Arbitrary Fraction Research Articles

Thermalized and mixed meanfield ADP potentials for magnesium hydrides

We develop meanfield approximation and numerical quadrature schemes for the evaluation of Angular-Dependent interatomic Potentials (ADPs) for magnesium and magnesium hydrides at finite temperature (thermalization) and arbitrary atomic molar fractions (mixing) within a non-equilibrium statistical mechanical framework and derive local equilibrium relations. We numerically verify and experimentally validate the accuracy and fidelity of the resulting thermalized/mixed ADPs (TADPs) by means of selected numerical tests including free entropy, heat capacity, thermal expansion, molar volumes, equation of state and elastic constants. We show that the local equilibrium properties predicted by TADPs agree closely with those computed directly from ADP by means of Molecular Dynamics (MD).

Design of Steel-Cu composites for enhancing thermal properties of plastic processing tools by using a numerical model of the microstructure

Limitationsof conventional materials used for plastic processing tools, particularly related to thermal conductivity, significantly influence production efficiency, with the cooling time of moulded parts appearing as one of the key factors. Therefore, this study focuses on designing Steel-Cu composites with the aid of a numerical model of the composite's microstructure for enhancing their overall thermal properties. We present a novel procedure for designing such composites, which facilitates the identification of the optimal shape for the phases to improve overall thermal conductivity. We have developed a data-driven homogenization model to aid the optimization process and ensure time-efficient solutions. The data has been generated through numerical homogenization based on the finite element method. The proposed shape optimization procedure has been applied to determine the optimal shape of the Cu phase across various volume fractions. We found out that the optimal shape of the Cu phase is not constant but depends on its volume fraction. Emphasizing the practical utility of the proposed procedure, it is noteworthy that once the data-driven model is established, it enables a time-efficient optimization of the Cu phase shape for arbitrary volume fractions of phases. Consequently, this may expedite the decision-making process for material manufacturers.

Jeans instability in the particle-antiparticle system with the different gravitational charges and the ALPHA-g experiment

The principle of binding energy conservation during charge conjugation and the hypothesis of gravitational repulsion of antiparticle masses is used to formulate appropriate two-component hydrodynamics. The dispersion relation for small perturbations is obtained and analyzed. The modified Jeans instability for matter-antimatter system is found as the function of arbitrary fraction of the repulsive matter. For the hydrogen-antihydrogen system, the recent ALPHA-g experimental result is used to apply to the early Universe evolution. It is shown that the non-damping sound mode exists if the annihilation damping is absent.

A data-driven model based on the numerical solution of the equivalent inclusion problem for the analysis of nonlinear short-fibre composites

The paper introduces a novel data-driven homogenization model developed for the computation of stress-strain curves for composites featuring arbitrary orientation distributions, aspect ratios, and volume fractions of fibres. The objective of the proposed model is to deliver both time-efficient and accurate results while taking into account a relatively small database. The database is generated through numerical solutions of the equivalent inclusion problem, encompassing results for predefined orientations and aspect ratios of the single inclusion (fibre). The database created for a specific matrix-fibre system can be employed by the surrogate model to predict outcomes for various cases involving different fibre configurations. The surrogate model comprises four key modules: aspect ratio interpolation, a discrete orientation averaging procedure involving a genetic algorithm, a spatial transformation procedure, and an iterative Mori-Tanaka scheme. The validity of the proposed data-driven model has been confirmed by comparing the obtained results with those acquired through analysis of the complex representative volume element (RVE) using Fast Fourier Transform (FFT)-based homogenization, as well as through comparisons with experimental results from the existing literature.

Semi-Supervised Clustering of Sparse Graphs: Crossing the Information-Theoretic Threshold.

The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase transition at the Kesten-Stigum threshold is particularly interesting both from a mathematical and an applied standpoint. It states that no estimator based on the network topology can perform substantially better than chance on sparse graphs if the model parameter is below a certain threshold. Nevertheless, if we slightly extend the horizon to the ubiquitous semi-supervised setting, such a fundamental limitation will disappear completely. We prove that with an arbitrary fraction of the labels revealed, the detection problem is feasible throughout the parameter domain. Moreover, we introduce two efficient algorithms, one combinatorial and one based on optimization, to integrate label information with graph structures. Our work brings a new perspective to the stochastic model of networks and semidefinite program research.

