Wide Range Of Initial Conditions Research Articles

Intermediate-mass Black Hole Progenitors from Stellar Collisions in Dense Star Clusters

Very massive stars (VMSs) formed via a sequence of stellar collisions in dense star clusters have been proposed as the progenitors of massive black hole seeds. VMSs could indeed collapse to form intermediate-mass black holes, which would then grow by accretion to become the supermassive black holes observed at the centers of galaxies and powering high-redshift quasars. Previous studies have investigated how different cluster initial conditions affect the formation of a VMS, including mass segregation, stellar collisions, and binaries, among others. In this study, we investigate the growth of VMSs with a new grid of Cluster Monte Carlo star cluster simulations—the most expansive to date. The simulations span a wide range of initial conditions, varying the number of stars, cluster density, stellar initial mass function (IMF), and primordial binary fraction. We find a gradual shift in the mass of the most massive collision product across the parameter space; in particular, denser clusters born with top-heavy IMFs provide strong collisional regimes that form VMSs with masses easily exceeding 1000 M ⊙. Our results are used to derive a fitting formula that can predict the typical mass of a VMS formed as a function of the star cluster properties. Additionally, we study the stochasticity of this process and derive a statistical distribution for the mass of the VMS formed in one of our models, recomputing the model 50 times with different initial random seeds.

Freeze-out of perturbation growth for shocked heavy fluid layers by eliminating reverberating waves

The shock wave accelerating a heavy fluid layer can induce reverberating waves that continuously interact with the first and second interfaces. In order to manipulate the perturbation growths at fluid-layer interfaces, we present a theoretical framework to eliminate the reverberating waves. A model is established to predict the individual freeze-out (i.e. stagnation of perturbation growth) for the first and second interfaces under specific flow conditions determined based on the shock dynamics theory. The theoretical model quantifies the controllable parameters required for freeze-out, including the initial amplitudes of the first and second interfaces, the interface coupling strength and the maximum initial layer thickness preventing the second interface's phase reversal. The effectiveness of the model in predicting individual freeze-out for the first and second interfaces is validated numerically over a wide range of initial conditions. The upper and lower limits of initial amplitudes for the freeze-out of the whole fluid-layer width growth are further predicted. Within this amplitude range, a slightly higher initial amplitude for the second interface is specified, effectively arresting the growth of the entire fluid-layer width before the phase reversal of the second interface.

Numerical modeling of LEAP-2017 liquefiable sloping ground centrifuge tests using the ISA-hypoplasticity model

This article evaluates the prediction capabilities and limitations of the ISA-hypoplasticity constitutive model for sands in the simulation of liquefiable sloping ground dynamic centrifuge tests from the LEAP-2017 project. For that purpose, the experimental results of three centrifuge tests performed at different centrifuge facilities are considered. The corresponding dynamic coupled predictions were carried out using the finite element software Abaqus Standard. The material parameters of the adopted constitutive model were determined based on a detailed laboratory characterization of the tested Ottawa F-65 sand, which included drained monotonic triaxial and undrained cyclic triaxial tests considering a wide range of initial conditions and testing characteristics. The comparison between measured and computed sloping ground accelerations and spectral response suggests reasonable predictions by the model. Furthermore, the results suggest that the constitutive model is only able to realistically reproduce the trends of the experimental excess pore water pressure when considering cyclic mobility effects.

The impact of a top-heavy IMF on the formation and evolution of dark star clusters

ABSTRACT The Spitzer instability leads to the formation of a black hole subsystem (BHSub) at the centre of a star cluster providing energy to luminous stars (LSs) and increasing their rate of evaporation. When the self-depletion time of the BHSub exceeds the evaporation time of the LSs, a dark star cluster (DSC) will appear. Using the nbody7 code, we performed a comprehensive set of direct N-body simulations over a wide range of initial conditions to study the pure effect of the top-heaviness of the initial mass function (IMF) on the formation of the DSC phase. In the Galactic tidal field, top-heavy IMFs lead to the fast evaporation of LSs and the formation of DSCs. Therefore, DSCs can be present even in the outer region of the Milky Way (MW). To successfully transition to the DSC phase, the MW Globular Clusters (GCs) must possess an initial black hole (BH) mass fraction of $\widetilde {\mathit {M}}_\mathrm{BH}(0)\gt 0.05$. For star clusters with $\widetilde {\mathit {M}}_\mathrm{BH}(0)\gt 0.08$, the DSC phase will be created for any given initial density of the cluster and Galactocentric distance. The duration of the cluster’s lifetime spent in the DSC phase shows a negative (positive) correlation with the initial density, and Galactocentric distance of the star cluster if $\widetilde {\mathit {M}}_\mathrm{BH}(0)\le 0.12$ ($\widetilde {\mathit {M}}_\mathrm{BH}(0)\ge 0.15$). Considering the canonical IMF, it is unlikely for any MW GCs to enter the DSC phase. We discuss the BH retention fraction in view of the observed properties of the GCs of the MW.

