional dynamical systems allowing for boundary control and boundary observation. We give sufficient conditions that guarantee BIBO stability based on Lipschitz conditions with respect to interpolation spaces. Our results can be applied to guarantee feasibility of funnel control for coupled ODE-PDE systems, as shown by means of an example from chemical engineering.

In this article, the behaviour of tumour growth and its interaction with the immune system have been studied using a mathematical model in the form of partial differential equations. However, the development of tumours and how they interact with the immune system make up an extremely complex and little-understood system. A new mathematical model has been proposed to gain insight into the role of immune response in the tumour microenvironment when no treatment is applied. The resulting model is a set of partial differential equations made up of four variables: the population density of tumour cells, two different types of immune cells (CD4+ helper T cells and CD8+ cytotoxic T cells), and nutrition content. Such kinds of systems also occur frequently in science and engineering. The interaction of tumour and immune cells is exemplified by predator-prey models in ecology, in which tumour cells act as prey and immune cells act as predators. The tumour-immune cell interaction is expressed via Holling’s Type-III and Beddington-DeAngelis functional responses. The combination of finite volume and finite element method is used to approximate the system numerically because these approximations are more suitable for time-dependent systems having diffusion. Finally, numerical simulations show that the methods perform well and depict the behaviour of the model.

In this paper we study scale-free state synchronization of discrete-time homogeneous multi-agent systems (MAS) subject to unknown, nonuniform and arbitrarily large communication delays. The scale-free protocol utilizes localized information exchange and is designed solely based on the knowledge of agents' model and does not require any information about the communication network and the size of the network (i.e. number of agents).

Coronavirus has become a serious global phenomenon in recent times and has negative effects on the entire world economy. In this study, a fractional mathematical model formulated in fractional conformable derivative is studied. The model hinges on the concept of mammal hosts and humans. The basic properties of the coronavirus model are investigated. The stability analysis is carried out as well as sensitivity analysis based on the reproduction number. Numerical simulation is undertaken to give impetus to the analytical results which indicate that both fractional conformable order derivative and fractional-order derivative have serious consequences in numerical result outcomes.

The purpose of this paper is to find approximate solutions to the fractional telegraph differential equation (FTDE) using Laplace transform collocation method (LTCM). The equation is defined by Caputo fractional derivative. A new form of the trial function from the original equation is presented and unknown coefficients in the trial function are computed by using LTCM. Two different initial-boundary value problems are considered as the test problems and approximate solutions are compared with analytical solutions. Numerical results are presented by graphs and tables. From the obtained results, we observe that the method is accurate, effective, and useful.

This paper studies scalable global state synchronization of discrete-time double integrator multi-agent systems in presence of input saturation based on localized information exchange. A scale-free collaborative linear dynamic protocols design methodology is developed for discrete-time multi-agent systems with both full and partial-state couplings. And the protocol design methodology does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. Meanwhile, the protocols are parametric based on a parameter set in which the designed protocols can guarantee the global synchronization result. Furthermore, the proposed protocol is scalable and achieves synchronization for any arbitrary number of agents.

This paper presents a method for controlling the voltage of inverter-based Microgrids by proposing a new scale-free distributed cooperative controller. The main contribution of this paper is that the proposed distributed cooperative controller is scale-free where is independent of any information about the communication system and the number of distributed generators, as such it works for any Microgrids with any size. Moreover, the communication network is modeled by a general time-varying graph which enhances the resilience of the proposed protocol against communication link failure, data packet loss, and arbitrarily fast plug and play operation in the presence of arbitrarily finite communication delays as the protocol does not require the knowledge of the upper bound on the delay. The stability analysis of the proposed protocol is provided. The proposed method is simulated on the CIGRE medium voltage Microgrid test system. The simulation results demonstrate the feasibility of the proposed scale-free distributed nonlinear protocol for regulating voltage of Microgrids in the presence of communication failures, data packet loss, noise, and degradation.

During the global pandemic, a drastic change in higher-level education took place in assessment. The traditional closed book format had to evolve to a technology-mediated open book assessment for engineering students in a vector calculus course. It became evident that the traditional format was no longer in line with the modern world both functionally and didactically. Such change in the assessment places a responsibility upon us as teachers for constructive alignment of the teaching and learning environment. In this paper, we identify four categories of pedagogical implications and conclude with concrete suggestions for classroom practice.

We investigate the BIBO-stability (bounded-input-bounded-output stability) of infinite-dimensional dynamical systems represented in state space form. There the challenge lies within the intricate interplay between the L∞-norms and the Hilbert space structure. Apart from studying sufficient conditions guaranteeing BIBO-stability in the special case of Riesz-spectral systems, we discuss to which extent this notion is preserved under additive and multiplicative perturbations of the system. We find that, while the latter do in general not preserve BIBO-stability, certain additive perturbations of systems with analytic semigroups do. This contribution is based upon joint work with Felix L. Schwenninger and Hans Zwart.

