Horizon Size Research Articles

An immersed peridynamics model of fluid-structure interaction accounting for material damage and failure

This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an incompressible structure immersed in a viscous incompressible fluid. It expresses the momentum equation and incompressibility constraint in Eulerian form, and it describes the structural motion and resultant forces in Lagrangian form. Coupling between Eulerian and Lagrangian variables is achieved by integral transforms with Dirac delta function kernels, as in standard immersed boundary methods. The major difference between our approach and conventional immersed boundary methods is that we use peridynamics, instead of classical continuum mechanics, to determine the structural forces. We focus on non-ordinary state-based peridynamic material descriptions that allow us to use a constitutive correspondence framework that can leverage well-characterized nonlinear constitutive models of soft materials. The convergence and accuracy of our approach are compared to both conventional and immersed finite element methods using widely used benchmark problems of nonlinear incompressible elasticity. We demonstrate that the immersed peridynamics method yields comparable accuracy with similar numbers of structural degrees of freedom for several choices of the size of the peridynamic horizon. We also demonstrate that the method can generate grid-converged simulations of fluid-driven material damage growth, crack formation and propagation, and rupture under large deformations.

Predictive receding-horizon multi-robot task allocation applied to the mapping of direct normal irradiance in a thermosolar power plant

This article considers a robotic sensor network that measures the loss of irradiance in a thermosolar power plant due to moving clouds. To this end, a receding-horizon predictive algorithm is proposed for multi-robot task allocation. Despite the high nonlinearity of the problem, the experiments carried out varying the horizon size show that the proposed method has a good performance with small horizons and tasks moving in similar directions, outperforming a previously published approach based on genetic algorithms. Finally, realistic simulations performed on a solar plant implemented in Robot Operating System/Gazebo prove the feasibility of the proposed method and its potential to provide significant performance gains with a much lower investment than an equivalent fixed sensor network.

Gravitational Waves from Rapid Structure Formation on Microscopic Scales before Matter-Radiation Equality.

The existence of scalar fields can be probed by observations of stochastic gravitational waves. Scalar fields mediate attractive forces, usually stronger than gravity, on the length scales shorter than their Compton wavelengths, which can be non-negligible in the early Universe, when the horizon size is small. These attractive forces exhibit an instability similar to the gravitational instability, only stronger. They can, therefore, lead to the growth of structures in some species. We identify a gravitational waves signature of such processes and show that it can be detected by future gravitational waves experiments.

On the statistical theory of self-gravitating collisionless dark matter flow

Dark matter, if it exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale-dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e., correlation, structure, dispersion, and spectrum functions, are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share the same kinematic relations for even order correlations. The limiting correlation of velocity ρL=1/2 on the smallest scale (r = 0) is a unique feature of collisionless flow (ρL=1 for incompressible flow). On large scale, transverse velocity correlation has an exponential form T2∝e−r/r2 with a constant comoving scale r2=21.3 Mpc/h that may be related to the horizon size at matter–radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of S2l∝r1/4. All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale r between 1 and 7 Mpc/h. Divergence is negatively correlated for r > 30 Mpc/h that leads to a negative density correlation.

Measurement of the matter-radiation equality scale using the extended baryon oscillation spectroscopic survey quasar sample