Adaptation rules inducing synchronization of heterogeneous Kuramoto oscillator network with triadic couplings.

A class of adaptation functions is found for which a synchronous mode with different number of phase clusters exists in a network of phase oscillators with triadic couplings. This mode is implemented in a fairly wide range of initial conditions and the maximum number of phase clusters is four. The joint influence of coupling strength and adaptation parameters on synchronization in the network has been studied. The desynchronization transition under variation of the adaptation parameter occurs abruptly and begins with the highest-frequency oscillator, spreading hierarchically to all other elements.

Librating Kozai–Lidov Cycles with a Precessing Quadrupole Potential Are Analytically Approximately Solved

The very long term evolution of the hierarchical restricted three-body problem with a slightly aligned precessing quadrupole potential is investigated analytically for librating Kozai–Lidov cycles (KLCs). Klein & Katz presented an analytic solution for the approximate dynamics on a very long timescale developed in the neighborhood of the KLCs' fixed point where the eccentricity vector is close to unity and aligned (or anti-aligned) with the quadrupole axis and for a precession rate equal to the angular frequency of the secular Kozai–Lidov equations around this fixed point. In this paper, we generalize the analytic solution to encompass a wider range of precession rates. We show that the analytic solution approximately describes the quantitative dynamics for systems with librating KLCs for a wide range of initial conditions, including values that are far from the fixed point, which is somewhat unexpected. In particular, using the analytic solution, we map the strikingly rich structures that arise for precession rates similar to the Kozai–Lidov timescale (ratio of a few).

A novel machine learning based lumping approach for the reduction of large kinetic mechanisms for plasma-assisted combustion applications

The development of skeletal mechanisms has become essential for multi-dimensional simulations of plasma-assisted combustion (PAC). However, reduction tools developed for traditional combustion applications are not always applicable to PAC, due to the complex interplay between non-equilibrium plasma and combustion kinetics. Plasma direct relation graph with error propagation (P-DRGEP) is a recent plasma-specific reduction method developed in order to incorporate plasma energy branching in the reduction. In the first part of this work, the applicability of P-DRGEP to large kinetic mechanisms is investigated. A detailed isooctane/air plasma mechanism containing 2805 species and 18457 reactions is reduced to 415 species and 4716 reactions, keeping errors on ignition time within 3% for a wide range of initial conditions: from 750 K to 1200 K, 10 atm and equivalence ratios from 0.75 to 1.50. The second part focuses on isomer lumping, which is another reduction technique widely used in combustion. When applied to PAC, it is shown that the resulting lumped mechanism produces poor results. A novel plasma-specific isomer lumping strategy using machine learning is proposed instead. With the supervised algorithm of gradient boosting, predictive regression models are generated, which describe rate coefficients of lumped reactions adequately. These models are trained with simulation data. Leveraging this newly proposed lumping approach on the reduced mechanism, allows for an additional 28% reduction in the number of species and 19% reduction in the number of reactions. Two different versions are presented: in the first one the models are trained using one input feature (1D), while in the second one, two input features are selected (2D). The resulting lumped mechanism is shown to produce accurate predictions of PAC over the entire parameter space of interest, while significantly decreasing the computational time. Indicatively, with the 1D version the maximum error on ignition time in this range of conditions is 6%. The 2D approach produces even lower errors, which do not exceed 3%.Novelty and significance statementIn this work, a novel approach for isomer lumping, in plasma-assisted combustion mechanisms, is demonstrated. This plasma-specific approach, uses predictive machine learning regression models to describe the complex evolution of lumped reaction rate coefficients. Combining it with the plasma direct relation graph with error propagation, a powerful reduction framework is created, which is successfully demonstrated on a detailed isooctane/air plasma kinetic mechanism, via zero-dimensional ignition simulations. This framework constitutes a useful tool towards the creation of highly accurate skeletal mechanisms, which significantly reduce the computational costs of simulations.

