Free Parameters Research Articles

Accretion tori around rotating neutron stars II. Oscillations and precessions

The four characteristic oscillation frequencies of accretion flows (in addition to the Keplerian orbital frequency) are often discussed in the context of the time variability of black hole and neutron star (NS) low-mass X-ray binaries (LMXBs). These four frequencies are the frequencies of the axisymmetric radial and vertical epicyclic oscillations, and the frequencies of non-axisymmetric oscillations corresponding to the periastron (radial) and Lense-Thirring (vertical) precessions. In this context, we investigated the effect of the quadrupole moment of a slowly rotating NS and provide complete formulae for calculating these oscillation and precession frequencies, as well as convenient approximations. Simple formulae corresponding to the geodesic limit of a slender torus (and test-particle motion) and the limit of a marginally overflowing torus (a torus exhibiting a critical cusp) are presented, and more general approximate formulae are included to allow calculations for arbitrarily thick tori. We provide the Wolfram Mathematica code used for our calculations together with the C++ and PYTHON codes for calculating the frequencies. Our formulae can be used for various calculations regarding the astrophysical signatures of the NS super-dense matter equation of state. For instance, we demonstrate that even for a given fixed number of free parameters, a model that accounts for fluid flow precession matches the frequencies of twin-peak quasiperiodic oscillations observed in NS LMXBs better than a model that uses geodesic precession.

Improving Predictions of Spin-Crossover Complex Properties through DFT Calculations with a Local Hybrid Functional.

We conducted a study on the performance of the local hybrid exchange-correlation functional PBE0r for a set of 95 experimentally characterized iron spin-crossover (SCO) complexes [Vennelakanti, V.; J. Chem. Phys. 2023, 159, 024120]. The PBE0r functional is a variant of PBE0 where the exchange correction is restricted to on-site terms formulated on the basis of local orbitals. We determine the free parameters of the PBE0r functional against the experimental data and other hybrid functionals. With a Hartree-Fock (HF) exchange factor of 4%, the PBE0r functional accurately reproduces the electronic and free-energy trends predicted in prior DFT studies for these 95 complexes by using the B3LYP functional. Larger values of HF exchange stabilize high-spin states. The PBE0r-predicted bond lengths tend to exceed the experimental bond lengths, although bond lengths are less sensitive to HF exchange than in global hybrids. The predicted SCO transition temperatures T1/2 from PBE0r correlate moderately with the experimental transition temperatures, showing a slight improvement compared to the previous modB3LYP-predicted T1/2. This study suggests that the PBE0r functional is computationally cost-effective and offers the possibility of simulating larger complexes with accuracy comparable to global hybrid functionals, provided the HF-exchange parameter is carefully optimized.

Parallel cyclic reduction of padded bordered almost block diagonal matrices

The solution of linear systems is a crucial and indispensable technique in the field of numerical analysis. Among linear system solvers, the cyclic reduction algorithm stands out for its natural inclination to parallelization. So far, the cyclic reduction has been applied primarily to linear systems with almost block diagonal matrices. Some of its variants widen the usage to almost block diagonal matrices with a last block of rows introducing a set of non-zero elements in the first group of columns. In this work, we extend cyclic reduction to matrices with additional non-zero elements below and to the right without any limitations. These matrices, called padded bordered almost block diagonal, arise from the discretization of optimal control problems featuring arbitrary boundary conditions and free parameters. Nonetheless, they also appear in two-point boundary value problems with free parameters. The proposed algorithm is based on the LU factorizations, and it is designed to be executed in parallel on multi-thread architectures. The algorithm performance is assessed through numerical experiments with different matrix sizes and threads. The computation times and speedups obtained with the parallel implementation indicate that the suggested algorithm is a robust solution for solving padded bordered almost block diagonal linear systems. Furthermore, its structure makes it suitable for the use of different matrix factorization techniques, such as QR or SVD. This flexibility enables tailored customization of the algorithm on the basis of the specific application requirements.

Generalized flow-composed symplectic methodsfor post-Newtonian Hamiltonian systems

Due to the nonseparability of the post-Newtonian (PN) Hamiltonian systems of compact objects, the symplectic methods that admit the linear error growth and the near preservation of first integrals are always implicit as explicit symplectic methods have not been currently found for general nonseparable Hamiltonian systems. Since the PN Hamiltonian has a particular formulation that includes a dominant Newtonian part and a perturbation PN part, we present the generalized flow-composed Runge-Kutta (GFCRK) method with a free parameter λ to PN Hamiltonian systems. It is shown that the GFCRK method is symplectic once the underlying RK method is symplectic, and it is symmetric once the underlying RK method is symmetric under the setting λ = 1/2. Numerical experiments with the 2PN Hamiltonian of spinning compact binaries demonstrate the higher accuracy and efficiency of the symplectic GFCRK method than the underlying symplectic RK method in the case of weak PN effect. Meanwhile, the numerical results also support higher efficiency of the symplectic GFCRK method than the semi-explicit mixed symplectic method of the same order.