ABSTRACT The position of the peak of the matter power spectrum, the so-called turnover scale, is set by the horizon size at the epoch of matter-radiation equality. It can easily be predicted in terms of the physics of the universe in the relativistic era, and so can be used as a standard ruler, independent of other features present in the matter power spectrum, such as baryon acoustic oscillations (BAOs). We use the distribution of quasars measured by the extended Baryon Oscillation Spectroscopic Survey (eBOSS) to determine the turnover scale in a model-independent fashion statistically. We avoid modelling the BAO by down-weighting affected scales in the covariance matrix using the mode deprojection technique. We measure the wavenumber of the peak to be $k_\mathrm{TO} = \left(17.6^{+1.9}_{-1.8} \right) \times 10^{-3}h/\mathrm{Mpc}$, corresponding to a dilation scale of $D_\mathrm{V}(z_\mathrm{eff} = 1.48) = \left(31.1^{+4.1}_{-3.4}\right)r_\mathrm{H}$. This is not competitive with current BAO distance measures in terms of determining the expansion history but does provide a useful cross-check. We combine this measurement with low-redshift distance measurements from type-Ia supernova data from Pantheon and BAO data from eBOSS to make a sound-horizon free estimate of the Hubble–Lemaître parameter and find it to be $H_0=64.8^{+8.4}_{-7.8} \ \mathrm{km/s/Mpc}$ with Pantheon, and $H_0=63.3^{+8.2}_{-6.9} \ \mathrm{km/s/Mpc}$ with eBOSS BAO. We make predictions for the measurement of the turnover scale by the Dark Energy Spectroscopic Instrument (DESI) survey, the Maunakea Spectroscopic Explorer (MSE), and MegaMapper, which will make more precise and accurate distance determinations.

Double horizon peridynamics

In this study, a new double horizon peridynamics formulation was introduced by utilising two horizons instead of one as in traditional peridynamics. The new approach allows utilisation of large horizon sizes by controlling the size of the inner horizon size. To demonstrate the capability of the current approach, four different numerical cases were examined by considering static and dynamic conditions, different boundary and initial conditions, and different outer and inner horizon size values. For both static and dynamic cases, it was observed that as the inner horizon decreases, peridynamic solutions converge to classical continuum mechanics solutions even by using a larger horizon size value. Therefore, the proposed approach can serve as an alternative approach to improve computational efficiency of peridynamic simulations by obtaining accurate results with larger horizon sizes.

A nonlocal method to compute effective properties of viscoelastic composite materials based on peridynamic computational homogenization theory

This article presents a computational homogenization framework for viscoelastic composites within the framework of non-ordinary state-based peridynamic theory. The motivation to develop this framework stems from the desire to develop a homogenization scheme that can model processes and phenomena that are driven by nonlocal behaviour such as size effect and fracture for which frameworks based on the classical continuum theory lack the capability of modelling. The proposed framework was used to calculate the effective properties in both time and frequency domains of two viscoelastic matrix-inclusion composite systems, one with an elastic inclusion and viscoelastic matrix, and the other with viscoelastic inclusion and matrix. The results of calculations were found to compare well with results from the literature. A parametric study was also conducted to investigate the influence of nonlocal interaction on the effective properties by varying the horizon size. Results showed that increasing the degree of nonlocality reduces the stiffness of the composite system as well as increase its rate of creep. The capability to account for nonlocal interaction highlights the potential of this proposed scheme to provide a more comprehensive understanding of the behaviour of viscoelastic composite materials over a wide range of material behaviour.

Ordinary state-based peri-ultrasound modeling to study the effects of multiple cracks on the nonlinear response of plate structures

Since it is almost impossible to carry out a comprehensive parametric investigation experimentally for internal cracks with different geometry and orientation, a good numerical modeling and simulation technique is necessary to have a clear understanding of the physics of wave propagation and its interaction with cracks. Such investigation is helpful for structural health monitoring (SHM) with ultrasonic techniques. This work presents a nonlocal peri-ultrasound theory based on ordinary state-based (OSB) peridynamics for modeling elastic wave propagation in three-dimensional (3-D) plate structures containing multiple cracks. A relatively new and promising nonlinear ultrasonic technique called Sideband Peak Count – Index (or SPC-I) is adopted to extract the nonlinearity generated from the interactions between elastic waves and multiple cracks. Effects of three main parameters – the distance between the acoustic source and the crack, the crack spacing and the number of cracks are investigated using the proposed OSB peri-ultrasound theory together with the SPC-I technique. For each of these three parameters investigation, different crack thicknesses were considered − 0 mm (crack-free), 1 mm (thin crack), 2 mm (intermediate thickness) and 4 mm (thick crack); thin and thick cracks are defined after comparing the crack thickness value with the horizon size mentioned in the peri-ultrasound theory. It is found that for obtaining consistent results the acoustic source should be placed at least one wavelength away from the crack and crack spacings also play an important role on the nonlinear response. It is concluded that the nonlinear response diminishes when the cracks become too thick, and thin cracks show higher nonlinearity than that of thick cracks and no cracks. Finally, the proposed method which is combining the peri-ultrasound theory and SPC-I technique is used for monitoring cracks’ evolution process. The numerical modeling results are compared with the experimental findings reported in the literature. Consistent qualitative trends in SPC-I variations predicted numerically and obtained experimentally are observed, thus it gives confidence in the proposed method.

