Free Parameters Research Articles

The cosmic web from perturbation theory

Context. Analysing the large-scale structure (LSS) in the Universe with galaxy surveys demands accurate structure formation models. Such models should ideally be fast and have a clear theoretical framework in order to rapidly scan a variety of cosmological parameter spaces without requiring large training data sets. Aims. This study aims to extend Lagrangian perturbation theory (LPT), including viscosity and vorticity, to reproduce the cosmic evolution from dark matter N-body calculations at the field level. Methods. We extend LPT to a Eulerian framework, which we dub eALPT. An ultraviolet regularisation through the spherical collapse model provided by Augmented LPT turns out to be crucial at low redshifts. This iterative method enables modelling of the stress tensor and introduces vorticity. The eALPT model has two free parameters apart from the choice of cosmology, redshift snapshots, cosmic volume, and the number of particles. Results. We find that compared to N-body solvers, the cross-correlation of the dark matter distribution increases at k = 1 h Mpc−1 and z = 0 from ∼55% with the Zel’dovich approximation (∼70% with ALPT), to ∼95% with the three-timestep eALPT, and the power spectra show percentage accuracy up to k ≃ 0.3 h Mpc−1.

Probing the physical properties of the intergalactic medium using SRG/eROSITA spectra from blazars

Most baryonic matter resides in the intergalactic medium (IGM). This diffuse gas is primarily composed of ionized hydrogen and helium and fills the space between galaxies. Observations of this environment are crucial for better understanding the physical processes in it. We present an analysis of the IGM absorption using blazar spectra from the first eROSITA all-sky survey (eRASS1) performed onboard of the Spectrum-Roentgen-Gamma mission (SRG) and XMM-Newton X-ray observations. First, we fit the continuum spectra using a log-parabolic spectrum model and fixed the Galactic absorption. Then, we included a collisional ionization equilibrium model, namely IONeq, to account for the IGM absorption. The column density N(H) and metallicity (Z) were set as free parameters. At the same time, the redshift of the absorber was fixed to half the blazar redshift as an approximation of the full line-of-sight absorber. We measured IGM-N(H) for 147 sources for SRG and 10 sources for XMM-Newton. We found a clear trend between IGM-N(H) and the blazar redshifts that scales as (1 + z)1.63 ± 0.12. The mean hydrogen density at z = 0 is n0 = (2.75 ± 0.63)×10−7 cm−3. The mean temperature over the redshift range is log(T/K) = 5.6 ± 0.6, and the mean metallicity is Z = 0.16 ± 0.09. We found no acceptable fit using a power-law model for the temperatures or metallicities as a function of the redshift. These results indicate that the IGM contributes substantially to the total absorption seen in the blazar spectra.

Numerical analyses of M31 dark matter profiles

In this paper, we reproduce the rotation curve of the Andromeda galaxy (M31) by taking into account its bulge, disk and halo components, considering the last one to contain the major part of dark matter mass. Hence, our prescription is to split the galactic bulge into two components, namely, the inner and main bulges, respectively. Both bulges are thus modeled by exponential density profiles since we underline that the widely accepted de Vaucouleurs law fails to reproduce the whole galactic bulge rotation curve. In addition, we adopt various well-known phenomenological dark matter profiles to estimate the dark matter mass in the halo region. Moreover, we apply the least-squares fitting method to determine from the rotation curve the model free parameters, namely, the characteristic (central) density, scale radius and consequently the total mass. To do so, we perform Markov chain Monte Carlo statistical analyses based on the Metropolis algorithm, maximizing our likelihoods adopting velocity and radii data points of the rotation curves. We do not fit separately the components for bulges, disk and halo, but we perform an overall fit including all the components and employing all the data points. Thus, we critically analyze our corresponding findings and, in particular, we employ the Bayesian information criterion to assess the most accredited model to describe M31 dark matter dynamics.

