Unbounded Configurations Research Articles

Deep Learning Surrogate for the Temporal Propagation and Scattering of Acoustic Waves

A deep learning surrogate for the direct numerical temporal prediction of two-dimensional acoustic waves propagation and scattering with obstacles is developed through an autoregressive spatiotemporal convolutional neural network. A single database of high-fidelity lattice Boltzmann simulations is employed in the training of the network, achieving accurate predictions for long simulation times for a variety of test cases representative of bounded and unbounded configurations. The capacity of the network to extrapolate outside the manifold of examples seen during the training phase is demonstrated by obtaining accurate acoustic predictions for relevant applications, such as the scattering of acoustic waves on an airfoil trailing edge, an engine nacelle, or an in-duct propagation. The study focuses on the influence of three main design parameters that allow rolling out accurate and stable long-term predictions: 1) the choice of a dataset-related characteristic time, 2) the normalization of the input data, and 3) the number of input temporal frames into the neural network. The results show that for the optimum choice of design parameters, the presented data-driven model is able to systematically obtain low-error prediction at a lower computational cost than the reference high-fidelity computational code.

Real‐time hybrid simulations including rocking effects: The case of a frame‐structure with unbounded elastomeric isolators

Real-time hybrid simulations (RTHS) have become an attractive alternative for the study of structural systems by conveniently separating an experimental substructure from a numerical component. Due to the technical and economic benefits of applying fiber-reinforced elastomeric isolators (FREIs) in unbounded configuration, the analysis of this device using RTHS is gaining interest among researchers. However, there are aspects associated with the complexity of the unbounded isolators that alter the dynamic behavior of the structure. One of these aspects is the rocking effect, which generally is disregarded when conducting RTHS. This paper addresses the role of rocking effects in the representation of isolated structures through RTHS. The results of different RTHS architectures show that when rocking is not taken into account, the base displacement and interstory drifts can be underestimated by more than 50%. Results from the RTHS are compared to shaking table tests (STTs) of a mock-up structure isolated with unbounded FREIs, with a maximum error less than 8% in peak and root-mean-square values of displacement and force.

Experimental testing of full-scale fiber reinforced elastomeric isolators (FREIs) in unbounded configuration

Fiber reinforced elastomeric isolators (FREIs) have shown to be a promising option as an alternative to classical steel reinforced elastomeric isolators (SREIs). Previous investigations were limited to scaled-geometries without any attempt to test such devices under code-compliant protocols as per international standards. In the present study the authors investigated two circular full-scale (diameter 620 mm) FREIs manufactured with a non-standard process adopting a soft rubber compound and polyester fibers. Experimental tests were performed in unbounded configuration through the large anti-seismic device test facility at the EUROLAB of the University of Messina, Italy. A significant number of protocols were imposed to the prototypes in order to demonstrate the effect of different loading conditions, i.e., strain level, frequency of the excitation, axial load and repeated loading. The tests confirmed the significant dependency of mechanical behavior on axial load which tends to increase damping (i.e., higher friction mechanisms) while reducing stiffness (i.e., lower stability limits). Due to internal slippage at the fiber-rubber layers interface, damping capacity of FREIs achieved 20% of critical, i.e., significantly higher than that commonly achieved in SREIs with the same rubber compound. Even if adequate capacity was reached in compression, the run-in effect would limit the axial stiffness of FREIs. A significant roll-over phenomenon was detected under lateral loading up to a maximum shear strain of 100% without damage and permanent deformation after unloading. A numerical study finally demonstrated the effectiveness of FREIs when compared to SREIs in a base isolation system designed for a 3-storey reinforced concrete frame located in a high seismicity region in Italy. Lower axial stiffness of FREIs did not affect the seismic performance of the building due to limited rocking motion component and beneficial higher damping mechanism. This paper provides a significant contribution to the standardization of FREIs to be adopted in base isolation of conventional buildings.

A hierarchical decomposition of internal wave fields

Internal gravity wave fields are decomposed into temporal modes revealing the hierarchical structure of nonlinear wave–wave interactions. We present a novel fusion of Green's functions for solving the forced internal wave equation with a weakly nonlinear perturbation expansion. Our approach is semi-analytical, based on integration over finite elements with the perturbation expansion ensuring source terms at each order are only dependent on the solutions at lower orders. Thus, the procedure is purely inductive and efficient to compute. To perform a thorough validation of our new method, we diagnose experiments using synthetic Schlieren and apply sophisticated post-processing techniques, including dynamic mode decomposition, to obtain these temporal modes for systems with discrete input frequencies. By decomposing the experimental field and comparing individual constituents against equivalents synthesised by our model, we are able to present the first truly comprehensive, validated, mechanistic picture of wave–wave interactions to arbitrary order. This synergy enables us to identify non-wave oscillatory behaviour at frequencies shared by waves in the hierarchy and leads us to discover an important open question regarding transmission efficiency within individual wave–wave interactions. Although our experiments are generated by boundary displacements, we present equivalences between source terms and boundary displacements so that the class of applicable systems may be broadened. Our technique also generalises to aperiodic and unbounded configurations and to any weakly nonlinear wave-governed system for which there is an available Green's function.