Tabulated equations of state from models informed by chiral effective field theory

Abstract We construct four equation of state (EoS) tables, tabulated over a range of temperatures, densities, and charge fractions, relevant for neutron star applications such as simulations of neutron star mergers. The EoS are computed from a relativistic mean-field theory constrained by the pure neutron matter EoS from chiral effective field theory, inferred properties of isospin-symmetric nuclear matter, and astrophysical observations of neutron star structure. To model nuclear matter at low densities, we attach an EoS that models inhomogeneous nuclear matter at arbitrary temperatures and charge fractions. The four EoS tables we develop are available from the CompOSE EoS repository https://compose.obspm.fr/eos/297 and gitlab.com/ahaber/qmc-rmf-tables.

Precise description of medium-induced emissions

We study jet fragmentation via final-state parton splittings in the medium. These processes are usually calculated theoretically by invoking the large-Nc limit. In this paper we perform the first computation of a 1 → 2 parton splitting in a thermal medium at finite numbers of colors Nc, for arbitrary momentum-sharing fraction z and with full transverse dynamics. We show how the problem can be transformed into a system of coupled Schrödinger equations, that we solve numerically. The novel numerical results are used to estimate the accuracy of several widely used approximations. We check the error introduced while going from finite Nc (i.e. Nc = 3) to the large-Nc limit, which we find to be small. For unbalanced splittings, e.g. when z → 0, only one of the partons is affected by transverse momentum exchanges with the medium. The emission process then separates into a term responsible for the 1 → 2 splitting and the subsequent independent broadening of the daughter partons. This is also referred to as the factorizable term. For finite z, further contributions arise that are responsible for the coherent color dynamics of the two-parton system, and these are referred to as non-factorizable terms. These were argued to be small for soft (unbalanced) splittings and for large media. In this work we therefore determine the accuracy of keeping only the factorizable term of the large-Nc solution. We find that the error is insignificant at a small splitting fraction z ~ 0, but can be sizable in a more balanced splitting with z ~ 0.5. Finally, we also examine the eikonal approximation, which amounts to approximating the partons’ paths through the medium as straight lines. We find that it is associated with a substantial error for the parameter values we explored in this work.

Slip length for a viscous flow over spiky surfaces

For a model of a 3D coating composed of a bi-periodic system of parallel riblets with gaps we analytically derive an approximate formula for the effective slip length (an offset from the flat surface at which the flow velocity would extrapolate to zero) as a function of the geometry of the system (riblet period, riblet height, and relative gap size). This formula is valid for an arbitrary fraction of gaps (i.e., from narrow riblets to narrow gaps) and agrees with the known analytical results for the 2D periodic coating of riblets without gaps. We validate our analytical results with the numerical solution of the equations of the viscous (creeping) flow over the riblets with gaps.

Modular Representation of Rational Fractions

The computer is designed to perform calculations, therefore it is a device for automatically processing machine data formats that display structured information. In machine data formats, the digit grid of typical and specialized computers displays numerical values on which calculations are performed in various number systems. A new modular packed representation of numerical values by rational fractions with fixed denominators, previously unknown, is introduced. For such modular representations of numerical quantities, a basic algorithm for the formation of vector components of types of representations is given with an estimate of complexity. A method of optimal approximation by packed modular representations of arbitrary irregular fractions has been found. The features of algorithms for performing additive and multiplicative operations for packed representations in a modular processor are analyzed.

