Quasi-static Systems Research Articles

Scaling of buccal mass growth and muscle activation determine the duration of feeding behaviours in the marine mollusc Aplysia californica.

The mechanical forces experienced during movement and the time constants of muscle activation are important determinants of the durations of behaviours, which may both be affected by size-dependent scaling. The mechanics of slow movements in small animals are dominated by elastic forces and are thus quasistatic (i.e. always near mechanical equilibrium). Muscular forces producing movement and elastic forces resisting movement should scale identically (proportional to mass2/3), leaving the scaling of the time constant of muscle activation to play a critical role in determining behavioural duration. We tested this hypothesis by measuring the duration of feeding behaviours in the marine mollusc Aplysia californica whose body sizes spanned three orders of magnitude. The duration of muscle activation was determined by measuring the time it took for muscles to produce maximum force as A. californica attempted to feed on tethered inedible seaweed, which provided an in vivo approximation of an isometric contraction. The timing of muscle activation scaled with mass0.3. The total duration of biting behaviours scaled identically, with mass0.3, indicating a lack of additional mechanical effects. The duration of swallowing behaviour, however, exhibited a shallower scaling of mass0.17. We suggest that this was due to the allometric growth of the anterior retractor muscle during development, as measured by micro-computed tomography (micro-CT) scans of buccal masses. Consequently, larger A. californica did not need to activate their muscles as fully to produce equivalent forces. These results indicate that muscle activation may be an important determinant of the scaling of behavioural durations in quasistatic systems.

Krylov complexity of open quantum systems: from hard spheres to black holes

We examine the complexity of quasi-static chaotic open quantum systems. As a prototypical example, we analytically compute the Krylov complexity of a slowly leaking hard-sphere gas using Berry’s conjecture. We then connect it to the holographic complexity of a d + 1-dimensional evaporating black hole using the Complexity=Volume proposal. We model the black hole spacetime by stitching together a sequence of static Schwarzschild patches across incoming negative energy null shock waves. Under certain identification of parameters, we find the late time complexity growth rate during each quasi-static equilibrium to be the same in both systems.

Crushing responses and energy absorption of bionic inspired corrugated honeycombs

To improve the energy absorption of traditional structures, impact resistant natural materials are usually mimicked to develop novel structures with desirable energy absorption. In this work, inspired by the unique 3D corrugated microstructure of vascular bundles in pomelo peel, a new design of honeycomb structure with corrugated characteristics is proposed. Further, motivated by special nodal bulkhead architecture of bamboo, layered honeycombs with diaphragms are designed and fabrication by metal 3D printing technology. The quasi-static and dynamic crushing responses and energy absorption characteristics of six types of bio-inspirational honeycombs (ISWH, LSWH, ISCH, LSCH, IPCH and LPCH) are studied using quasi-static testing machine and dynamic drop-weight impact experimental systems. To investigate the effect of impact speed on the crashworthiness performance of the honeycombs, the tests of the honeycombs impacted by the drop-weight with two different mass (106.07 and 59.60 Kg) and three impact velocity (V1=6.23, V2=8.82 and V3=11.77 m/s), respectively, are performed. The experimental results indicate that the crush failure mode of the layered honeycombs is more regular than that of the integrated honeycombs. Failure of all layered honeycombs occurs first at the junction of the honeycomb and diaphragms. Under impact loading, the layered corrugated wall honeycombs exhibit a greater final crushing distance than their corresponding integrated honeycombs. The design of corrugated wall can effectively reduce the initial peak force of the integrated honeycombs, while the layered honeycomb design also facilitates the reduction of the initial peak force, thus avoiding damage to personnel or equipment from excessive peak collision forces. The layered design will reduce the specific energy absorption of the integrated honeycombs in most cases, but a reasonable combination of layered and corrugated wall design can also effectively increase the specific energy absorption of the honeycombs under a specific loading speed. And, the layered design can also effectively improve the crush force efficiency of the corresponding integrated honeycombs.

