Relaxation Of System Research Articles

First Joint MUSE, Hubble Space Telescope, and JWST Spectrophotometric Analysis of the Intracluster Light: The Case of the Relaxed Cluster RX J2129.7+0005

We present the most detailed spectrum of intracluster light (ICL) in an individual cluster to date, the relaxed system RX J2129.7+0005, at z ∼ 0.234. Using 15 broadband, deep images observed with the Hubble Space Telescope and JWST in the optical and the infrared, plus deep integral field spectroscopy from MUSE, we computed a total of 3696 ICL maps spanning the spectral range ∼0.4−5 μm with our algorithm CICLE, a method that is extremely well suited to analyzing large samples of data in a fully automated way. We used both parametric and nonparametric approaches to fit the spectral energy distribution of the ICL and infer its physical properties, yielding a stellar mass log10(M*/M⊙) between 11.5 and 12.7 and an average age between 9.7 and 10.5 Gyr, from CIGALE and Prospector results. This implies that the ICL in RX J2129.7+0005 is, on average, older than that of disturbed clusters, suggesting that the contribution from different stellar populations to the ICL is at play depending on the cluster’s dynamical state. Coupled with X-ray observations of the hot gas distribution, we confirm the relaxed state of RX J2129.7+0005, showing clear signs of sloshing after a last major merger with a high-mass-ratio satellite that could have happened ∼6.6 Gyr ago in a relatively radial orbit. The presence of substructure in the ICL, such as shells, clouds with different densities and a certain degree of boxyness, and a clump, supports this scenario.

Controlling the Relaxation Dynamics of Polymer Networks by Combining Associative and Dissociative Dynamic Covalent Bonds.

Dynamic polymer networks offer a promising solution to key challenges in polymers such as recyclability, processability, and damage repair. However, the trade-off between combining facile processability, fast self-healing, and high creep resistance remains a major obstacle to implementation. To overcome this, two very distinct dynamic covalent chemistries, Diels-Alder and transesterification, is combined in a single network. The resulting dual dynamic networks offer an unprecedented set of properties and control over the relaxation times. The system decouples the relaxation dynamics of the network from the spatial motifs, and the tuning of the ratio between chemistries enables to control of the relaxation dynamics over six orders of magnitude. Taking advantage of this control, the composition and rheological behavior is optimized to drastically improve the resolution for extrusion-based additive manufacturing of dynamic covalent networks. Additionally, two well-defined and separated stress relaxation peaks are observed at compositions close to 50% of each dynamic chemistry, accentuating the double character of the system's relaxation dynamics. This atypical situation, enables to preparation of self-healing materials with negligible creep, and with shape-memory properties solely leveraging the two distinct relaxation dynamics, instead of the glass transition temperature or the melting point.

Equivalent conditions of null controllability for controlled stochastic relaxed system

ABSTRACT This paper focuses on the investigation of null controllability in the context of stochastic controlled relaxed systems with one control, aiming to establish several equivalent conditions for this property. More precisely, by the classical duality analysis, we present the equivalence between an observability inequality for the backward stochastic system associated with the relaxed system and null controllability. Furthermore, we characterize the null controllability through a minimal norm control problem, employing a constructed quadratic functional and leveraging a variational characterization of its minimizer. Finally, we provide an application of our findings and extend the analysis to relaxed systems with two controls.

Global convergence rates from relaxed Euler equations to Navier–Stokes equations with Oldroyd-type constitutive laws

In a previous work (Peng and Zhao 2022 J. Math. Fluid Mech. 24 29), it is proved that the 1D full compressible Navier–Stokes equations for a Newtonian fluid can be approximated globally-in-time by a relaxed Euler-type system with Oldroyd’s derivatives and a revised Cattaneo’s constitutive law. These two relaxations turn the whole system into a first-order quasilinear hyperbolic one with partial dissipation. In this paper, we establish the global convergence rates between the smooth solutions to the relaxed Euler-type system and the Navier–Stokes equations over periodic domains. For this purpose, we use stream function techniques together with energy estimates for error systems. These techniques may be applicable to more complicated systems.