Variation in the Pedersen Conductance Near Jupiter's Main Emission Aurora: Comparison of Hubble Space Telescope and Galileo Measurements

AbstractWe present the first large‐scale statistical survey of the Jovian main emission (ME) to map auroral properties from their ionospheric locations out into the equatorial plane of the magnetosphere, where they are compared directly to in‐situ spacecraft measurements. We use magnetosphere‐ionosphere (MI) coupling theory to calculate currents from the auroral brightness as measured with the Hubble Space Telescope and from plasma flow speeds measured in‐situ with the Galileo spacecraft. The effective Pedersen conductance of the ionosphere remains a free parameter in this comparison. We calculate the Pedersen conductance from the combined data sets, and find it ranges from mho overall with averages of mho in the north and mho in the south. Considering the HST‐derived field‐aligned currents per radian of azimuth only, we find values of MA rad−1 and MA rad−1 in the north and south, respectively, in general agreement with previous results. Taking the currents and effective Pedersen conductance together, we find that the average ME intensity and plasma flow speed in the middle magnetosphere (10–30 RJ) are broadly consistent with one another under MI coupling theory. We find evidence for peaks in the distribution of near dawn, then again near 12 and 14 hr magnetic local time (MLT). This variation in Pedersen conductance with MLT may indicate the importance of conductance in modulating MLT‐ and local‐time‐asymmetries in the ME, including the apparent subcorotation of some auroral features within the ME.

A high-efficiency adaptive TENO scheme with optimal accuracy order for compressible flow simulation

In this paper, we propose a new adaptive cut-off function and develop a fifth-order targeted ENO scheme that achieves optimal accuracy at any order of critical points, which performs excellently in conventional compressible gas dynamics. The cut-off value CT is crucial for controlling the dissipation in TENO schemes. Adjusting CT can improve shock capture and increase dissipation for small-scale features. To address this issue, Fu et al. [27] and Peng et al. [28] developed the TENO-A and TENO-LAD schemes, respectively, with adaptive cut-off values CT. However, these adaptive cutoffs CT are computationally expensive due to additional free parameters and complexity. Furthermore, all TENO schemes, including the adaptive versions, can suffer from loss of accuracy at higher-order critical points. In this paper, a new adaptive cut-off function is proposed that uses a global smoothness indicator correction so that it can be automatically tuned between 0 and a given positive constant λd, ensuring that the new TENO scheme achieves optimal accuracy in smooth regions and good shock-capturing in the less smooth parts. A series of benchmark simulations demonstrate that the presented scheme provides optimal accuracy, better robustness, resolution, and numerical stability, and higher resolution than existing TENO schemes while improving computational efficiency. Due to the simplicity of the new cut-off structure, it can be easily extended to improve other TENO schemes.Program files associated to this article may be found at https://github.com/fourhairs/cfd.

A new approach for fast field calculation in electrostatic electron lens design and optimization

In electron optics, calculation of the electric field plays a major role in all computations and simulations. Accurate field calculation methods such as the finite element method (FEM), boundary element method and finite difference method, have been used for years. However, such methods are computationally very expensive and make the computer simulation challenging or even infeasible when trying to apply automated design of electrostatic lens systems with many free parameters. Hence, for years, electron optics scientists have been searching for a fast and accurate method of field calculation to tackle the aforementioned problem in the design and optimization of electrostatic electron lens systems. This paper presents a novel method for fast electric field calculation in electrostatic electron lens systems with reasonably high accuracy to enable the electron-optical designers to design and optimize an electrostatic lens system with many free parameters in a reasonably short time. The essence of the method is to express the off-axis potential in an axially symmetrical coordinate system in terms of derivatives of the axial potential up to the fourth order, and equate this to the potential of the electrode at that axial position. Doing this for a limited number of axial positions, we get a set of equations that can be solved to obtain the axial potential, necessary for calculating the lens properties. We name this method the fourth-order electrode method because we take the axial derivatives up to the fourth order. To solve the equations, a quintic spline approximation of the axial potential is calculated by solving three sets of linear equations simultaneously. The sets of equations are extracted from the Laplace equation and the fundamental equations that describe a quintic spline. The accuracy and speed of this method is compared with other field calculation methods, such as the FEM and second order electrode method (SOEM). The new field calculation method is implemented in design/optimization of electrostatic lens systems by using a genetic algorithm based optimization program for electrostatic lens systems developed by the authors. The effectiveness of this new field calculation method in optimizing optical parameters of electrostatic lens systems is compared with FEM and SOEM and the results are presented. It should be noted that the formulation is derived for general axis symmetrical electrostatic electron lens systems, however the examples shown in this paper are with cylindrical electrodes due to the simplicity of the implementation in the software.