BIFROST: simulating compact subsystems in star clusters using a hierarchical fourth-order forward symplectic integrator code

ABSTRACT We present BIFROST, an extended version of the GPU-accelerated hierarchical fourth-order forward symplectic integrator code FROST. BIFROST (BInaries in FROST) can efficiently evolve collisional stellar systems with arbitrary binary fractions up to $f_\mathrm{bin}=100~{{\ \rm per\ cent}}$ by using secular and regularized integration for binaries, triples, multiple systems, or small clusters around black holes within the fourth-order forward integrator framework. Post-Newtonian (PN) terms up to order PN3.5 are included in the equations of motion of compact subsystems with optional three-body and spin-dependent terms. PN1.0 terms for interactions with black holes are computed everywhere in the simulation domain. The code has several merger criteria (gravitational-wave inspirals, tidal disruption events, and stellar and compact object collisions) with the addition of relativistic recoil kicks for compact object mergers. We show that for systems with N particles the scaling of the code remains good up to NGPU ∼ 40 × N/106 GPUs and that the increasing binary fractions up to 100 per cent hardly increase the code running time (less than a factor ∼1.5). We also validate the numerical accuracy of BIFROST by presenting a number of star clusters simulations the most extreme ones including a core collapse and a merger of two intermediate mass black holes with a relativistic recoil kick.

Wave Conversion, Decay, and Heating in a Partially Ionized Two-fluid Magneto-atmosphere

A ray-theoretic phase-space description of linear waves in a two-fluid (charges and neutrals) magnetized plasma is used to calculate analytic decay rates and mode transmission and conversion coefficients between fast and slow waves in two dimensions due to finite ion–neutral collision frequencies at an arbitrary ionization fraction. This is relevant to partially ionized astrophysical plasmas, in particular solar and stellar atmospheres. The most important parameter governing collisional effects is the ratio of the wave frequency to the neutral–charges collision frequency, ϵ = ω/ν nc, with secondary dependence on ionization fraction and wave attack angle. Comparison is made to the one-fluid magnetohydrodynamic case, and it is found that acoustic-to-acoustic and magnetic-to-magnetic transmission through the Alfvén-acoustic equipartition layer is decreased by a term of relative to one-fluid (infinite collision frequency), and correspondingly acoustic-to-magnetic and magnetic-to-acoustic conversion is increased. The neutral-acoustic mode is shown to dissipate rapidly as ν nc → ∞. Away from the mode conversion region, dissipative decay along the remaining magneto-acoustic rays scales as and is found to be much more effective on magnetically dominated rays compared to acoustically dominated rays. This produces a steep jump in dissipation in mode conversion regions, where the rays change character, and can produce localized heating there and beyond. Applications to the solar chromosphere are discussed.

Nuclear Equation of State for Arbitrary Proton Fraction and Temperature Based on Chiral Effective Field Theory and a Gaussian Process Emulator.

We calculate the equation of state of asymmetric nuclear matter at finite temperature based on chiral effective field theory interactions to next-to-next-to-next-to-leading order. Our results assess the theoretical uncertainties from the many-body calculation and the chiral expansion. Using a Gaussian process emulator for the free energy, we derive the thermodynamic properties of matter through consistent derivatives and use the Gaussian process to access arbitrary proton fraction and temperature. This enables a first nonparametric calculation of the equation of state in beta equilibrium, and of the speed of sound and the symmetry energy at finite temperature. Moreover, our results show that the thermal part of the pressure decreases with increasing densities.

Modeling of radiation heat transfer in dense-bed flows of solids in indirectly heated rotary kilns