Comparing sampling techniques to chart parameter space of 21 cm global signal with Artificial Neural Networks

Understanding the first billion years of the universe requires studying two critical epochs: the Epoch of Reionization (EoR) and Cosmic Dawn (CD). However, due to limited data, the properties of the Intergalactic Medium (IGM) during these periods remain poorly understood, leading to a vast parameter space for the global 21cm signal. Training an Artificial Neural Network (ANN) with a narrowly defined parameter space can result in biased inferences. To mitigate this, the training dataset must be uniformly drawn from the entire parameter space to cover all possible signal realizations. However, drawing all possible realizations is computationally challenging, necessitating the sampling of a representative subset of this space. This study aims to identify optimal sampling techniques for the extensive dimensionality and volume of the 21cm signal parameter space. The optimally sampled training set will be used to train the ANN to infer from the global signal experiment. We investigate three sampling techniques: random, Latin hypercube (stratified), and Hammersley sequence (quasi-Monte Carlo) sampling, and compare their outcomes. Our findings reveal that sufficient samples must be drawn for robust and accurate ANN model training, regardless of the sampling technique employed. The required sample size depends primarily on two factors: the complexity of the data and the number of free parameters. More free parameters necessitate drawing more realizations. Among the sampling techniques utilized, we find that ANN models trained with Hammersley Sequence sampling demonstrate greater robustness compared to those trained with Latin hypercube and Random sampling.

Quasi-normal modes of loop quantum black holes formed from gravitational collapse

In this paper, we study the quasi-normal modes (QNMs) of a scalar field in the background of a large class of quantum black holes that can be formed from gravitational collapse of a dust fluid in the framework of effective loop quantum gravity. The loop quantum black holes (LQBHs) are characterized by three free parameters, one of which is the mass parameter, while the other two are purely due to quantum geometric effects. Among these two quantum parameters, one is completely fixed by black hole thermodynamics and its effects are negligible for macroscopic black holes, while the second parameter is completely free (in principle). In the studies of the QNMs of such LQBHs, we pay particular attention to the difference of the QNMs between LQBHs and classical ones, so that they can be observed for the current and forthcoming gravitational wave observations, whereby place the LQBH theory directly under the test of observations.

Robust preference for Dynamical Dark Energy in DESI BAO and SN measurements

Recent Baryon Acoustic Oscillation (BAO) measurements released by DESI, when combined with Cosmic Microwave Background (CMB) data from Planck and two different samples of Type Ia supernovae (Pantheon-Plus and DESY5) reveal a preference for Dynamical Dark Energy (DDE) characterized by a present-day quintessence-like equation of state that crossed into the phantom regime in the past. A core ansatz for this result is assuming a linear Chevallier-Polarski-Linder (CPL) parameterization w(a) = w 0 + wa (1-a) to describe the evolution of the DE equation of state (EoS). In this paper, we test if and to what extent this assumption impacts the results. To prevent broadening uncertainties in cosmological parameter inference and facilitate direct comparison with the baseline CPL case, we focus on 4 alternative well-known models that, just like CPL, consist of only two free parameters: the present-day DE EoS (w0 ) and a parameter quantifying its dynamical evolution (wa ). We demonstrate that the preference for DDE remains robust regardless of the parameterization: w0 consistently remains in the quintessence regime, while wa consistently indicates a preference for a dynamical evolution towards the phantom regime. This tendency is significantly strengthened by DESY5 SN measurements. By comparing the best-fit χ2 obtained within each DDE model, we notice that the linear CPL parameterization is not the best-fitting case. Among the models considered, the EoS proposed by Barboza and Alcaniz consistently leads to the most significant improvement.