Isopointal intermetallics: the cP24, dca phases as a representative set of examples, along with their vacancy-ordered variants β-Mn and SrSi2

Abstract The crystal-chemical relationship of the cubic Laves phase MgCu2 (space group F d 3 ‾ $d\overline{3}$ m, cF24) with the ternary phases Cd2Cu3In, Na2Au3Al, Mg2Rh3P, Li2Pd3B, Ag2Pd3S, Cu3Pt2B, Mo3Al2C, Mo3Ni2N, and V3Ga2N (subgroup P4132, cP24, dca) is discussed based on a group-subgroup scheme. The course of the lattice parameters and the free positional parameters show substantially different distortions and thus clear differences in chemical bonding, classifying these phases as isopointal rather than isotypic (usually they are all assigned to the Mo3Al2C type). The group-subgroup scheme further shows that the β-Mn and SrSi2 structures are vacancy-ordered variants of the cP24, dca phases. The structures of Mn3IrSi and LaIrSi (space group types P213; translationengleiche subgroups) are their ternary ordered versions.

Study of explicit travelling wave solutions of nonlinear (2 + 1)-dimensional Zoomeron model in mathematical physics

Abstract This article studeis the nonlinear (2 + 1)-dimensional Zoomeron equation by utilizing the various prominent analytical approaches namely the unified method and the extended hyperbolic function approach. The analysis in the current paper demonstrates the presence of travelling wave solutions. The applied methods are utilized as powerful tools to investigate and solve the model. The results obtained through these analytical methods reveal insightful patterns in the behavior of the Zoomeron equation. The significance of our work lies in the uniqueness of the methods employed. The two methods are applied to systematically analyze the equation, revealing hidden patterns and structures within its solution space. This leads to the discovery of a collection of solitary wave solutions such as kink waves, singular kink waves, periodic waves and dark soliton using contour plots, 3D and 2D graphics. In this article, we definitely prove that as the free parameters change, the wave amplitude changes as well. It is shown that the applied strategies are more effective and may be implemented to a variety of contemporary nonlinear evolution models emerging in mathematical physics.

Semi-analytic modelling of Pop. III star formation and metallicity evolution - I. Impact on the UV luminosity functions at z = 9 − 16

Abstract We implemented Population III (Pop. III) star formation in mini-halos within the meraxes semi-analytic galaxy formation and reionisation model, run on top of a N-body simulation with L = 10h−1 cMpc with 20483 particles resolving all dark matter halos down to the mini-halos (∼105M⊙). Our modelling includes the chemical evolution of the IGM, with metals released through supernova-driven bubbles that expand according to the Sedov-Taylor model. We found that SN-driven metal bubbles are generally small, with radii typically of 150 ckpc at z = 6. Hence, the majority of the first galaxies are likely enriched by their own star formation. However, as reionization progresses, the feedback effects from the UV background become more pronounced, leading to a halt in star formation in low-mass galaxies, after which external chemical enrichment becomes more relevant. We explore the sensitivity of the star formation rate density and stellar mass functions on the unknown values of free parameters. We also discuss the observability of Pop. III dominated systems with JWST, finding that the inclusion of Pop. III galaxies can have a significant effect on the total UV luminosity function at z = 12 − 16. Our results support the idea that the excess of bright galaxies detected with JWST might be explained by the presence of bright top-heavy Pop. III dominated galaxies without requiring an increased star formation efficiency.

Scenario of FLRW Dark Energy Universe and f(Q) Gravity

In this paper, we discuss the accelerated expansion of the Universe in the context of f(Q) gravity theory, where Q is the non-metricity scalar. We consider a well-established parametrization of the Hubble parameter in order to determine the solution of the field equations in the FLRW universe. To obtain the best-fit value for the model parameters we use the combined Hubble, BAO, and Pantheon datasets. In order to analyze the cosmological parameters, we take two different f(Q) models into consideration, Specifically, f(Q)=λQ2 and f(Q)=Q+mQ2, where λ is a constant and m is the free parameter. Additionally, we examine how statefinder analysis, the jerk parameter, and the Om diagnostic parameter behave. Finally, we came to the conclusion that the parameters of both f(Q) models show quintessential behavior and that the cosmos is in an accelerating phase.