Photoconductivity in BxCyNz decorated ZnO 2D/1D system: Conjugation of charge transfer and piezo-phototronic effects

We present the improvisation of photoresponse characteristics of BxCyNz/ZnO system through the amalgamation of the charge transfer process and piezo-phototronic effect. The nanoflakes of BxCyNz obtained through simple chemical route are characterized by N-deficiency related defects in the network. In contrast to bare ZnO, the enhancement of current under light (by 145 %) in BxCyNz decorated system has been correlated to the defect-assisted charge transfer from BxCyNz to ZnO. Further, the interplay of trap-related space charge current due to excess charge transfer under UV illumination is found to exhibit an anomalous dependency of photocurrent with light intensity. The charge transfer process becomes more effective under the application of strain on the BxCyNz/ZnO system and thus exhibits 6 times higher photoresponsivity (∼44 AW−1) compared to the relaxed system. In this context, the negative piezo-potential mediated modification at the interface is held responsible for favouring the transport of transferred charge. Apart from that, the influence of the structural organization of ZnO system on the piezo-phototronic effect-led UV photodetection has also been observed. Eventually, the moderate photoresponse characteristics in g-C3N4/ZnO system in relaxed and strained platforms, ensure the superior role of N-deficiency related electronic states of BxCyNz in elevating the photoresponse property.

Exploration of New Lipid Nutrients and Their Characterization in Herbal Teas Using Non-Targeted Liquid Chromatography-Mass Spectrometry.

Herbal teas are blends of leaves, seeds, fruits, and flowers from various plants that provide relaxation, anti-inflammatory benefits, and immune system support for conditions such as diabetes and asthma. Despite their health benefits, comprehensive lipidomic data on herbal teas are limited in the literature. We used non-targeted liquid chromatography-linear ion trap orbitrap mass spectrometry to identify and correlate the lipid species in the following six herbal tea samples: fennel, ginger, juniper, lemon peel, orange peel, and rosehip. A total of 204 lipid molecular species were identified, and multivariate analysis revealed a significant difference between lipid species in herbal teas. Saturated fatty acids (SFAs) and polyunsaturated fatty acids (PUFAs) are significantly abundant in juniper, including ω-3 and ω-6 fatty acids, followed by fennel. Cluster correlations showed that ginger contained mainly sphingolipids and lysophospholipids, whereas fennel was rich in phospholipids. No significant variations in the content of triacylglycerols were observed in any of the herbal teas analyzed. The ratio of PUFAs to SFAs in herbal teas showed that orange peel had the highest ratio, followed by lemon peel and fennel, indicating their potential health benefits. In addition, using high-resolution mass spectrometry, various lipids such as fatty acid esters of hydroxy fatty acids and N-acyl-lysophosphatidylethanolamines were identified and characterized in these herbal teas. This study provides a comprehensive lipid analysis and detailed characterization of lipids in six herbal teas, highlighting their plausible applications in the field of nutrition and various food industries for the development of functional foods.

A “MeerKAT-meets-LOFAR” study of the complex multi-component (mini-)halo in the extreme sloshing cluster Abell 2142

Context. Clusters of galaxies are known to be turbulent environments, whether they are merging systems where turbulence is injected via the conversion of gravitational potential energy into the intracluster medium (ICM), or whether they are relaxed systems in which small-scale core sloshing is occurring within the potential well. In many such systems, diffuse radio sources associated with the ICM are found: radio haloes and mini-haloes. Aims. Abell 2142 is a rich cluster undergoing an extreme episode of core sloshing, which has given rise to four cold fronts and a complex multi-component radio halo. Recent work revealed that there are three primary components to the halo that spans a distance of up to around 2.4 Mpc. The underlying physics of particle acceleration on these scales is poorly explored, and requires high-quality multi-frequency data with which to perform precision spectral investigation. We aim to perform such an investigation. Methods. We used new deep MeerKAT L-band (1283 MHz) observations in conjunction with LOFAR HBA (143 MHz) data as well as X-ray data from XMM-Newton and Chandra to study the spectrum of the halo and the connection between the thermal and non-thermal components of the ICM. Results. We confirm the presence of the third halo component, detecting it for the first time at 1283 MHz and confirming its ultra-steep spectrum nature, as we recovered an integrated spectrum of αH3, total = −1.68 ± 0.10. All halo components follow power-law spectra with increasingly steep spectra moving towards the cluster outskirts. We profiled the halo in three directions, finding evidence of asymmetry and spectral steepening along an axis perpendicular to the main axis of the cluster. Our investigation of the thermal non-thermal connection shows sub-linear correlations that are steeper at 1283 MHz than 143 MHz, and we find evidence of different connections in different components of the halo. In particular, we find both a moderate anti-correlation (H1, the core) and positive correlation (H2, the ridge) between the radio spectral index and X-ray temperature. Conclusions. Our results are broadly consistent with an interpretation of turbulent (re-)acceleration following an historic minor cluster merger scenario in which we must invoke some inhomogeneities. However, the anti-correlation between the radio spectral index and X-ray temperature in the cluster core is more challenging to explain; the presence of three cold fronts and a generally lower temperature may provide the foundations of an explanation, but detailed modelling is required to study this further.