Analytical solutions of peridynamic equations. Part II: Elastic wave propagation

We use the separation of variables technique to construct analytical solutions for peridynamic models of dynamic elasticity. We show that, similar to the case of peridynamic models for transient diffusion, infinite series nonlocal solutions for peridynamic elasticity can be obtained directly from the solutions of the corresponding classical model by inserting “peridynamic/nonlocal factors” in the time-exponential part of the solution. The analytical solutions show that wave dispersion, caused by nonlocality, is contained in the horizon-dependent nonlocal factor. We obtain formulas for wave dispersion and group velocities for 1D and 2D peridynamic elastic wave propagation with three commonly-used peridynamic kernels. We observe interesting complexity in nonlocal solutions, generated by nonlocal wave dispersion, and “proportional” to the size of the nonlocal interaction region. Different from the diffusion case, as time goes to infinity, the nonlocal solution for elasticity does not converge to the classical one for a fixed horizon size, meaning that nonlocal effects persist in time. We solve several examples of wave propagation with Dirichlet boundary conditions and smooth or discontinuous initial conditions and compare these analytical solutions with those corresponding to the classical model, which is seen as a particular case of the PD model for horizon equal to zero. Interestingly, we find that in PD solutions, initial discontinuities in space persist at the same location, in time. While most of the analytical solutions we present here are formal, for some of the cases, we are able to prove uniform convergence of the series solutions. This work is the first presentation of a systematic analytical treatment of peridynamic problems in 2D finite domains.

Quintessential cosmological tensions

Several cosmological tensions have emerged in light of recent data, most notably in the inferences of the parameters ${H}_{0}$ and ${\ensuremath{\sigma}}_{8}$. We explore the possibility of alleviating both these tensions simultaneously by means of the Albrecht-Skordis ``quintessence'' potential. The field can reduce the size of the sound horizon ${r}_{s}^{*}$ while concurrently suppressing the power in matter density fluctuations before it comes to dominate the energy density budget today. Interestingly, this rich set of dynamics is governed entirely by one free parameter that is of $\mathcal{O}(10)$ in Planck units. We find that the inferred value of ${H}_{0}$ can be increased, while that of ${\ensuremath{\sigma}}_{8}$ can be decreased, both by $\ensuremath{\approx}1\ensuremath{\sigma}$ compared to the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ case. However, ultimately the model is disfavored by Planck and BAO data alone, compared to the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, with a $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}^{2}\ensuremath{\approx}+6$. When including large scale structure and supernova data we find $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}^{2}\ensuremath{\approx}+1$. We note that historically much attention has been focused on preserving the three angular scales ${\ensuremath{\theta}}_{D}$, ${\ensuremath{\theta}}_{\mathrm{EQ}}$, and ${\ensuremath{\theta}}_{s}^{*}$ to their $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ values. Our work presents an example of how, while doing so indeed maintains a relatively good fit to the cosmic microwave background data for an increased number of ultrarelativistic species, it is a priori insufficient in maintaining such a fit in more general model spaces.

Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black holes

Ricci flow is a natural gradient flow of the Einstein-Hilbert action. Here we consider the analog for the Einstein-Maxwell action, which gives Ricci flow with a stress tensor contribution coupled to a Yang-Mills flow for the Maxwell field. We argue that this flow is well-posed for static spacetimes with pure electric or magnetic potentials and show it preserves both non-extremal and extremal black hole horizons. In the latter case we find the flow of the near horizon geometry decouples from that of the exterior. The Schwarzschild black hole is an unstable fixed point of Ricci flow for static spacetimes. Here we consider flows of the Reissner-Nordström (RN) fixed point. The magnetic RN solution becomes a stable fixed point of the flow for sufficient charge. However we find that the electric RN black hole is always unstable. Numerically solving the flow starting with a spherically symmetric perturbation of a non-extremal RN solution, we find similar behaviour in the electric case to the Ricci flows of perturbed Schwarzschild, namely the horizon shrinks to a singularity in finite time or expands forever. In the magnetic case, a perturbed unstable RN solution has a similar expanding behaviour, but a perturbation that decreases the horizon size flows to a stable black hole solution rather than a singularity. For extremal RN we solve the near horizon flow for spherical symmetry exactly, and see in the electric case two unstable directions which flow to singularities in finite flow time. However, even turning these off, and fixing the near horizon geometry to be that of RN, we numerically show that the flows appear to become singular in the vicinity of its horizon.

Correlation length of the angular mode for an approximate U(1) symmetry during inflation

It is known that a light scalar field obtains fluctuations in the de Sitter inflationary background. Such fluctuations could provide an initial condition for baryogenesis through the Affleck-Dine mechanism, where an approximate U(1)B symmetry is usually assumed. However, an interpretation of the baryon number generation in this way is strongly related to the correlation length of the angular mode. In this work, we calculate the correlation length of the angular mode for a model exhibiting an approximate U(1) symmetry. We find that for a massive nearly non-interacting field, the correlation length of the angular mode is determined by the mass parameter of the model and it is similar to H−1exp⁡(H2/m2). Applying this result to baryogenesis via the Affleck-Dine mechanism with a stochastic origin, we find that only for m≪O(0.1)H (assuming N⁎=60) can the correlation length of the baryon number density be much larger than our current horizon size, such that we live in the baryon-rich region. If this is not true, at early times our universe would consist of numerous patches of baryon-rich and anti-baryon-rich regions with the average baryon number being nearly zero.

Finite Impulse Response Filtering Algorithm with Adaptive Horizon Size Selection and Its Applications

It is known, that unlike the Kalman filter (KF) finite impulse response (FIR) filters allow to avoid the divergence and unsatisfactory object tracking connected with temporary perturbations and abrupt object changes. The main challenge is to provide the appropriate choice of a sliding window size for them. In this paper, the new finite impulse response (FIR) filtering algorithm with the adaptive horizon size selection is proposed. The algorithm uses the receding horizon optimal (RHOFIR) filter which receives estimates, an abrupt change detector and an adaptive recurrent mechanism for choosing the window size. Monotonicity and asymptotic properties of the estimation error covariance matrix and the RHOFIR filter gain are established. These results form a solid foundation for justifying the principal possibility to tune the filter gain using them and the developed adaptation mechanism. The proposed algorithm (the ARHOFIR filter) allows reducing the impact of disturbances by varying adaptively the sliding window size. The possibility of this follows from the fact that the window size affects the filter characteristics in different ways. The ARHOFIR filter chooses a large horizon size in the absence of abrupt disturbances and a little during the time intervals of their action. Due to this, it has better transient characteristics compared to the KF and RHOFIR filter at intervals where there is temporary uncertainty and may provide the same accuracy of estimates as the KF in their absence. By simulation, it is shown that the ARHOFIR filter is more robust than the KF and RHOFIR filter for the temporarily uncertain systems.