Neutrality in plant-herbivore interactions.

Understanding the distribution of herbivore damage among leaves and individual plants is a central goal of plant-herbivore biology. Commonly observed unequal patterns of herbivore damage have conventionally been attributed to the heterogeneity in plant quality or herbivore behaviour or distribution. Meanwhile, the potential role of stochastic processes in structuring plant-herbivore interactions has been overlooked. Here, we show that based on simple first principle expectations from metabolic theory, random sampling of different sizes of herbivores from a regional pool is sufficient to explain patterns of variation in herbivore damage. This is despite making the neutral assumption that herbivory is caused by randomly feeding herbivores on identical and passive plants. We then compared its predictions against 765 datasets of herbivory on 496 species across 116° of latitude from the Herbivory Variability Network. Using only one free parameter, the estimated attack rate, our neutral model approximates the observed frequency distribution of herbivore damage among plants and especially among leaves very well. Our results suggest that neutral stochastic processes play a large and underappreciated role in natural variation in herbivory and may explain the low predictability of herbivory patterns. We argue that such prominence warrants its consideration as a powerful force in plant-herbivore interactions.

A new paradigm for multi-fidelity continuation using parallel model refinement

Numerical path continuation is commonly applied to determine how limit states of dynamical systems evolve with a free parameter. For high-fidelity models of complicated nonlinear systems, the sequential nature inherent to continuation can become an unsurmountable obstacle. In the present work, we propose a new paradigm for obtaining the targeted solution curves in a parallelized way. The point of departure is a low-fidelity model, which is of lower order and/or neglects certain nonlinear/coupling terms. The simplifications must be as drastic as necessary to obtain an approximate solution curve with reasonable effort. A subset of relevant points along this approximate solution curve is then selected, and, departing there, points on the targeted solution branch of the high-fidelity model are then iteratively computed. It is important to note that the iterative correction towards the high-fidelity solution branch can be applied independently for each point, and is thus predestined for parallel computation. The proposed generic concept is exemplified for a selection of nonlinear vibration problems. Different types of system models, nonlinearities and analyses are considered, and the Harmonic Balance method is used in all cases to compute periodic limit states. In particular, it is shown that the proposed concept is applicable to modal and harmonic order refinement. Finally, it is shown that the concept is also interesting when instead of a model refinement a second system parameter (besides the continuation parameter) is varied, and it permits to robustly reach parameter ranges that are extremely difficult to obtain with conventional path continuation. The method is available, along with the presented numerical examples, as a branch PEACE (Parallelized Re-analysis Of Solution Curves) of the open source tool NLvib.

A reactive electrochemomechanical theory for growth and remodeling of polyelectrolyte hydrogels and application to dynamic polymerization of DNA hydrogels

This study develops a framework for growth and remodeling of active polyelectrolyte hydrogels that accounts for effects of compositional changes on the mechanical response. By developing a reactive electrochemomechanical theory, thermodynamical constraints upon reactive and remodeling processes are elucidated within a general framework that allows any number of chemical reactions to evolve the response of the gel and transfer mass and charge between constituents. Fully coupled, nonlinear constitutive relations are adopted for molar fluxes, allowing exploration of effects including cross-diffusion, electrophoresis, and electro-osmosis. A robust finite element implementation is developed in the open source FEBio software (febio.org) by exploiting an equivalence between electrochemomechanics and mixture theory. The implementation is verified against analytical solutions for free swelling, and a proper reduction to a prior chemomechanical theory is demonstrated for neutral gels swollen only by a solvent with no solutes. The theory and implementation are then applied to model the tunable large swelling achieved through dynamic polymerization of DNA crosslinkers seen in our recently developed experimental hydrogel system (Cangialosi et al., 2017). A novel constitutive model for reaction-driven evolution of the locking stretch λL in a non-Gaussian mechanical free energy was developed, where the increasing concentration of DNA crosslinkers makes further swelling energetically favorable. With a single free parameter, excellent agreement was found between measured and predicted equilibrium swelling ratios. This study demonstrated the ability to extend the electrochemomechanical framework to include chemical reactions and composition-aware constitutive models, and showed that development of reactive models allows simulation of complex dynamic polymerization phenomena not treated before. The theoretical frame here can be further expanded in scope to incorporate additional non-ideal and nonlinear phenomena.