ARTIFICIAL INTELLIGENCE CONTROLLED RELAXATION SYSTEM FOR AUTISTIC CHILDREN – IT TECHNOLOGY THAT ADDRESSES SOCIAL ISSUES

The article presents the development and research of technological tools - a relaxation system for children with autism. The article describes the means and methods of emotional stabilization of children with autism spectrum disorders. The design, operation, and control of the relaxation system controlled by artificial intelligence with image processing and machine learning are described. The relaxation effect on children is carried out with audio-musical signals, by combining them with colored light and mechanical vibration of the back area. The practical research results are described, demonstrating the system's effectiveness for children with autism spectrum disorders. Under normal conditions, if a child takes 3 to 4 hours to calm down, the relaxation system shortens this time to 10 to 15 minutes. Finally, the relaxation system controlled by artificial intelligence-based software, created by scientists from three Lithuanian universities and the students of Vilnius Kolegija, is presented as a technological tool designed to address social issues in society.

A Deep Redshift Survey of the Perseus Cluster (A426): Spatial Distribution and Kinematics of Galaxies

We study the global kinematics of the Perseus galaxy cluster (A426) at redshift z = 0.017 using a large sample of galaxies from our new MMT/Hectospec spectroscopic observation for this cluster. The sample includes 1447 galaxies with measured redshifts within 60′ from the cluster center (1148 from this MMT/Hectospec program and 299 from the literature). The resulting spectroscopic completeness is 67% at r-band apparent magnitude r Petro,0 ≤ 18.0 within 60′ from the cluster center. To identify cluster member galaxies in this sample, we develop a new open-source Python package, CausticSNUpy. This code implements the algorithm of the caustic technique and yields 418 member galaxies within 60′ of the cluster. We study the cluster using this sample of member galaxies. The cluster shows no significant signal of global rotation. A statistical test shows that the cluster does not have a noticeable substructure within 30′. We find two central regions where the X-ray-emitting intracluster medium and galaxies show significant velocity differences (>7σ). On a large scale, however, the overall morphology and kinematics between the intracluster medium and galaxies agree well. Our results suggest that the Perseus cluster is a relaxed system and has not experienced a recent merger.

Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

An extended Gauss-Newton method for full-waveform inversion

Full-waveform inversion (FWI) is a large-scale nonlinear ill-posed problem for which computationally expensive Newton-type methods can become trapped in undesirable local minima, particularly when the initial model lacks a low-wavenumber component and the recorded data lack low-frequency content. A modification to the Gauss-Newton (GN) method is developed to address these issues. The standard GN system for multisource multireceiver FWI is reformulated into an equivalent matrix equation form, with the solution becoming a diagonal matrix rather than a vector as in the standard system. The search direction is transformed from a vector to a matrix by relaxing the diagonality constraint, effectively adding a degree of freedom to the subsurface offset axis. The relaxed system can be explicitly solved with only the inversion of two small matrices that deblur the data residual matrix along the source and receiver dimensions, which simplifies the inversion of the Hessian matrix. When used to solve the extended-source FWI objective function, the extended GN (EGN) method integrates the benefits of model and source extension. The EGN method effectively combines the computational effectiveness of the reduced FWI method with the robustness characteristics of extended formulations and offers a promising solution for addressing the challenges of FWI. It bridges the gap between these extended formulations and the reduced FWI method, enhancing inversion robustness while maintaining computational efficiency. The robustness and stability of the EGN algorithm for waveform inversion are demonstrated numerically.