Effects of the long-term aging of glass-fiber reinforced bearings (FRBs) on the seismic response of a base-isolated residential building

Rubber based devices for seismic isolation have been adopted worldwide to protect buildings and bridges from seismic events. Very recently, a significant research effort has been dedicated to the study of Fiber Reinforced Bearings (FRBs), a low cost rubber based device for seismic hazard mitigation. In some applications, FRBs could be preferred over traditional steel reinforced isolators as: (i) they are lighter than conventional devices, (ii) FRBs can be produced with an easy manufacturing process where each bearing is cut to size and shape from a pad of large dimensions, (iii) FRBs require materials with low mechanical properties and cost. This is because FRBs are generally adopted in unbounded configurations and they are free to roll off from the supports. While these devices have shown to be an effective passive protection strategy in many applications, the effects of aging and other environmental conditions on the mechanical properties of these bearings are still to be addressed. With this consideration in mind, the aims of this work are those of: (i) studying the long-term performance and durability of FRBs through experimental testing, (ii) verifying the effects of aging on the response of FRBs both in compression and shear, (iii) determining the effects of aging of the bearings on the seismic response of a benchmark base isolated building, while (iv) comparing the as new and aged response of neoprene FRBs against that of conventional steel reinforced bearings. This work contributes toward determining the viability of FRBs as base isolation devices for residential buildings and toward determining the effects of their aging on the seismic response of a typical residential building.

Recycled versus Natural-Rubber Fiber-Reinforced Bearings for Base Isolation: Review of the Experimental Findings

ABSTRACT Over the last decade, significant efforts have been dedicated to develop novel low-cost seismic protection systems that could be used on a large scale in developing regions of the world. In the attempt of reducing the cost of conventional base isolation devices, the feasibility of using flexible reinforcements to replace the steel sheets of traditional steel-reinforced elastomeric isolators (SREIs) has been validated. It has also been verified that these bearings can be installed in unbonded configurations. Previous research has verified the performance of fiber-reinforced elastomeric isolators in unbounded configuration (U-FREIs) using recycled elastomers. The use of recycled rubber to manufacture U-FREIs is very appealing because of its low-cost and its limited environmental impact. In this paper a thorough comparison of the performance of natural-rubber unbounded fiber-reinforced elastomeric isolators (NU-FREIs) and that of recycled rubber bearings (RU-FREIs) is proposed. To this end, the paper discusses the manufacturing and the main features of the two different technologies, as well as the results of experimental tests on the devices and small-scale structures tested on a shaking-table. Overall, the performance of NU-FREIs was found to be better than that of RU-FREIs. Nevertheless, recycled rubber devices are very promising when it comes to protecting non-engineered constructions from moderate to high seismic inputs at a fraction of the cost of conventional technologies.

Large deviations of empirical measures of diffusions in weighted topologies

We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the standard Cramér condition in the context of diffusion processes, which turns out to be related to a spectral gap condition for a Witten–Schrödinger operator. Secondly, we study more precisely the properties of the Donsker–Varadhan rate functional associated with the LDP. We revisit and generalize some standard duality results as well as a more original decomposition of the rate functional with respect to the symmetric and antisymmetric parts of the dynamics. Finally, we apply our results to overdamped and underdamped Langevin dynamics, showing the applicability of our framework for degenerate diffusions in unbounded configuration spaces.

Experimental assessment and analytical modeling of novel fiber-reinforced isolators in unbounded configuration

Base isolation system is one of the most commonly used technologies implemented around the world for seismic protection of infrastructure. Its objectives are the protection of human life and the reduction of damage to buildings as a result of earthquakes. However, the system is rarely used in developing countries such as Colombia, due to its relatively high costs, including the cost of importing the devices. The development of an isolation system using local technology therefore eliminates the latter expense. This paper focuses on the experimental assessment and analytical modeling of low-cost seismic isolators for low-rise buildings, which represent most construction projects worldwide. Two types of unbonded isolator with a high damping rubber matrix and different reinforcement fibers were employed: carbon and polyester. Scaled prototypes were manufactured and tested under compression and shear loads. Despite the lower mechanical properties of polyester, the results revealed an adequate comparison between the vertical and horizontal properties of the two isolators, with both satisfying minimum required design values. Nevertheless, when taking into account the fact that the price of polyester fiber is one order of magnitude less than of carbon, this seems to be the option with greater potential to be implemented as a low-cost seismic isolation system. Based on the experimental results, an analytical model was proposed to estimate the horizontal stiffness of unbounded isolators, taking into account the reinforcement characteristics, the effective area and the shear modulus of the rubber. In comparison with other formulations, the proposed model was found to be sufficiently accurate to be used in the preliminary design of unbonded fiber-reinforced elastomeric isolators.