Mixed-state entanglement and transport in Einstein–Maxwell–Axion–Horndeski theory

We present a comprehensive study exploring the relationship between transport properties and measures of quantum entanglement in the Einstein–Maxwell–Axion–Horndeski theory. By using holographic duality, we study the entanglement measures, holographic entanglement entropy (HEE) and entanglement wedge cross-section (EWCS), and transport coefficients, for this model and analyze their dependence on free parameters which we classify into action parameters, observable parameters and axion factor. We find contrasting behaviors between HEE and EWCS with respect to observable parameters (charge and temperature), and the axion factor, indicating that they capture different types of quantum correlations. We also find that HEE exhibits positive correlation with both charge and thermal excitations, whereas EWCS exhibits a negative correlation with charge-related conductivities and thermal fluctuations. Furthermore, we find that the Horndeski coupling term, as the modification to standard gravity theory, does not change the qualitative behaviors of the conductivities and the entanglement measures.

Convergence properties of fine structure constant measurements using quasar absorption systems

ABSTRACT Searches for space–time variations of fundamental constants have entered an era of unprecedented precision. New, high-quality quasar spectra require increasingly refined analytical methods. In this paper, a continuation in a series to establish robust and unbiased methodologies, we explore how convergence criteria in non-linear least-squares optimization impact on quasar absorption system measurements of the fine structure constant α. Given previous claims for high-precision constraints, we critically examine the veracity of a so-called blinding approach, in which α is fixed at the terrestrial value during the model building process, releasing it as a free parameter only after the ‘final’ absorption system kinematic structure has been obtained. We show that this approach results in such small consecutive parameter steps during minimization that convergence is unlikely to be reached, even after as many as 1000 iterations. The fix is straightforward: α must be treated as a free parameter from the earliest possible stages of absorption system model building. The implication of the results presented here is that all previous measurements that have used initially fixed α should be reworked.

Phase-field lattice Boltzmann model with singular mobility for quasi-incompressible two-phase flows.

In this paper, a lattice Boltzmann for quasi-incompressible two-phase flows is proposed based on the Cahn-Hilliard phase-field theory, which can be viewed as an improved model of a previous one [Yang and Guo, Phys. Rev. E 93, 043303 (2016)2470-004510.1103/PhysRevE.93.043303]. The model is composed of two LBE's, one for the Cahn-Hilliard equation(CHE) with a singular mobility, and the other for the quasi-incompressible Navier-Stokes equations(qINSE). Particularly, the LBE for the CHE uses an equilibrium distribution function containing a free parameter associated with the gradient of chemical potential, such that the variable (and even zero) mobility can be handled. In addition, the LBE for the qINSE uses an equilibrium distribution function containing another free parameter associated with the local shear rate, such that the large viscosity ratio problems can be handled. Several tests are first carried out to test the capability of the proposed LBE for the CHE in capturing phase interface, and the results demonstrate that the proposed model outperforms the original LBE model in terms of accuracy and stability. Furthermore, by coupling the hydrodynamic equations, the tests of double-stationary droplets and droplets falling problems indicate that the proposed model can reduce numerical dissipation and produce physically acceptable results at large time scales. The results of droplets falling and phase separation of binary fluid problems show that the present model can handle two-phase flows with large viscosity ratio up to the magnitude of 10^{4}.

Mean-field method for generic conductance-based integrate-and-fire neurons with finite timescales.