Observational Test of f(Q) Gravity with Weak Gravitational Lensing

In this article we confront a class of f(Q) gravity models with observational data of galaxy–galaxy lensing. Specifically, we consider f(Q) gravity models containing a small quadratic correction when compared with general relativity (GR), and quantify this correction by a model parameter, α. To derive the observational constraints, we start by extracting spherically symmetric solutions, which correspond to deviations from the Schwarzschild solution that depends on the model parameters in a twofold way, i.e., a renormalized mass and a new term proportional to r −2. Then, we calculate the effective lensing potential, the deflection angle, the shear component, and the effective excess surface density profile. After that, we employ a group catalog and a shape catalog from the Sloan Digital Sky Survey Data Release 7 for the lens and source samples, respectively. Moreover, we handle the off-center radius as a free parameter and constrain it using a Markov Chain Monte Carlo method. Concerning the deviation parameter from GR we derive α=1.202−0.179+0.277×10−6Mpc−2 at the 1σ confidence level, and then compare the fitting efficiency with the standard Λ cold dark matter paradigm by applying the Akaike information criterion and Bayesian information criterion. Our results indicate that the f(Q) corrections alongside the off-center effect yield a scenario that is slightly favored.

Semi-implicit schemes for modeling water flow and solute transport in unsaturated soils

The coupled model of water flow and solute transport in unsaturated soils is addressed in this study. Building upon previous research findings by Keita, Beljadid, and Bourgault, we investigate a class of second-order time-stepping techniques where two free parameters are introduced, to identify the most stable and accurate scheme. The spatial discretization of the Richards equation is accomplished using the mixed finite element method. The proposed approach involves formulating noniterative schemes using an extrapolation formula and Taylor approximation in time to linearize nonlinear terms. Additionally, a specialized regularization technique is applied to ensure the convergence of the proposed numerical methods. Numerical simulations are conducted to determine the optimal scheme for solving the Richards equation, which is subsequently extended to the transport equation.Numerical simulations of water flow reveal the good accuracy of three schemes—SBDF, MSBDF, and Richards-M2 for homogeneous and heterogeneous soils. Notably, the SBDF scheme stands out for its computational efficiency and stability, especially when gravity forces dominate over capillary forces. Through numerical analysis of the coupled semi-implicit schemes, our results affirm the SBDF scheme’s superior robustness, establishing it as the optimal choice among the proposed numerical methods. Therefore, the SBDF scheme is employed to solve the coupled model of water flow and solute transport. We conducted various numerical experiments to solve the coupled model, addressing scenarios including single and multispecies nitrogen transport, pore water electrical conductivity, and nitrate transport. The SBDF scheme’s accuracy was rigorously verified through comparisons with reference solutions and experimental data. This establishes the SBDF scheme as an efficient alternative to traditional implicit methods for modeling water flow and solute transport in unsaturated soils.

Investigating innovative optical solitons for a (3+1)- dimensional nonlinear Schrödinger’s equation under the influences of 4th-order dispersive and parabolic law of nonlinearities

This study tackles a nonlinear Schrödinger’s equation in three dimensions, using three dispersive components of fourth order, often resulting in pure-quartic solitons. Pure-quartic bullets are known to deviate from conventional solitons due to their balance of fourth-order dispersion and nonlinearity. As bright and dark optically modulated bullets, we derive many solutions. Experiments on bullet transmission using optical nanofibers can benefit from the solutions found. Our creative solutions are produced by implementing the well-known scheme which is the improved modified extended tanh-function scheme. We find novel kinds of solutions (dark, bright, singular solitons, exponential, singular periodic, Weierstrass elliptic doubly periodic solutions, and Jacobi elliptic functions) that make their originality for the problem at hand evident by using the previously described approach. Contour plots and 2D and 3D visualizations in Wolfram Mathematica software are used to show how the well-furnished results propagate for various values of the necessary free parameters. The results demonstrate the computational processes’ precise, well-informed, and efficient nature. Through their integration with representational computations, they may be applied to increasingly complex phenomena. This work constitutes a major advancement in our comprehension of the intricate and erratic behavior of this mathematical model.

To the problem of digital immortality

The idea of reproducing personality by means of digital (neural network) technologies (“digital immortality”), together with the concept of Digital Twin (DT), still attracts great attention. Recent advances in the DT industry permit to expect the production of perfect “mirror” DT in the near future. We argue that the “immortality in the memory of other people” could be approached quite closely due to creating an analogue of personal DT by simulating the personality. For this purpose, it is necessary to compose the “constructive portrait” of a chosen person (by extracting the key features and traits of personality) and try to reproduce it by means of a chosen model. We are developing an original model Natural Constructive Cognitive Architecture (NCCA) that inherently provides the interpretation of logical and intuitive thinking, subconscious, etc. This model should be adjusted to specific set of knowledge inherent in a particular person (books, films, photographs, etc.), with an emphasis on personal lexicons (verbal, emotion, behavioral). NCCA contains a large set of free model parameters, which enables us to reproduce a wide range of personality features, from thinking style to temperament. It is shown that popular Generative Pre-trained Transformers (GPTs) have much in common with NCCA and could be adapted and used as an analog of DT of a specific person. We argue that the proposed program would provide the possibility to create an analog of DT, which could give an impression (at least, an illusion) of communication with the desired specific person.