Rate-Limited and Energy-Efficient Feedforward Control for Multi-Fuel Unmanned Aircraft Systems Engine

Abstract Surrogate-model or data-driven model-based control frameworks are becoming increasingly popular in recent years due to their ease of model development and enhanced computational power, making them suitable for real-time use. However, when it comes to modeling aspects related to time, difficulties arise as many of the models deal with quasi-static systems. In this paper, we propose a method to model time-dependent actuator constraints in a surrogate-model-based control framework for controlling the combustion phasing in a multi-fuel UAS engine. Along with this, a conducive method for designing an energy-efficient ignition assistant control is discussed. The developed methods are then tested on a diesel engine, and the results show a more robust and energy-efficient combustion phasing control as the fuel property varies in real-time.

Weak-form homogenization of two and three-dimensional fluid acoustical systems.

A one-dimensional weak-form homogenization method [Muhlestein, J. Acoust. Soc. Am. 147(5), 3584-3593 (2020)] is extended to two and three-dimensional for quasi-static fluid systems. This homogenization approach uses a local multiple-scales approximation to estimate the acoustical fields within a representative volume element, substitutes these approximations into a weak formulation of the mechanics, and then globally homogenizes the system by averaging the integrand of the weak-form integral. An important consequence of including more spatial dimensions is that the local particle velocity does not approach a uniform macroscopic particle velocity. Instead, the effective material properties are used to describe the behavior of the mean particle velocity. A localization tensor may be used to convert from the mean particle velocity to the local particle velocity. The generalized homogenization method is then applied to two special cases. The first case is stratified media, chosen because it has an exact analytical solution. The second case is a cubic lattice of spheres, which has a benchmark solution to compare with. This second case utilizes finite element software to provide estimates of the effective mass density. Finally, three further generalizations to the homogenization method, including extension to finite frequency values, complex media, and elasticity, are briefly discussed.

Continuous Mobile Thin-Layer On-Site Printing

Quasi-static robotic systems and discrete fabrication strategies fall short of the capabilities needed for automating on-site plastering, which involves operating over large spans and maintaining material continuity. This paper presents continuous, mobile Robotic Plaster Spraying (RPS) – a thin-layer, spray-based printing-in-motion technique using cementitious plaster – realized on a prototypical construction site. The experimental setup consists of a fully mobile, custom wheeled base that is synchronized with a robotic arm, and an integrated pumping and spraying system. In this 1:1 scale application, the print layers are executed during the motion of the mobile robot and they are printed vertically on the walls of an existing building structure. The experiments showcase the potentials of producing bespoke – three-dimensional – or standardized – flat – plasterwork with the proposed technique. The results demonstrate the applicability and scalability of RPS and the findings contribute to the research on mobile additive fabrication.

Magnetic energy in quasistatic systems

Magnetic energy is often presented solely as an energy stored by an inductor or in a magnetic field, in contrast to electrostatic energy which is introduced through the concepts of electric interaction between point-charges. Quasistatics, with its many applications in everyday life and important pedagogical appeal, has many similarities to statics and can allow a discussion of magnetic energy in terms which reinforces the parallel between magnetostatics and electrostatics. With this goal in mind, we consider two simple examples in textbooks involving a parallel plate capacitor and a flattened solenoid, to discuss the interplay between the work of external forces, the work of the electric interaction forces between the charges and currents and the electric and magnetic energies stored in these devices.

Energy and dynamic analysis of quasi-static toggling mechanical energy harvester

The self-powered wireless switch is one of the successful battery-free electronic products, which can be fully powered by a small mechanical energy harvesting (MEH). In most existing designs, bistable toggling electromagnetic energy harvesters are utilized to extract the mechanical energy associated with the switch toggling motions. Although such MEH modules are already put into volume production, the toggling dynamics and their energy profile have not been seriously investigated yet. This paper gives a comprehensive study of this toggling MEH. The released energy in a toggling action is quantified based on a varying potential well theoretical model. The mechanical–magnetic–electrical interaction within this dynamic system is better revealed with a simulation model built in Matlab Simulink. Experimental results further validate both the theory and simulation. The new insight into these quasi-static MEH systems and their essential potential energy precharging mechanism fills the gap between leading engineering practice and lagging academic study, in terms of application significance, over the last two decades.

Sensitivity of D<sub>it</sub> Extraction at the SiO<sub>2</sub>/SiC Interface Using Quasi-Static Capacitance-Voltage Measurements

In this work, we compare different quasi-static capacitance-voltage measurement systems by analyzing 4H-SiC n-type MOS capacitors and studying the influence of systematic errors when extracting the interface trap density (Dit). We show that the extracted Dit strongly depends on the calculation of the surface potential due to variations of the integration constant. In addition, the ramp-rate during the quasi-static measurement is identified as a sensitive measurement parameter whose noise level is amplified in the Dit extraction.