The construction of transfer functions in theoretical neuroscience plays an important role in determining the spiking rate behavior of neurons in networks. These functions can be obtained through various fitting methods, but the biological relevance of the parameters is not always clear. However, for stationary inputs, such functions can be obtained without the adjustment of free parameters by using mean-field methods. In this work, we expand current Fokker-Planck approaches to account for the concurrent influence of colored and multiplicative noise terms on generic conductance-based integrate-and-fire neurons. We reduce the resulting stochastic system through the application of the diffusion approximation to a one-dimensional Langevin equation. An effective Fokker-Planck is then constructed using Fox Theory, which is solved numerically using a newly developed double integration procedure to obtain the transfer function and the membrane potential distribution. The solution is capable of reproducing the transfer function and the stationary voltage distribution of simulated neurons across a wide range of parameters. The method can also be easily extended to account for different sources of noise with various multiplicative terms, and it can be used in other types of problems in principle.

Solitonic rogue and modulated wave patterns in the monoatomic chain with anharmonic potential

Modulation instability and rogue wave structures have been investigated in this work. This study is an extension of the work in Abbagari (2023), where a nonlinear Schrödinger equation with higher-order dispersion is derived to show only the development of the modulated waves bounded to bright soliton as a nonlinear exhibition of modulation instability. Here, the coupled nonlinear Schrödinger equation is derived by using the multi-scale scheme. An overview of the analytical calculations of the perturbed plane wave is carried out to show the effects of the nonlinear chain parameters on the modulation instability growth rate and bandwidths. The interest of this study lies equally in the nonlinear modes of excitation, where solitonic waves are generated under certain conditions in lower and upper frequency bands. On the other hand, relevant results have been developed to show the features of the type I and type II rogue waves of the Manakov system. Such investigations are obtained under the variation of the interaction potential parameters and the free parameter of the similarity method. Via a numerical simulation, rogue wave structures have been generated as a consequence of the long-time evolution of the perturbed plane wave. At a specific time of propagation, another localized object has been obtained to show the Akhmediev breathers and Kuznetsov-Ma solitons clusters under a strong perturbed wave number. These results have opened up new features, and many applications could follow in the future.

Signature of Scramblon Effective Field Theory in Random Spin Models.

Information scrambling refers to the propagation of information throughout a quantum system. Its study not only contributes to our understanding of thermalization but also has wide implications in quantum information and black hole physics. Recent studies suggest that information scrambling in large-N systems with all-to-all interactions is mediated by collective modes called scramblons. However, a criterion for the validity of scramblon theory in a specific model is still missing. In this work, we address this issue by investigating the signature of the scramblon effective theory in random spin models with all-to-all interactions. We demonstrate that, in scenarios where the scramblon description holds, the late-time operator size distribution can be predicted from its early-time value, requiring no free parameters. As an illustration, we examine whether Brownian circuits exhibit a scramblon description and obtain a positive confirmation both analytically and numerically. Our findings provide a concrete experimental framework for unraveling the scramblon field theory in random spin models using quantum simulators.

Triad resonance for internal waves in a uniformly stratified fluid: Rogue waves and breathers.

Three-wave (triad) resonance in a uniformly stratified fluid is investigated as a case study of energy transfer among oscillatory modes. The existence of a degenerate triad is demonstrated explicitly, where two components have identical group velocity. An illuminating example is a resonance involving waves from modes 1, 3, 5 families, but many other combinations are possible. The physical applications and nonlinear dynamics of rogue waves derived analytically in the literature are examined. Exact solutions with four free parameters (two related to the amplitudes of the background plane waves, two related to the frequencies of slowly varying envelopes) describe motions localized in both space and time. The differences between rogue waves of the degenerate versus the nondegenerate cases are highlighted. The phase and profile of the degenerate case rogue waves are correlated. The volume or energy of the rogue wave (defined as the total extent or energy contents of the fluid set in motion for the duration of the rogue wave) may change drastically, if the wave envelope parameters vary. Pulsating modes (breathers) have been studied previously by layered-fluid and modified Korteweg-de Vries models. Here we extend the consideration to stratified fluids but for the simpler case of nondegenerate triads. Instabilities of fission and fusion of breathers are confirmed computationally with Floquet analysis. This knowledge should prove useful for energy transfer processes in the oceans.