H0 Tension on the Light of Supermassive Black Hole Shadows Data

Cosmological tensions in current times have opened a wide door to study new probes to constrain cosmological parameters, specifically, to determine the value of the Hubble constant H0 through independent techniques. The two standard methods to measure/infer H0 rely on: (i) anchored observables for the distance ladder, and (ii) establishing the relationship of the H0 to the angular size of the sound horizon in the recombination era assuming a standard Cosmological Constant Cold Dark Matter (ΛCDM) cosmology. However, the former requires a calibration with observables at nearby distances, while the latter is not a direct measurement and is model-dependent. The physics behind these aspects restrains our possibilities in selecting a calibration method that can help minimise the systematic effects or in considering a fixed cosmological model background. Anticipating the possibility of deeply exploring the physics of new nearby observables such as the recently detected black hole shadows, in this paper we propose standard rules to extend the studies related to these observables. Supermassive black hole shadows can be characterised by two parameters: the angular size of the shadow and the black hole mass. We found that it is possible to break the degeneracy between these parameters by forecasting and fixing certain conditions at high(er) redshifts, i.e., instead of considering the ≈10% precision from the EHT array, our results reach a ≈4%, a precision that could be achievable in experiments in the near future. Furthermore, we found that our estimations provide a value of H0=72.89±0.12 km/s/Mpc and, for the baryonic mass density, Ωm=0.275±0.002, showing an improvement in the values reported so far in the literature. We anticipate that our results can be a starting point for more serious treatments of the physics behind the SMBH shadow data as cosmological probes to relax tension issues.

Information paradox and island in quasi-de Sitter space

Whereas a static observer in de Sitter (dS) space detects thermal radiation emitted by the horizon, the dS isometries impose that the radiation is in equilibrium with the background. This implies that for the static observer to find the information paradox, the background must be deformed to quasi-dS space in which the dS isometries are spontaneously broken. We study the condition that the information paradox arises in quasi-dS space with the monotonically increasing horizon size which is used to describe the inflationary cosmology. For this purpose, the dimensional reduction of three-dimensional dS space with thermal radiation modelled by the JT gravity coupled to CFT is considered. We argue that when the central charge monotonically increases in time, the information paradox arises but the conditions for the existence of the island become more restrictive. As the central charge can be interpreted as the number of degrees of freedom, the absence of the island in quasi-dS space supports the entropy argument for the dS swampland conjecture.

Going beyond the galaxy power spectrum: An analysis of BOSS data with wavelet scattering transforms

We perform the first application of the wavelet scattering transform (WST) to actual galaxy observations, through a WST analysis of the BOSS DR12 CMASS dataset. We included the effects of redshift-space anisotropy, non-trivial survey geometry, systematic weights, and the Alcock-Paczynski distortion effect, following the commonly adopted steps for the power spectrum analysis. In order to capture the cosmological dependence of the WST, we use galaxy mocks obtained from the state-of-the-art ABACUSSUMMIT simulations, tuned to match the anisotropic correlation function of the BOSS CMASS sample in the redshift range $0.46<z<0.60$. Using our model for the WST coefficients, as well as for the first 2 multipoles of the galaxy power spectrum, that we use as reference, we perform a likelihood analysis of the CMASS data. We obtain the posterior probability distributions of 4 cosmological parameters, $\{\omega_b,\omega_c,n_s,\sigma_8\}$, as well as the Hubble constant, derived from a fixed value of the angular size of the sound horizon at last scattering measured by the Planck satellite, all of which are marginalized over the 7 nuisance parameters of the Halo Occupation Distribution model. The WST is found to deliver a substantial improvement in the values of the predicted $1\sigma$ errors compared to the regular power spectrum, which are tighter by a factor of $3-5$ in the case of flat and uninformative priors and by a factor of $3-8$, when a Big Bang Nucleosynthesis prior is applied on the value of $\omega_b$. Our results are investigative and subject to certain approximations, which we discuss in the text.

Bubble Nucleation from a de Sitter–Planck Background with Quantum Boltzmann Statistics

Every physical theory involving quantum fields requires a model of quantum vacuum. The vacuum associated to quantum gravity must incorporate the prescriptions from both the theory of relativity and quantum physics. In this work, starting from the hypothesis of nucleation of sub-Planckian bubbles from a de Sitter vacuum, we study the necessary conditions to obtain baby universes, black holes and particles. The de Sitter-Planck background is described by an “infinite” Quantum Boltzmann statistics that generates fermions and bosons, and manifests itself as a deformation of the geometry that leads to a generalized uncertainty principle, a unified expression for the generalized Compton wavelength and event horizon size, drawing a connection between quantum black holes and elementary particles, seen as a collective organization of the bubbles of the vacuum described by the generalized Compton wavelength. The quantum thermodynamics of black holes is then outlined and the physical history of each bubble is found to depend on the cosmological constant described in terms of thermodynamic pressure. A treatment of the Casimir effect is provided in the de Sitter-Planck background, and finally wormholes are explored as bubble coalescence processes.