Weak solutions in nonlinear poroelasticity with incompressible constituents

We consider quasi-static nonlinear poroelastic systems with applications in biomechanics and, in particular, tissue perfusion. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid pressure are considered. The system under consideration represents a nonlinear, implicit, degenerate evolution problem, which falls outside of the well-known implicit semigroup monotone theory. Previous literature related to proving existence of weak solutions for these systems is based on constructing solutions as limits of approximations, and energy estimates are obtained only for the constructed solutions. In comparison, in this treatment we provide for the first time a direct, fixed point strategy for proving the existence of weak solutions, which is made possible by a novel result on the uniqueness of weak solutions of the associated linear system (where the permeability is given as a function of space and time). The uniqueness proof for the associated linear problem is based on novel energy estimates for arbitrary weak solutions, rather than just for constructed solutions. The results of this work provide a foundation for addressing strong solutions, as well as uniqueness of weak solutions for nonlinear poroelastic systems.

Uplink Performance Of Coordinated Multipoint In 5G Cellular Network

The study aims to study the uplink performance of coordinated multipoint in 5G cellular network. Nonetheless, this approach cannot deal with inter-cluster intrusion, and adjusts only the cell borders of the interference. In the other side, because CoMP relies on static clusters and the whole spectrum is dedicated to each, we cannot ignore the issue of edge MS, whether for full spectrum, quasi-static, or non-spectrum systems. Clustering of spectrum distribution is mentioned here; issues with the CoMP approach are discussed in this paper. One-to-many point-to-many grid network grid network (B4G/5G) is essential in connecting disparate geographical locations. The prior studies have analyzed how to better load-balancing would help with static fault tolerance and improve device throughput were concerned. We expand the cooperating collection when needed to service traffic on demand, dynamically composing the cells on the base stations in order to give cells more transmit power for larger scale operations or to accommodate more users. Doing it dynamically in real-time to manage members' radio energy more effectively enables the device to offload traffic through usable cells to eliminate capacity concerns. There are two kinds of methods of clustering MSs according to their movement speeds: In the low mobility method, hybrid cells are found for each subband; in the high mobility approach, a new configuration of subbands is chosen to overcome an unanticipated shift in mobility The Monte Carlo simulations have proof and demonstrate our next-generation connectivity ability. The current approaches demonstrate an improvement in device throughput, radio resource consumption, and electricity usage, which means they are beneficial when it comes to overall energy efficiency. As a result, an alternative that is both intra- and inter-cluster conflict is presented to the Cloud Radio Access Network (C-RAN) is introduced to counter both demand and power fluctuation—dynamic joint processing.

Sunklodas’ Approach to Normal Approximation for Time-Dependent Dynamical Systems

We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general normalizing sequence $b(N)$ of invertible square matrices, are approximated by a normal distribution with respect to a metric of regular test functions. Depending on the metric and the normalizing sequence $b(N)$, the conditions imply that the error in the approximation decays either at the rate $O(N^{-1/2})$ or the rate $O(N^{-1/2} \log N)$, under the additional assumption that $\Vert b(N)^{-1} \Vert \lesssim N^{-1/2}$. The error comes with a multiplicative constant whose exact value can be computed directly from the conditions. The proof is based on an observation due to Sunklodas regarding Stein's method of normal approximation. We give applications to one-dimensional random piecewise expanding maps and to sequential, random, and quasistatic intermittent systems.

Off‐board and on‐board energy storage versus reversible substations in DC railway traction systems

The present study describes and analyses a set of quasi-static railway power systems models and simulations considering on-board and off-board energy storage systems but also reversible and non-reversible substations and regenerative braking trains. The advantages and drawbacks of each technology are discussed. Then, several case studies considering different technological combinations are introduced and simulated, while the attained results are compared and analysed. In this regard, to cover all the casuistic, two simple explanatory cases are first exposed and then eight realistic scenarios are examined, which are simulated for a long time interval and also explained considering aggregated results.