Bjorken polarised sum rule with IR-finite QCD coupling

We evaluate the Bjorken polarised sum rule (BSR) Γ‾1p−n(Q2) with truncated Operator Product Expansion (OPE) up to the dimension D=4 terms; the leading-twist (D=0) contribution is evaluated with a renormalon motivated resummation, where we use the IR-finite running coupling free of Landau singularities. The free residue parameters at the D=2 and D=4 terms are then extracted by fits to the experimental BSR data. In comparison to the case when perturbative QCD coupling is used in this approach (cf. Refs. [1,2]), many advantages become manifest in the present case: (a) no regularisation in the resummation integral is needed; (b) the Q2-interval in the fit can be significantly extended to lower Q2-values; (c) the extracted residue parameter values are more stable, this being reflected in the significantly reduced experimental uncertainties of these values and the suppressed (almost negligible) central extracted value of the D=4 residue parameter (μ6).

Halo Bias in the Peak Model: A First-principles Nonparametric Approach

The Press–Schechter (PS) and excursion set (ES) models of structure formation fail in reproducing the halo bias found in simulations, while the ES-peaks' formalism built in the peak model reproduces it only at high masses and does not address in a fully satisfactory manner peak nesting, and the mass and time of ellipsoidal collapse of triaxial peaks in the Gaussian-smoothed density field. Here, we apply the confluent system of peak trajectories formalism fixing all these issues from first principles and with no free parameters to infer the Lagrangian local peak bias parameters, which adopt very simple analytic expressions similar to those found in the PS and ES models. The predicted Eulerian linear halo bias recovers the results of simulations. More specifically, we show that the only small departure observed at intermediate and low masses can be due to the spurious halo splitting and grouping caused by the spherical overdensity halo-finding algorithm used in simulations.

Tolman VII (TVII) Solution with Theory of Energy-Momentum Squared Gravity (EMSG) in Neutron Stars

Abstract We study the Tolman VII (TVII) solution for the Energy-Momentum Squared Gravity (EMSG) as well as the solution’s compatibility with stars properties. We perform a systematic analysis of the suitability of the equation of state (EoS) for energy density and pressure profiles. In calculations, for convenience, all physical quantities are expressed in the form of dimensionless quantities by introducing the quantity ζ = r/R. This dimensionless quantity will be used to determine the ratio between a star’s mass and its radius. The TVII solution provides limits on compactness C ∈ [0.01, 0.27] and neutron star’s mass 2.60M ⊙. Having α as a free parameter of the EMSG model gives the new range compactness C ∈ [0.01, 0.386] for ζ[0, 1] with α ∈ [0.01, ∞] and shows a star mass of 2.97M⊙. The metric eλ effective and the metric eν effective produce the range of α ∈ [0.1, 0.6], which represents both metric to be physical.

Conservative deep neural networks for modeling competition of ribosomes with extended length

We develop a network model that combines several ribosome flow models with extended objects (RFMEO) competing for the finite pool of ribosomes. This alleviates the need to systematically coarse-grain the mRNA molecules. The dynamics of the network is described by a system of non-linear ordinary differential equations. It is shown that the network always converges to a steady state for a fixed number of ribosomes. Our analysis shows that increasing any of the transition rates along an RFMEO increases its output rate and either the output rates of the other RFMEOs all increase or all decrease. Simulations also demonstrate a counterintuitive result that increasing the ribosomal footprint may sometimes lead to an increase in the network production rate. Next, we propose a conservative deep neural network (CDNN) framework to approximate the solution of the network. The proposed loss function also incorporates the term satisfying the first integral property of the network. Point-wise comparison of the solutions by CDNN is in good agreement with the Runge–Kutta based numerical solution. Also, the CDNN framework offers a closed-form solution of the RFMEONP as a function of free parameters, thus allowing evaluation of the solution at any parameter value without again simulating the system.