A shear history model for capturing the liquefaction resistance of sands at various cyclic stress ratios

Various constitutive formulations have been developed over the years to reproduce the cyclic resistance of sands. A common challenge for existing models is the accurate simulation of the cyclic strength of sands for a wide range of initial conditions and different cyclic stress levels when adopting a single calibration. Many liquefaction models tend to overpredict the resistance of the soil under large-amplitude loading, while underestimating the strength at low-amplitude cyclic shearing. This manifests itself in slopes of simulated cyclic resistance ratio curves (CRR-curves) which are steeper than experimental studies indicate. This paper provides a discussion on the effects of large-amplitude and low-amplitude cyclic shearing on a granular material based on micromechanical and experimental investigations presented in the literature. A constitutive model with a shear-history threshold is proposed, which accounts for a shift of the apparent angle of phase transformation under cyclic loading. In addition, a novel expression for a deviatoric fabric tensor is introduced to describe the evolution of shear-induced fabric anisotropy while a soil is dilating and contracting. Combining these two features in one formulation within the bounding surface plasticity framework enables an accurate prediction of cyclic strength of sands under a wide range of cyclic stress ratios.

Evolutionary swarm formation: From simulations to real world robots

Swarms of autonomous robots have become an interesting alternative for space and aerospace applications due to their versatility, robustness, and self-organising capability. Some of those applications, such as asteroid observation, convoy escort, and counter-drone systems, rely on stable formations achieved around a central point of interest. However, the use of different numbers of robots and the existence of a wide range of initial conditions contribute to make it a challenging problem. We propose in this research work a novel approach for self-organising a swarm of autonomous robots where the members’ movements depend only on their relative position (range and bearing) obtained from their respective radio beacons. An optimisation approach based on an evolutionary algorithm is proposed to calculate the optimal swarm’s parameters, e.g. speed and attracting/repelling forces, to achieve robust formations under different initial conditions and failure rates. Experiments are conducted using realistic simulations of six case studies featuring three, five, ten, fifteen, twenty, and thirty robots. The best valued configurations were tested on 420 scenarios showing that our proposal is robust since it has always achieved the desired circular formation. Finally, we have used real E-Puck2 robots to validate the swarm’s capability of self-organising around a central point of interest as well as its resilience to robot failure, obtaining successful circular formations in all the experiments.

A real‐time critical‐scenario‐generation framework for defect detection of autonomous driving system

AbstractTo find the most‐likely‐failure scenarios given a certain operation domain, a critical‐scenario‐based test is supposed as an effective method. However, for the state of the art, critical‐scenario‐generation approaches commonly based on random‐search and take amounts of computing resource, some of them are also inapplicable in real time. Moreover, the approaches sometimes fail to obtain critical results, which are strongly relevant to the choice of initial condition. In order to address the above challenges, the authors proposed a Real‐time Critical‐scenario‐generation framework in this paper. The authors proposed an aggressive‐driving algorithm based on the model predictive control method to lead the agent vehicle. The agent vehicle will be controlled to directly create critical scenarios for a black‐box target under test, and the real‐time critical‐scenario test can be brought into reality. A specially designed cost function is presented that guides scenarios to evolve towards the interested conditions, and a self‐adaptive coefficient iteration is designed that enables the approach to be applied within a wider range of initial conditions. The authors carried out both simulation and Vehicle‐in‐the‐Loop (VIL) test; in the VIL test, the authors’ approach improves 15.45% criticality of scenarios with around 9.7 times of efficiency, or improves 38.67% criticality with still around 1.7 times of efficiency with further iterations.

Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows

This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate’s architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: (i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; (ii) It accelerates the prediction step by enabling adaptivity as the surrogate’s evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0-textrm{D} scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1-textrm{D} shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations.

Visualization and simulation study of ammonia blending with hydrogen as combustion application in lean-burn condition

Ammonia (NH3), as one of the two zero-carbon fuels, has attracted lots of attention. However, its poor properties, including slow laminar burning velocity (LBV), high ignition energy, and low flammability, make it unfavorable for use in engines. On the other hand, hydrogen (H2), another zero-carbon fuel, has a much higher LBV and flammability. Adding a certain amount of hydrogen to ammonia mixture has the potential to improve the combustion process and extend the lean-burn limit of ammonia. This paper investigates the combustion and emission improvements of ammonia blended with a small amount of hydrogen under lean-burn conditions, both experimentally and numerically. A new NH3/H2 chemical reaction mechanism was developed to accurately predict ignition delay time (IDT), LBV and NO generation under a wide range of initial conditions. The flame propagation schlieren and NO chemiluminescence measurements with a homogenous NH3/H2 mixture ignited by a spark plug in constant volume combustion chamber (CVCC) were conducted. The 3D numerical simulations in CVCC, coupled with the new mechanism, were validated with the experimental results. The hydrogen energy fraction up to 30 % (X30) and ER down to 0.4 (ER0.4) were studied in experiments and simulations. The results showed that, in comparison to pure ammonia (X0) at ER1.0, lean-burn conditions can be extended to ER0.6 and ER0.4 for X10 and X30, respectively, while still achieving a shorter combustion duration. NO is initially increased and then decreased with decreasing ER, regardless of hydrogen addition. Comparatively, X30ER0.4 can achieve relatively low NOx emissions, and maintaining an equivalent combustion rate with a low combustion temperature.