• modification and implementation of a DOM-radiation model which combines all required physical submodels to simulate heat radiation to dense beds of particles. • Full time and space resolved simulation of thermal conversion of wet moving bulk in a large-scale rotary kiln reactor. • Analytical validation of model and justification with laboratory-scale experiments. • Efficiency optimization of the numerical solver for industrial-scale and long-time simulations on parallel supercomputers. • Parameter studies for large-scale reactors to investigate conversion rate and product quality. This work presents further development and validation of the Discrete Ordinates Model for thermal radiation implemented in OpenFOAM® for application to packed beds of particles. The radiation model is an important part of a more comprehensive model for simulating the thermochemical conversion of the discrete phase (here for instance wet biomass particles). The comprehensive Eulerian-Lagrangian model is part of a three-dimensional, time-resolved simulation of the essential chemical and physical processes occurring within and in-between particles in a moving bed. For the thermal treatment of solid particles, convective and radiative heat transfer couple the energy exchange between the reactor wall, gas- and disperse phase. The original implementation of the finite volume Discrete Ordinate Model (fvDOM) present in OpenFOAM® is valid for a dilute particulate phase and neglects the effect of local opacity due to the existence of individual particles. In the present application, a dense-packed bed of the particulate phase exists in the reactor and, therefore, this direction-based radiation model is adjusted for a computational cell with arbitrary particle volume fractions. To validate the results with the present thermal radiation model, a simple test case is first presented, where a bed of particles is heated from the top of the computational domain. A second test case relates to an experimentally investigated laboratory-scale reactor. The results of the improved fvDOM are compared to the original implementation in OpenFOAM® and the more simple and computationally cheap P-1 radiation model. In the presence of a packed bed, the P-1 model largely overpredicts the radiative heat transfer while the original fvDOM underpredicts the heat flux by about 15 % for the first test case. The new improved model delivers results within 1% deviation at the expense of maximum of 10 % increase in the computational time. Large-scale parallel simulations of real setups are crucial tools to predict the efficiency of a process and improve the operational parameters. To achieve the pre-defined product quality at minimum cost, an example of the implemented radiation model in thermochemical conversion of wet biomass in a rotary drum is been given and the importance of the radiation heat transport to the bulk is highlighted.

Stress constrained topology optimization of energy storage flywheels using a specific energy formulation

A variable density, stress-constrained topology optimization approach is used, along with the solid isotropic material with penalization (SIMP) power law and a P-norm aggregated global stress measure to optimize the rotor of a flywheel energy storage systems (FESS). A new specific energy maximization optimization formulation is proposed which eliminates the need to impose an arbitrary volume fraction constraint to the optimization problem as it is done in traditional kinetic energy maximization approaches. The FESS rotors obtained with the specific energy formulation achieved a 15.8% increase in the specific energy compared to the kinetic energy based approach which improved the specific energy by 12.8%. Factors such as the operating speed, maximum stress, rotational symmetry and rotor material also influence the moment of inertia and stress distribution in the flywheel, and the effects of these parameters on the optimal topology and its energy capacity are investigated. At low speeds, the topology is seen to have elongated holes, which become rounded and move away from central shaft as the speed is increased. The reverse effect is seen when the upper limit on the stress constraint is increased. While the choice of rotor material affects the kinetic energy and mass of the flywheel, its optimal topology and specific energy is seen to be nearly identical for rotor materials with the same Eρ ratio, and slightly different for other cases. The size of the circular sections used as the topology design domain is seen to affect the number of spokes in the rotor, but the overall specific energy is unaffected, so manufacturing considerations can be used to choose the rotational symmetry of the rotor. Due to the frequent charge–discharge cycles associated with short term storage, both centrifugal and acceleration forces might play an important role in determining the peak stresses in the flywheel. Therefore, the influence of acceleration loads on the optimal rotor topology is also studied and shown to only have an impact for very large instantaneous accelerations of 5235.9 rad/s2 or higher.

Deep CNNs as universal predictors of elasticity tensors in homogenization

In the present work, 3D convolutional neural networks (CNNs) are trained to link random heterogeneous, multiphase materials to their elastic macroscale stiffness thus replacing explicit homogenization simulations. The proposed CNN model is universal in that it accounts for various types of microstructures, for arbitrary phase fractions, non-constant and thereby very large ranges of Young’s moduli of the constituent phases (from 1 to 1000 GPa) and of their Poisson’s ratios (from 0 to 0.4). Moreover, the CNN predicts the stiffness for periodic boundary conditions (BCs) along with its upper bound through kinematically uniform BCs and its lower bound through stress uniform BCs. The triple of BCs reduces the stiffness uncertainty due to the embedding of the material volume into arbitrary adjacent host materials. Beyond, the stiffness bounds provide an indicator for the proper size of a representative volume element. The proposed universal CNN model achieves high accuracy in its predictions. The reasons for the rare outliers with larger errors are rigorously analyzed. For a real, two-phase diamond–SiC coating material the universal CNN is almost as accurate as a CNN exclusively trained for fixed elastic phase properties of that material. The speedup compared to finite element computations for homogenization is above factor 20500. The proposed CNN model hence enables fast and accurate stiffness predictions in universal analyses of heterogeneous materials in their linear elastic regime.