This paper studies scale-free protocol design for and almost output and regulated output synchronization of heterogeneous multi-agent systems with linear, right-invertible and introspective agents in presence of external disturbances. The proposed collaborative linear dynamic protocol designs are based on localized information exchange over the same communication network which do not require any knowledge of the directed network topology, spectrum of the associated Laplacian matrix, and the number of agents. Moreover, the proposed scale-free protocols achieve and almost output and regulated output synchronization with a given arbitrary degree of accuracy for any size of the network.

The latest generation wafer scanners use extreme ultraviolet light to project a pattern of electronic connections onto a silicon wafer. A significant part of the projection light is absorbed by the mirrors in the projection system. This causes the mirrors to heat up and expand, which leads to a significant reduction in the imaging quality of the wafer scanner. The imaging quality can be improved by applying an additional actuation heat load to the mirrors. Because the wafer scanner can be used with a large number of different illumination settings (which lead to different load cases) and the number of thermal actuators is limited, designing an effective actuation heater layout is an important but nontrivial task. To assist this design process, this paper proposes a computational framework to optimize a small number of spatial actuation heat load shapes with their corresponding intensities for a large number of load cases. It is guaranteed that the obtained actuation heat load shapes can keep the steady-state temperature in the optical surface of the mirror sufficiently close to a desired temperature in all considered load cases. The proposed computational framework is applied to a representative three-dimensional finite element model of a mirror. The obtained actuation heat load shapes and their corresponding intensities provide insights for the design of a thermal actuation layout for mirror heating.

We introduce the geometric structure underlying the port-Hamiltonian models for distributed parameter systems exhibiting moving material domains. The first part of the paper aims at introducing the differential geometric tools needed to represent infinite-dimensional systems on time–varying spatial domains in a port–based framework. A throughout description on the way we extend the structure presented in the seminal work [25], where only fixed spatial domains were considered, is carried through. As application of the proposed structure, we show how to model in a completely coordinate-free way the 3D fluid–structure interaction model for a rigid body immersed in an incompressible viscous flow as an interconnection of open dynamical subsystems.

The location of the spectrum and the Riesz basis property of well-posed homogeneous infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain are studied. It is shown that the Riesz basis property is equivalent to the fact that the system operator generates a strongly continuous group. Moreover, in this situation the spectrum consists of eigenvalues only, located in a strip parallel to the imaginary axis and they can decomposed into finitely many sets each having a uniform gap.

In contrast to classical strongly continuous semigroups, the study of bi-continuous semigroups comes with some freedom in the properties of the associated locally convex topology. This paper aims to give minimal assumptions in order to recover typical features like tightness and equicontinuity with respect to the mixed topology as well as to carefully clarify on mutual relations between previously studied variants of these notions. The abstract results -- exploiting techniques from topological vector spaces -- are thoroughly discussed by means of several example classes, such as semigroups on spaces of bounded continuous functions.

We consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite-dimensional systems which are bounded-input, bounded-output stable. We describe under which conditions these systems belong to an abstract class for which funnel control is known to be feasible. As an illustrative example, we show that for a system whose internal dynamics are modelled by a transport equation, which is not exponentially stable, we obtain prescribed performance of the tracking error.

By Baillon's result, it is known that maximal regularity with respect to the space of continuous functions is rare; it implies that either the involved semigroup generator is a bounded operator or the considered space contains $c_{0}$. We show that the latter alternative can be excluded under a refined condition resembling maximal regularity with respect to $\mathrm{L}^{\infty}$., Comment: 17 pages, typos corrected, several references were added

Analysis of longitudinal vibration in a nanorod is an important subject in science and engineering due to its vast application in nanotechnology. This paper introduces a port-Hamiltonian formulation for the longitudinal vibrations in a nanorod, which shows that this model is essentially hyperbolic. Furthermore, it investigates the spectral properties of the associated system operator. Standard distributed control and feedback are shown not to be controllable nor stabilizing.

We study tracking control for a nonlinear moving water tank system modelled by the linearized Saint-Venant equations, where the output is given by the position of the tank and the control input is the force acting on it. For a given reference signal, the objective is that the tracking error evolves within a pre-specified performance funnel. Exploiting recent results in funnel control, this can be achieved by showing that inter alia the system's internal dynamics are bounded-input, bounded-output stable., 10 pages, the original version was revised and more details were added

We study a nonlinear, non-autonomous feedback controller applied to boundary control systems. Our aim is to track a given reference signal with prescribed performance. Existence and uniqueness of solutions to the resulting closed-loop system is proved by using nonlinear operator theory. We apply our results to both hyperbolic and parabolic equations., Comment: 26 pages, thoroughly revised version. The system class has been generalized considerably. Added general example class of parabolic problems