When is a quantum cellular automaton (QCA) a quantum lattice gas automaton (QLGA)?

Quantum cellular automata (QCA) are models of quantum computation of particular interest from the point of view of quantum simulation. Quantum lattice gas automata (QLGA - equivalently partitioned quantum cellular automata) represent an interesting subclass of QCA. QLGA have been more deeply analyzed than QCA, whereas general QCA are likely to capture a wider range of quantum behavior. Discriminating between QLGA and QCA is therefore an important question. In spite of much prior work, classifying which QCA are QLGA has remained an open problem. In the present paper we establish necessary and sufficient conditions for unbounded, finite QCA (finitely many active cells in a quiescent background) to be QLGA. We define a local condition that classifies those QCA that are QLGA, and we show that there are QCA that are not QLGA. We use a number of tools from functional analysis of separable Hilbert spaces and representation theory of associative algebras that enable us to treat QCA on finite but unbounded configurations in full detail.

Relativistic stars with a linear equation of state: analogy with classical isothermal spheres and black holes

We complete our previous investigations concerning the structure and the stability of “isothermal” spheres in general relativity. This concerns objects that are described by a linear equation of state, P = q� , so that the pressure is proportional to the energy density. In the Newtonian limit q → 0, this returns the classical isothermal equation of state. We specifically consider a self-gravitating radiation (q = 1/3), the core of neutron stars (q = 1/3), and a gas of baryons interacting through a vector meson field (q = 1). Inspired by recent works, we study how the thermodynamical parameters (entropy, temperature, baryon number, mass-energy, etc.) scale with the size of the object and find unusual behaviours due to the non-extensivity of the system. We compare these scaling laws with the area scaling of the black hole entropy. We also determine the domain of validity of these scaling laws by calculating the critical radius (for a given central density) above which relativistic stars described by a linear equation of state become dynamically unstable. For photon stars (self-gravitating radiation), we show that the criteria of dynamical and thermodynamical stability coincide. Considering finite spheres, we find that the mass and entropy present damped oscillations as a function of the central density. We obtain an upper bound for the entropy S and the mass-energy M above which there is no equilibrium state. We give the critical value of the central density corresponding to the first mass peak, above which the series of equilibria becomes unstable. We also determine the deviation from the Stefan-Boltzmann law due to self-gravity and plot the corresponding caloric curve. It presents a striking spiraling behaviour like the caloric curve of isothermal spheres in Newtonian gravity. We extend our results to d-dimensional spheres and show that the oscillations of mass-versus-central density disappear above a critical dimension dcrit(q). For Newtonian isothermal stars (q → 0), we recover the critical dimension dcrit = 10. For the stiffest stars (q = 1), we find dcrit = 9 and for a self-gravitating radiation (q = 1/d )w e fi nddcrit = 9.96404372... very close to 10. Finally, we give simple analytical solutions of relativistic isothermal spheres in two-dimensional gravity. Interestingly, unbounded configurations exist for a unique mass Mc = c 2 /(8G).

Mixed Convection From a Heated Square Cylinder to Newtonian and Power-Law Fluids

Steady laminar mixed convection flow and heat transfer to Newtonian and power-law fluids from a heated square cylinder has been analyzed numerically. The full momentum and energy equations along with the Boussinesq approximation to simulate the buoyancy effects have been solved. A semi-explicit finite volume method with nonuniform grid has been used for the range of conditions as: Reynolds number 1–30, power-law index: 0.8–1.5, Prandtl number 0.7–100 (Pe⩽3000) for Richardson number 0–0.5 in an unbounded configuration. The drag coefficient and the Nusselt number have been reported for a range of values of the Reynolds number, Prandtl number, and Richardson number for Newtonian, shear-thickening (n>1) and shear-thinning (n<1) fluids. In addition, detailed streamline and isotherm contours are also presented to show the complex flow field, especially in the rear of the cylinder. The effects of Prandtl number and of power-law index on the Nusselt number are found to be more pronounced than that of buoyancy parameter (Ri⩽0.5) for a fixed Reynolds number in the steady cross-flow regime (Re⩽30).