Finite-temperature effects in dynamical spacetime binary neutron star merger simulations: validation of the parametric approach

ABSTRACT Parametric equations of state (EoSs) provide an important tool for systematically studying EoS effects in neutron star merger simulations. In this work, we perform a numerical validation of the M*-framework for parametrically calculating finite-temperature EoS tables. The framework, introduced by Raithel et al., provides a model for generically extending any cold, β-equilibrium EoS to finite temperatures and arbitrary electron fractions. In this work, we perform numerical evolutions of a binary neutron star merger with the SFHo finite-temperature EoS, as well as with the M*-approximation of this same EoS, where the approximation uses the zero-temperature, β-equilibrium slice of SFHo and replaces the finite-temperature and composition-dependent parts with the M*-model. We find that the approximate version of the EoS is able to accurately recreate the temperature and thermal pressure profiles of the binary neutron star remnant, when compared to the results found using the full version of SFHo. We additionally find that the merger dynamics and gravitational wave signals agree well between both cases, with differences of $\lesssim 1\!-\!2\,{\textrm{per cent}}$ introduced into the post-merger gravitational wave peak frequencies by the approximations of the EoS. We conclude that the M*-framework can be reliably used to probe neutron star merger properties in numerical simulations.

Energetic and exergetic efficiency comparison of recuperative transcritical organic Rankine cycles under different pure and mixture fluids

AbstractA thermodynamic model of basic and recuperative transcritical organic Rankine cycles (TRCs) associated with using five pure and six mixed fluids as working fluids has been developed. This model can be employed to investigate the effects of recuperators at inlet expander temperatures (Texp,in) of 150–200°C and inlet expander pressures (Pexp,in) of 3.7–6.9 MPa. The ratio of change (ROC) of the first‐ and second‐law efficiencies (ηI and ηII) was positively correlated with the heat transfer rate of the recuperator and exhibited an opposite trend for a specific volume ratio. ROC was substantially affected by operating parameters and working fluid. However, the recuperator heat transfer rate was negligibly affected by the mixture temperature glide (Tglide). A universal empirical equation of ηI,II was proposed for both TRC configurations. The equation, a function of the specific volume ratio, can predict the system efficiencies for pure and mixed fluids, even if a mixture has an arbitrary mole fraction. As Tglide of R600a‐base mixture and R245fa/R134a was lower than 16 K, they had low error rates and low standard deviations. Finally, the equation was highly accurate in ηII prediction, particularly at a Texp,in of 160°C and 170°C and a Pexp,in of 4.9–5.8 MPa.

Missed reporting of nonfatal occupational injuries: estimation using the International Labor Organization datasets.