Asymptotic preserving methods for quasilinear hyperbolic systems with stiff relaxation: a review

Hyperbolic systems with stiff relaxation constitute a wide class of evolutionary partial differential equations which describe several physical phenomena, ranging from gas dynamics to kinetic theory, from semiconductor modeling to traffic flow. Peculiar features of such systems is the presence of a small parameter that determines the smallest time scale of the system. As such parameter vanishes, the system relaxes to a different one with a smaller number of equations, and sometime of a different mathematical nature. The numerical solution of such systems may present some challenges, in particular if one is interested in capturing all regimes with the same numerical method, including the one in which the small parameter vanishes (relaxed system). The design, analysis and application of numerical schemes which are robust enough to solve this class of systems for arbitrary value of the small parameter is the subject of the current paper. We start presenting different classes of hyperbolic systems with relaxation, illustrate the properties of implicit–explicit (IMEX) Runge–Kutta schemes which are adopted for the construction of efficient methods for the numerical solution of the systems, and then illustrate how to apply IMEX schemes for the construction of asymptotic preserving schemes, i.e. scheme which correctly capture the behavior of the systems even when the relaxation parameter vanishes.

LOFAR detection of extended emission around a mini halo in the galaxy cluster Abell 1413

Context. The relation between giant radio halos and mini halos in galaxy clusters is not understood. The former are usually associated with merging clusters, while the latter are found in relaxed systems. In recent years, the advent of low-frequency radio observations has challenged this dichotomy by finding intermediate objects with a hybrid radio morphology. Aims. We aim to investigate the presence of diffuse radio emission in the cluster Abell 1413 and determine its dynamical status to explore the relation between mini halos and giant radio halos. Methods. We used LOFAR observations centred at 144 MHz to study the diffuse radio emission. To investigate the dynamical state of the system, we used newly analysed XMM-Newton archival data. Abell 1413 shows features that are typically present in both relaxed (e.g., peaked X-ray surface brightness distribution and some large-scale inhomogeneities) and disturbed (e.g., flatter temperature and metallicity profiles) clusters. Results. This suggests that Abell 1413 is neither disturbed nor fully relaxed, and we argue that it is an intermediate-phase cluster. At 144 MHz, we discover a wider diffuse component surrounding the previously known mini halo at the cluster center. By fitting the radio surface-brightness profile with a double-exponential model, we can disentangle the two components. We find an inner mini halo with an e-folding radius, re, 1 = 28 ± 5 kpc, and an extended component with re, 2 = 290 ± 60 kpc. We also evaluated the point-to-point correlation between the radio and X-ray surface brightness, finding a sublinear relation for the outer emission and a superlinear relation for the mini halo. The mini halo and the diffuse emission extend over different scales and show different features, confirming the double nature of the radio emission and suggesting that the mechanisms responsible for the re-acceleration of the radio-emitting particle might be different.

On a relaxation approximation of the 2-D incompressible magnetohydrodynamic equations

We study the Cauchy problem of a 2-D hyperbolic relaxation system for the incompressible magnetohydrodynamic (MHD) equations, which is related with the scientific computational aspects. We prove that this relaxed problem possesses a global strong solution, provided that the relaxation parameter is small and the appropriate norm of the initial data is not very large. We also show that such global solution converges to the one of the original incompressible MHD equations, as the relaxation parameter goes to zero.

Understanding random-walk dynamical phase coexistence through waiting times

We study the appearance of first-order dynamical phase transitions (DPTs) as “intermittent” coexisting phases in the fluctuations of random walks on graphs. We show that the diverging timescale leading to critical behavior is the waiting time to jump from one phase to another. This timescale is crucial for observing the system's relaxation to stationarity and demonstrate ergodicity of the system at criticality. We illustrate these results through three analytical examples which provide insights into random walks exploring random graphs. Published by the American Physical Society 2024

High-order relaxation methods for nonequilibrium two-phase flow equations

PurposeThe purpose of this paper is to investigate the two-phase flow problems involving gas–liquid mixture.Design/methodology/approachThe governed equations consist of a range of conservation laws modeling a classification of two-phase flow phenomena subjected to a velocity nonequilibrium for the gas–liquid mixture. Effects of the relative velocity are accounted for in the present model by a kinetic constitutive relation coupled to a collection of specific equations governing mass and volume fractions for the gas phase. Unlike many two-phase models, the considered system is fully hyperbolic and fully conservative. The suggested relaxation approach switches a nonlinear hyperbolic system into a semilinear model that includes a source relaxation term and characteristic linear properties. Notably, this model can be solved numerically without the use of Riemann solvers or linear iterations. For accurate time integration, a high-resolution spatial reconstruction and a Runge–Kutta scheme with decreasing total variation are used to discretize the relaxation system.FindingsThe method is used in addressing various nonequilibrium two-phase flow problems, accompanied by a comparative study of different reconstructions. The numerical results demonstrate the suggested relaxation method’s high-resolution capabilities, affirming its proficiency in delivering accurate simulations for flow regimes characterized by strong shocks.Originality/valueWhile relaxation methods exhibit notable performance and competitive features, as far as we are aware, there has been no endeavor to address nonequilibrium two-phase flow problems using these methods.