Handling Liveness Properties in (ω-)Regular Model Checking

Since the topic emerged several years ago, work on regular model checking has mostly been devoted to the verification of state reachability and safety properties. Though it was known that liveness properties could also be checked within this framework, little has been done about working out the corresponding details, and experimentally evaluating the approach. This paper addresses these issues in the context of regular model checking based on the encoding of states by finite or infinite words. It works out the exact constructions to be used in both cases, and solves the problem resulting from the fact that infinite computations of unbounded configurations might never contain the same configuration twice, thus making cycle detection problematic. Several experiments showing the applicability of the approach were successfully conducted.

The motion generated by a rising particle in a rotating fluid – numerical solutions. Part 2. The long container case

Numerical finite-difference results from the full axisymmetric incompressible Navier–Stokes equations are presented for the problem of the slow axial motion of a disk particle in an incompressible, rotating fluid in a long cylindrical container. The governing parameters are the Ekman number, E = ν*/(Ω*a*2), Rossby number, Ro = W*/(Ω*a*), and the dimensionless height of the container, 2H (the scaling length is the radius of the particle, a*; Ω* is the container angular velocity, W* is the particle axial velocity and ν* the kinematic viscosity). The study concerns the flow field for small values of E and Ro while HE is of order unity, and hence the appearance of a free Taylor column (slug) of fluid ‘trapped’ at the particle is expected. The numerical results are compared with predictions of previous analytical approximate studies. First, developed (quasi-steady-state) cases are considered. Excellent agreement with the exact linear (Ro = 0) solution of Ungarish & Vedensky (1995) is obtained when the computational Ro = 10−4. Next, the time-development for both an impulsive start and a start under a constant axial force is considered. A novel unexpected behaviour has been detected: the flow field first attains and maintains for a while the steady-state values of the unbounded configuration, and only afterwards adjusts to the bounded container steady state. Finally, the effects of the nonlinear momentum advection terms are investigated. It is shown that when Ro increases then the dimensionless drag (scaled by μ*a*W*) decreases, and the Taylor column becomes shorter, this effect being more pronounced in the rear region (μ* is the dynamic viscosity). The present results strengthen and extend the validity of the classical drag force predictions and therefore the issue of the large discrepancy between theory and experiments (Maxworthy 1970) concerning this force becomes more acute.

The small-energy three-body systems

We study near-Lagrange collinear configurations in the three-dimensional three-body problem, with arbitrary gravitating masses. A general method, previously developed for Coulombian systems, which provides a unique formalism for treating few-body systems close to the breakup threshold, has been employed to study the motion of three bodies both for bounded and unbounded configurations. The dependence of the triple-escape function on the small total energy E has been evaluated, as well as ‘rovibronic configurations’ for bounded motion. An approximate characteristic constant is found for symmetrical systems, ω′/ζκ, where ω′ and ω are the vertical libration mode and rotational mode angular frequencies, respectively, and κ is the threshold exponent. For equal-mass systems this constant acquires the value 1.05288.

Application of finite-element method to arbitrarily shaped discontinuities in a dielectric slab waveguide

A combined method, using the finiteelement approach and the analytical approach, is described for the solution of arbitrarily shaped discontinuities in a dielectric slab waveguide. Both TE and TM mode incidences are treated. The method is based on replacing the unbounded configuration by a corresponding bounded structure. The validity of the method is confirmed by comparing numerical results for step discontinuities with other available results. Computed results are also presented for typical boundary deformations in optical fibres caused by a fusion splice.

Numerical analysis of the discontinuities in slab dielectric waveguides

We propose an approximate method, of general applicability, for analyzing the discontinuities in slab dielectric waveguides. The method is based on replacing the unbounded configuration by a corresponding periodic multilayer structure. Hence the entire spectrum becomes discrete, and this makes the problem easier. The characteristic equation for the modal solution in a periodical multilayer dielectric waveguide is expressed in a matrix form which can be readily solved with a computer. In order to solve the discontinuity problems of slab waveguides, we expressed the reflected and transmitted fields by truncated modal expansions. The unknown amplitudes of the reflected and transmitted modes are determined by the boundary conditions. Numerical results are graphically shown including the cases which have been difficult to analyze by other methods. The accuracy of our results is checked by evaluating the relative errors and comparing with other available results.

Relativistic Klein-Gordon systems

A static spherical distribution of incoherent matter which is a source of the Klein-Gordon field is considered in equilibrium under its gravitational attraction and short-range repulsion. Numerical solutions of the full Einstein-scalar equations are obtained. The solutions are regular everywhere, and have simple physical interpretation. The stability of the system under various degrees of concentration is discussed. The impossibility of a bounded, static configuration of massless Klein-Gordon charges under its self-gravitation is deduced; furthermore, it is shown that unbounded configurations are exact solutions of the vacuum equations with cosmological constant.