Most previous studies about missed reporting of nonfatal occupational injuries have four limitations: (i) mostly qualitative methods, (ii) arbitrary fraction used to estimate missed nonfatal occupational injuries based on subjective opinions, (iii) use of datasets derived from only one country, and (iv) use of a relatively simple estimation method. In contrast, (i) using quantitative approaches, this study will calculate the (ii) objective estimates on (iii) a multinational scale. (iv) A newly devised logical approach for estimation will be applied. Through this study, the fraction of missed reports of nonfatal occupational injuries will be estimated in a new way. Four International Labor Organization (ILO) datasets were analyzed in this study: (i) fatal occupational injuries per 100,000 workers by sex and migrant status, (ii) nonfatal occupational injuries per 100,000 workers by sex and migrant status, (iii) inspectors per 10,000 employed persons, and (iv) labor inspection visits per inspector. The ratification status of 27 ILO conventions, classified into 12 categories, was used for the analyses. The GDP dataset from the World Bank Open Data was also used. In addition to basic descriptive analyses, a multilevel Poisson regression method was applied. The primary outcome was the risk ratio of the above-mentioned four selected measures when an ILO convention was ratified compared to when the convention was not ratified. Finally, for the estimation of the fraction of missed reports of nonfatal occupational injuries, a newly devised estimation method was applied. This method was devised based on a unique characteristic of reporting systems for fatal occupational injuries (duplicate reporting through multiple reporting systems). The ratio of discovered nonfatal occupational injuries to total estimated nonfatal occupational injuries ranged from 0.13 (95% CI 0.13-0.14) to 0.89 (95% CI 0.84-0.95). In other words, the minimum estimate of the percentage of missed injury reports is 11% (1-0.89 = 0.11) and the maximum is 87% (1-0.13 = 0.87). The mean value of the ratios of discovered nonfatal occupational injuries to total estimated nonfatal occupational injuries was 0.52. In other words, the most likely estimate for the fraction of missed injury reports is 48% (1-0.52 = 0.48). Underreporting of nonfatal occupational injuries could hinder the efforts of governments to address and improve the occupational safety and health status of the country. Accurate assessment of the current status of nonfatal occupational injuries is important for devising effective strategies to reduce this type of injury.

Opportunistic Temporal Fair Mode Selection and User Scheduling in Full-Duplex Systems

In-band full-duplex (FD) communication has emerged as one of the promising techniques to improve data rates in next generation wireless systems. Typical FD scenarios considered in the literature assume FD base stations (BSs) and half-duplex (HD) users activated either in uplink (UL) or downlink (DL), where inter-user interference (IUI) is treated as noise at the DL user. This paper considers more general FD scenarios where an arbitrary fraction of the users are capable of FD and/or they can perform successive interference cancellation (SIC) to mitigate IUI. Consequently, one user can be activated in either UL or DL (HD-UL and HD-DL modes), or simultaneously in both directions requiring self-interference mitigation (SIM) at that user (FD-SIM mode). Furthermore, two users can be scheduled, one in UL and the other in DL (both operating in HD), where the DL user can treat IUI as noise (FD-IN mode) or perform SIC to mitigate IUI (FD-SIC mode). This paper studies opportunistic mode selection and user scheduling under long-term and short-term temporal fairness in single-carrier and multi-carrier (OFDM) FD systems, with the goal of maximizing system utility (e.g. sum-rate). First, the feasible region of temporal demands is characterized for both long-term and short-term fairness. Subsequently, optimal temporal fair schedulers as well as practical low-complexity online algorithms are devised. Simulation results demonstrate that using SIC to mitigate IUI as well as having FD capability at users can improve FD throughput gains significantly especially, when user distribution is concentrated around a few hotspots.

FLatt Pack: A research-focussed lattice design program

Lattice structures are an important aspect of design for additive manufacturing (DfAM). They enable significant component light-weighting and the tailoring of a wide range of physical responses; mechanical, thermal, acoustic, etc. In turn, lattice design relies on fundamental research to uncover useful structure-property relationships, such as the influence of cell geometry and volume fraction. A number of commercial computer-aided-design (CAD) programs exist that offer lattice generation, but these tend to prioritise product design. This paper describes the FLatt Pack program (or Functional Lattice Package), which was created to address the paucity of research-focussed lattice design software. It possesses a number of features with this in mind, including; (i) it is free to use for research, (ii) it is standalone software with minimal, and also free, dependencies, and (iii) it undergoes frequent and rapid development based on state of the art lattice information and modelling methods. FLatt Pack includes twenty-three lattice cell types covering a broad range of pore connectivity, structural anisotropy, and surface area; a clear GUI presenting the lattice design stages in a sequential manner; and the option to export designs in appropriate formats for AM and finite element (FE) simulation. The program also features conformal lattice generation in arbitrary shapes, arbitrary volume fraction grading, and resource-efficient computation through an adaptive spatial resolution based on the user’s design choices. The most recent version of FLatt Pack is freely available at: www.github.com/ian27ax/FLatt_Pack_dist .