Connecting primordial gravitational waves and dark energy

Cosmic acceleration manifested in the early universe as inflation, generating primordial gravitational waves detectable in the cosmic microwave background (CMB) radiation. Cosmic acceleration is occurring again at present as dark energy, detectable in cosmic distance and structure surveys. We explore the intriguing idea of connecting the two occurrences through quintessential inflation by an α-attractor potential without a cosmological constant. For this model we demonstrate robustness of the connection 1 + w 0 ≈ 4/(3N 2 r) between the present day dark energy equation of state parameter w 0 and the primordial tensor to scalar ratio r for a wide range of initial conditions. Analytic and numerical solutions produce current thawing behavior, resulting in a tight relation w a ≈ -1.53(1 + w 0)≈ -0.2 (4 × 10-3/r). Upcoming CMB and galaxy redshift surveys can test this consistency condition. Within this model, lack of detection of a dark energy deviation from Λ predicts a higher r, and lack of detection of r predicts greater dark energy dynamics.

Resonant dynamical friction around a supermassive black hole: analytical description

ABSTRACT We derive an analytical model for the so-called phenomenon of resonant dynamical friction, where a disc of stars around a supermassive black hole interacts with a massive perturber, so as to align its inclination with the disc’s orientation. We show that it stems from a singular behaviour of the orbit-averaged equations of motion, which leads to a rapid alignment of the argument of the ascending node Ω of each of the disc stars, with that of the perturber, Ωp, with a phase difference of 90°. This phenomenon occurs for all stars whose maximum possible $\dot{\Omega }$ (maximized over all values of Ω for all the disc stars) is greater than $\dot{\Omega }_{\rm p}$; this corresponds approximately to all stars whose semi-major axes are less than twice that of the perturber. The rate at which the perturber’s inclination decreases with time is proportional to its mass and is shown to be much faster than Chandrasekhar’s dynamical friction. We find that the total alignment time is inversely proportional to the root of the perturber’s mass. This persists until the perturber enters the disc. The predictions of this model agree with a suite of numerical N-body simulations, which we perform to explore this phenomenon, for a wide range of initial conditions, masses, etc., and are an instance of a general phenomenon. Similar effects could occur in the context of planetary systems, too.

Attractor solutions in interacting dark energy models

We investigate a cosmological model in which dark energy, represented by a quintessential scalar field, is coupled to a dark-matter perfect fluid in the spatially flat Friedmann–Robertson–Walker Universe. This allows an energy exchange in the dark sector which could happen both at early times before recombination era or at late times. We use the coupling function Q=γρdmφ̇ which is induced by conformal transforming scalar-tensor and f(R) gravity theories to Einstein frame. It is argued that there is a connection between this coupling function and Q∝ρdmH. A dynamical analysis is used to show that there are early- and late-time attracting solutions for which the system evolves for a wide range of initial conditions. These attractors generalize the scaling solutions which have been already found in the non-interacting case.

Application of the New Iterative Method (NIM) to the Generalized Burgers–Huxley Equation

In this paper, we propose the new iterative method (NIM) for solving the generalized Burgers–Huxley equation. NIM provides an approximate solution without the need for discretization and is based on a set of iterative equations. We compared the NIM with other established methods, such as Variational Iteration Method (VIM), Adomian Decomposition Method (ADM), and the exact solution, and found that it is efficient and easy to use. NIM has the advantage of quick convergence, easy implementation, and handling of a wide range of initial conditions. The comparison of the present symmetrical results with the existing literature is satisfactory.

Black hole discs and spheres in galactic nuclei – exploring the landscape of vector resonant relaxation equilibria

ABSTRACT Vector resonant relaxation (VRR) is known to be the fastest gravitational process that shapes the geometry of stellar orbits in nuclear star clusters. This leads to the realignment of the orbital planes on the corresponding VRR time-scale tVRR of a few million years, while the eccentricity e and semimajor axis a of the individual orbits are approximately conserved. The distribution of orbital inclinations reaches an internal equilibrium characterized by two conserved quantities, the total potential energy among stellar orbits, Etot, and the total angular momentum, Ltot. On time-scales longer than tVRR, the eccentricities and semimajor axes change slowly, and the distribution of orbital inclinations are expected to evolve through a series of VRR equilibria. Using a Monte Carlo Markov Chain method, we determine the equilibrium distribution of orbital inclinations in the microcanonical ensemble with fixed Etot and Ltot for isolated nuclear star clusters with a power-law distribution of a, e, and m, where m is the stellar mass. We explore the possible equilibria for nine representative Etot–Ltot pairs that cover the possible parameter space. For all cases, the equilibria show anisotropic mass segregation, where the distribution of more massive objects is more flattened than that for lighter objects. Given that stellar black holes are more massive than the average main-sequence stars, these findings suggest that black holes reside in disc-like structures within nuclear star clusters for a wide range of initial conditions.