Central limit theorems with a rate of convergence for time-dependent intermittent maps

We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate of convergence. For maps chosen from a certain parameter range, but without additional assumptions on how the maps vary with time, we obtain a self-norming CLT provided that the variances of the partial sums grow sufficiently fast. When the maps are chosen randomly according to a shift-invariant probability measure, we identify conditions under which the quenched CLT holds, assuming fiberwise centering. Finally, we show a multivariate CLT for intermittent quasi-static systems. Our approach is based on Stein’s method of normal approximation.

Suitable rolling resistance model for quasi-static shear tests of non-spherical particles via discrete element method

Rolling resistance is a main consideration in quasi-static shear test simulations of particles via the discrete element method. However, not all rolling resistance models can satisfy the required objectivity and rate independence. A suitable model for spherical particles has been selected from five models in our previous works. In the current study, this model is combined with four normal and tangential contact models to confirm its applicability. After confirmation, the model is generalized to simulate direct shear tests on non-spherical particles. The stress–strain and dilatancy curves are rate-independent, and the relative rolling velocity between particles is objective. Furthermore, objectivity and rate independence for arbitrarily shaped particles are unchanged when normal stresses, volume fractions, or normal and tangential contact models are changed. Simulation results are also consistent with other experiment findings. For comparison, results are calculated for two other rolling resistance models; the shear curve at a single speed is consistent with the experiment, which has three stages: elastoplastic increasing, yielding, and keeping. However, the stress–strain curves at different shear rates do not coincide, which means that the models conflict with the rate independence of quasi-static granular systems. The virtues and defects of the five rolling resistance models are discussed from the perspectives of objectivity and rate independence. These two properties provide criteria for determining the appropriateness of a model, which has been rarely discussed in former studies.

Intermittent quasistatic dynamical systems: weak convergence of fluctuations

Abstract This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influences. We focus on the case where the time-evolution is described by intermittent interval maps (Pomeau-Manneville maps) with time-dependent parameters. In a suitable range of parameters, we obtain a description of the statistical properties as a stochastic diffusion, by solving a well-posed martingale problem. The results extend those of a related recent study due to Dobbs and Stenlund, which concerned the case of quasistatic (uniformly) expanding systems.

A generalized finite element method for linear thermoelasticity

We propose and analyze a generalized finite element method designed for linear quasistatic thermoelastic systems with spatial multiscale coefficients. The method is based on the local orthogonal decomposition technique introduced by Målqvist and Peterseim (Math. Comp. 83 (2014) 2583–2603). We prove convergence of optimal order, independent of the derivatives of the coefficients, in the spatial H1-norm. The theoretical results are confirmed by numerical examples.

An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

We prove almost sure ergodic theorems for a class of systems called quasistatic dynamical systems. These results are needed, because the usual theorem due to Birkhoff does not apply in the absence of invariant measures. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then verify the conditions of the theorems and identify physical families of measures for two concrete models, quasistatic expanding systems and quasistatic dispersing billiards.

Quasistatic dynamical systems

We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where the observed system transforms (infinitesimally) slowly due to external influence, tracing out a continuous path of thermodynamic equilibria over an (infinitely) long time span. Time evolution of states under a quasistatic dynamical system is entirely deterministic, but choosing the initial state randomly renders the process a stochastic one. In the prototypical setting where the time evolution is specified by strongly chaotic maps on the circle, we obtain a description of the statistical behavior as a stochastic diffusion process, under surprisingly mild conditions on the initial distribution, by solving a well-posed martingale problem. We also consider various admissible ways of centering the process, with the curious conclusion that the ‘obvious’ centering suggested by the initial distribution sometimes fails to yield the expected diffusion.

Identification of some nonsmooth evolution systems with illustration on adhesive contacts at small strains

A class of evolution quasi-static systems which leads, after a suitable time discretization, to recursive non-linear programs, is considered and optimal control or identification problems governed by such systems are investigated. The resulting problem is an evolutionary Mathematical Programs with Equilibrium Constraints. A subgradient information of the (in general nonsmooth) composite objective function is evaluated and the problem is solved by the implicit programming approach. The abstract theory is illustrated on an identification problem governed by delamination of a unilateral adhesive contact of elastic bodies discretized by finite-element method in space and a semiimplicit formula in time. Being motivated by practical tasks, an identification problem of the fracture toughness and of the elasticity moduli of the adhesive is computationally implemented and tested numerically on a two-dimensional example. Other applications including frictional contacts or bulk damage, plasticity or phase transformations are outlined.