Sediment Corrections for Distributed Acoustic Sensing

AbstractOn continental margins, sediments cause significant and spatially variable delays in seismic phase arrival times. The strong impedance contrast of the sediment‐bedrock interface causes P‐wave splitting that is clearly seen on distributed acoustic sensing recordings of earthquakes, resulting in additional phase arrivals that must be picked separately. We introduce sediment corrections to correctly account for those additional phases in the hypocenter localization procedure. Conceptually, the sediment correction method differs from the commonly‐used station corrections; instead of introducing a mathematically optimal constant time delay for each station and each phase, the corrections are derived from a physical, first‐order modeling of the wave propagation in the sediments. To calibrate the sediment corrections, a two‐step procedure is adopted: (a) the delay between the P‐phase and the converted Ps‐phase is taken as a proxy of the sediment thickness; (b) the P‐ and S‐wave speeds are determined through inversion. We show that sediment corrections are able to account for most of the observed bias while considerably reducing the number of free parameters compared to classical station correction. Moreover, the observed local delays are almost fully explained by the presence of the sedimentary layer, rather than by the 3D velocity variations of the bedrock. We retrieve and values that are compatible with values commonly found for sediments. Given the simplicity and physical foundation of the proposed method, we recommend the use of sediment corrections over station corrections whenever significant P‐wave splitting can be observed.

WIMP Dark Matter in bulk viscous non-standard cosmologies

In this paper, we explore an extension of the classical non-standard cosmological scenario in which the new field, ϕ, which interacts with the radiation component in the early universe, experiences dissipative processes in the form of a bulk viscosity. Assuming an interaction term given by Γ ϕ ρ ϕ , where Γ ϕ accounts for the decay rate of the field and ρ ϕ corresponds to its energy density, and a bulk viscosity according to the expression ξ=ξ 0 ρ ϕ ϕ1/2 in the framework of Eckart's theory, we apply this novel non-standard cosmology to study the parameters space for WIMPs Dark Matter candidate production. This parameter space shows deviations from the classical non-standard cosmological scenario, obtaining new regions to search for this candidate. In particular, for certain combinations of the free parameters, we found large regions in which the model can establish the DM and reproduce the current observable relic density.

Baryonification extended to thermal Sunyaev Zel’dovich

Baryonification algorithms model the impact of galaxy formation and feedback on the matter field in gravity-only simulations by adopting physically motivated parametric prescriptions. In this paper, we extend these models to describe gas temperature and pressure, allowing for a self-consistent modelling of the thermal Sunyaev-Zel’dovich effect, weak gravitational lensing, and their cross-correlation, down to small scales. We validate our approach by showing that it can simultaneously reproduce the electron pressure, gas, stellar, and dark matter power spectra as measured in all BAHAMAS hydrodynamical simulations. Specifically, with only two additional free parameters, we can fit the electron pressure auto- and cross-power spectra at 10% while reproducing the suppression in the matter power spectrum induced by baryons at the per cent level, for different active galactic nuclei (AGN) feedback strengths in BAHAMAS. Furthermore, we reproduce BAHAMAS convergence and thermal Sunyaev Zel’dovich angular power spectra within 1% and 10% accuracy, respectively, down to ℓ = 5000. When used jointly with cosmological rescaling algorithms, the baryonification presented here allows for a fast and accurate exploration of cosmological and astrophysical scenarios. Therefore, it can be employed to create mock catalogues, lightcones, and large training sets for emulators aimed at interpreting forthcoming multi-wavelength observations of the large-scale structure of the Universe.

Thermal Expansion of Hexagonal Boron Nitride

A heuristic model is proposed for the dependence with temperature of the linear coefficients of thermal expansion (TEC) of hexagonal boron nitride (hBN) parallel to the crystallographic a and c axes, namely and . The model proposed for the linear TECs of hBN is consistent with physical constraints at the low‐ and high‐temperature limits. The model's free parameters are determined by a multi‐objective fitting to literature data on lattice parameters and linear TECs versus temperature, as determined experimentally by X‐ray diffraction and interferometric techniques. For hBN, is negative up to 1290(170) K (more than twice the corresponding temperature for graphite), with a minimum of around 230 K. According to the calculations and literature data, the linear TEC should remain negative at least up to 9 GPa. Furthermore, the linear coefficient of thermal expansion should decrease with pressure as = .

Extended B-Spline Collocation Method for Singularly Perturbed Time Delay Parabolic Differential-Difference Problems

The paper presents a robust collocation B-spline numerical scheme for solving singularly perturbed time lag parabolic differential–difference problems. The method uses Taylor’s series expansion for the approximation of retarded terms, the [Formula: see text]-method (when [Formula: see text]) for time discretization, and the extended third-degree B-spline collocation method for spatial discretization in a piecewise uniform Shishkin mesh. The advantage of using an extended cubic B-spline rather than the classical third-degree B-spline method is that it introduces one additional free parameter to control the global shape parameter. The stability and uniform convergence of the proposed scheme are investigated. The method is first-order accurate in [Formula: see text] and almost second-order accurate in [Formula: see text], surpassing existing literature methods.