Interactions of bioactive trace metals in shipboard Southern Ocean incubation experiments

AbstractIn the Southern Ocean, it is well‐known that iron (Fe) limits phytoplankton growth. Yet, other trace metals can also affect phytoplankton physiology. This study investigated feedbacks between phytoplankton growth and dissolved Fe, manganese (Mn), cobalt (Co), nickel (Ni), copper (Cu), zinc (Zn), and cadmium (Cd) concentrations in Southern Ocean shipboard incubations. Three experiments were conducted in September–October 2016 near the West Antarctic Peninsula: Incubations 1 and 3 offshore in the Antarctic Circumpolar Current, and Incubation 2 inshore in Bransfield Strait. Additions of Fe and/or vitamin B12 to inshore and offshore waters were employed and allowed assessment of metal (M) uptake relative to soluble reactive phosphorus (P) across a wide range of initial conditions. Offshore, treatments of >1 nmol L−1 added Fe were Fe‐replete, whereas inshore waters were already Fe‐replete. Results suggest Mn was a secondary limiting nutrient inshore and offshore. No Fe‐vitamin B12 colimitation was observed. Overall, M:P uptake in the incubations was closely related to initial dissolved M:P for Fe, Mn, Co, Ni, and Cd, and for Cu inshore. Final concentrations of Fe and Zn were similar across light treatments of the experiments despite very different phytoplankton responses, and we observed evidence for Co/Cd/Zn substitution and for recycling of biogenic metals as inventories plateaued. In dark bottles, the absence of Mn oxidation may have allowed more efficient recycling of Fe and other trace metals. Our results provide insight into factors governing trace metal uptake, with implications for phytoplankton community composition locally and preformed micronutrient bioavailability in Southern Ocean water masses.

The influence of cyclic preloadings on cyclic response of Zbraslav sand

This article presents a comprehensive experimental investigation on Zbraslav sand under monotonic and cyclic loading. Initially, the material response at large strains was investigated by means of undrained monotonic triaxial tests with different initial mean effective stresses and relative densities. A set of oedometric compression tests with multiple unloading–reloading cycles and different initial relative densities was as well included to evaluate the material compressibility. In addition, several undrained cyclic triaxial tests were performed and analyzed under a wide range of initial conditions. In the aforementioned tests, the undrained cyclic resistance was investigated considering different types of drained or undrained cyclic preloadings and reconsolidation stages. The experimental results suggested that drained cyclic preloadings remarkably modified the subsequent rate of pore water pressure accumulation and increased the number of cycles to reach the defined failure criterion without affecting the stress–strain response. On the other hand, undrained cyclic preloadings presented a threshold which separated positive and negative effects in the subsequent undrained cyclic resistance. A comparison of the undrained cyclic resistance variation depending on the number of drained or undrained cyclic preloadings was also included.

Further insights into the core mechanism of H2/CO/NOx reaction system

The core H2/CO/NOx mechanism is important in understanding the mechanism of NOx formation during combustion as it forms the base model in developing kinetic models of larger hydrocarbons/NOx systems. Recently, the Goldsmith group at Brown University performed high-level ab-initio calculations of the chemistry of HONO and HNO2 and proposed that the thermal rate constant of isomerization of HONO to HNO2 is orders of magnitude lower than that used in all previous models. This discrepancy may lead to a deviation in understanding the formation mechanism of NOx. With this in mind, coupling with the latest rate constants obtained by experimental measurements and high-level quantum chemistry calculations, the H2/CO/NOx model was circularly updated and re-verified against multi-type datasets over a wide range of initial conditions and experimental devices. The proposed model (XJTUNO-2021) can accurately reproduce almost all of the fundamental combustion data including 156 shock tube datasets, 87 JSR datasets, 114 flow reactor datasets and six laminar flame speed datasets in the literature from 1959 to 2021. Moreover, this study clarifies the shortcomings of the Zhang mechanism of CO/NOx systems. Finally, the updated model has been used to simulate the formation of NO at practical gas-turbine conditions to give more kinetically information of NO control technologies.