Sideband peak count-index technique for monitoring multiple cracks in plate structures using ordinary state-based peri-ultrasound theory.

This work presents a peri-ultrasound theory based on ordinary state-based peridynamics for modeling elastic waves propagating in three-dimensional (3-D) plate structures and interacting with multiple cracks. A recently developed nonlinear ultrasonic technique called sideband peak count-index (or SPC-I) is adopted for monitoring one or more cracks with thickness values equal to 0 mm (crack-free), 1, 2, and 4 mm. Three separate scenarios-one crack, two cracks, and four cracks in 3-D plate structures-are investigated. These cracks can be classified as thin and thick cracks depending on the horizon size, which is mentioned in peri-ultrasound theory. Computed results for all three cases show larger SPC-I values for thin cracks than for thick cracks and the case of no cracks. This observation is in line with the previously reported results in the literature and proves that the state-based peri-ultrasound theory can capture the expected nonlinear response of elastic waves interacting with multiple cracks without changing the cracks' surface locations artificially, and this is always needed in most of the other numerical methods. The proposed state-based peri-ultrasound theory is more flexible and reliable for solving 3-D problems, and the out-of-plane wave field can be obtained for engineering analysis.

Continuous‐time optimal unbiased FIR filter for input‐delayed systems

ABSTRACTMost existing finite impulse response (FIR) filters are restricted to models without delays. This paper proposes an continuous‐time optimal unbiased FIR filter for input‐delayed systems (CTOUFFID). A new integral transformation relation was introduced to derive the FIR filter. By applying this relation, the CTOUFFID problem is represented as an optimal control problem with zero terminal state. The filter gain function is obtained by solving two coupled matrix differential equations using initial conditions. The paper also offers discussion on the horizon size and a few special cases. The main benefit of the proposed solution is that it provides the maximum likelihood estimate with no requirements for the initial values. Finally, an application with the ‐404 turbofan engine model is presented to demonstrate the highly robust nature of the proposed FIR filer against incomplete noise information and unspecified model uncertainties.

An empirical investigation into cosmological tensions

The possibility that the \(H_0\) tension is a sign of a physics beyond the \(\Lambda\)CDM model is one of the most exciting possibilities in modern cosmology. The challenge of solving this problem is complicated by several factors, including the worsening of the tension on \(\sigma _8\) parameter when that on \(H_0\) is raised. Furthermore, the perspective from which the problem is viewed should not be underestimated, since the tension on \(H_0\) can also be interpreted as a tension on the size of the acoustic horizon, \(r_{\mathrm{s}}\), which deserves proper discussion. The common approach in the literature consists in proposing a new model that can resolve the tension and treat the new parameters of the theory as free in the analysis. However, allowing additional parameters to vary often results in larger uncertainties on the inferred cosmological parameters, causing an apparent relaxing in the tension due to the broaden in the posterior, instead of a genuine shift in the central value of \(H_{0}\). To avoid this, we consider here an empirical approach that assumes specific non-standard values of the \(\Lambda\)CDM extensions and we analyse how the important parameters in the context of the tension vary accordingly. For our purposes, we study simple extensions of the standard cosmological model, such as a phantom DE component (with Equation of State \(w < -1\)) and extra relativistic species in the early universe (so that \(N_{\mathrm{eff}} > 3.046\)). We obtain relations between variation in the value of w and \(N_{\mathrm{eff}}\) and changes in \(H_0\), \(r_s\) and \(\sigma _8\). In this way an empirical relation between \(H_0\) and \(\sigma _8\) is provided, that is a first step in understanding which classes of theoretical models, and with which characteristics, could be able to break the correlation between the two tensions.