A Central Scheme for Two Coupled Hyperbolic Systems

A novel numerical scheme to solve two coupled systems of conservation laws is introduced. The scheme is derived based on a relaxation approach and does not require information on the Lax curves of the coupled systems, which simplifies the computation of suitable coupling data. The coupling condition for the underlying relaxation system plays a crucial role as it determines the behaviour of the scheme in the zero relaxation limit. The role of this condition is discussed, a consistency concept with respect to the original problem is introduced, the well-posedness is analyzed and explicit, nodal Riemann solvers are provided. Based on a case study considering the p-system of gas dynamics, a strategy for the design of the relaxation coupling condition within the new scheme is provided.

Magnetic helicity, weak solutions and relaxation of ideal MHD

AbstractWe revisit the issue of conservation of magnetic helicity and the Woltjer‐Taylor relaxation theory in magnetohydrodynamics (MHD) in the context of weak solutions. We introduce a relaxed system for the ideal MHD system, which decouples the effects of hydrodynamic turbulence such as the appearance of a Reynolds stress term from the magnetic helicity conservation in a manner consistent with observations in plasma turbulence. As by‐products we answer two open questions in the field: We show the sharpness of the L3 integrability condition for magnetic helicity conservation and provide turbulent bounded solutions for ideal MHD dissipating energy and cross helicity but with (arbitrary) constant magnetic helicity.

On strictly convex entropy functions for the reactive Euler equations

This work is concerned with entropy functions of the reactive Euler equations describing inviscid compressible flow with chemical reactions. In our recent work (W. Zhao, Math. Comput. 91 (2022) 735–760.) we point out that for these equations as a hyperbolic system, the classical entropy function associated with the thermodynamic entropy is no longer strictly convex under the equation of state (EoS) for the ideal gas. In this work, we propose two strategies to address this issue. The first one is to correct the entropy function. Namely, we present a class of strictly convex entropy functions by adding an extra term to the classical one. Such strictly entropy functions contain that constructed in (W. Zhao, Math. Comput. 91 (2022) 735–760.) as a special case. The second strategy is to modify the EoS. We show that there exists a family of EoS (for the nonideal gas) such that the classical entropy function is strictly convex. Under these new EoS, the reactive Euler equations are proved to satisfy the Conservation-Dissipation Conditions for general hyperbolic relaxation systems, which guarantee the existence of zero relaxation limit. Additionally, an elegant eigen-system of the Jacobian matrix is derived for the reactive Euler equations under the proposed EoS. Numerical experiments demonstrate that the proposed EoS can also generate ZND detonations. Extension of the present results to high dimensions is direct.

A radio bridge connecting the minihalo and phoenix in the Abell 85 cluster

ABSTRACT Galaxy clusters are located at the nodes of cosmic filaments and therefore host a lot of hydrodynamical activity. However, cool core clusters are considered to be relatively relaxed systems without much merging activity. The Abell 85 cluster is a unique example where the cluster hosts both a cool core and multiple ongoing merging processes. In this work, we used 700 MHz uGMRT as well as MeerKAT L-band observations, carried out as part of the MeerKAT Galaxy Cluster Legacy Survey (MGCLS), of the Abell 85. We reconfirm the presence of a minihalo in the cluster centre at 700 MHz that was recently discovered in MGCLS. Furthermore, we discovered a radio bridge connecting the central minihalo and the peripheral radio phoenix. The mean surface brightness, size, and flux density of the bridge at 700 MHz are found to be ∼0.14 µJy arcsec−2, ∼220 kpc, and ∼4.88 mJy, respectively, with a spectral index of $\alpha _{700}^{1.28} = -0.92$. Although the origin of the seed relativistic electrons is still unknown, turbulent reacceleration caused by both the spiralling sloshing gas in the intracluster medium and the post-shock turbulence from the outgoing merging shock associated with the phoenix formation may be responsible for the bridge.