Relaxation Of System Research Articles

Bir Florlu Aminoimidazolin Olan Midaflur'un Karşılaştırmalı Kuantum Kimyasal Analizi

Inspired by the striking achievements of fluorine-containing heterocyclic compounds in pharmaceutical chemistry, in this study quantum chemical calculations were carried out on the midaflur compound, which has skeletal-muscle relaxant and central nervous system (CNS) depressant properties. First of all, the total energy (ΔETotal), enthalpy (ΔH), and Gibbs free energy (ΔG) values for both tautomeric structures of midaflur were calculated and it was determined which form was more stable and the rest of the study was continued on this structure. For the stable amino form, the HF method and B3LYP/B3PW91 DFT functionals with different basis sets were used in order to examine the geometric parameters. The results were found to be in good agreement with the experimental values given in the literature. Furthermore, FT-IR analysis, Mulliken population analysis, frontier molecular orbital (FMO) analysis, natural bond orbital (NBO) analysis, nonlinear optical (NLO) properties, and electrostatic surface properties were studied in detail. In another part of the study, the logPow (logarithm of the n-octanol/water partition coefficient) value, which is the numerical expression of the lipophilicity of a drug for entry into the CNS, was estimated for midaflur. For this purpose, the calculations were repeated for the water and n-octanol phases using the universal solvation model based on density (SMD) for all the methodologies used in this study, and the free energies of solvation were predicted. It was concluded that the predictive power of the computational methods increased in the order of HF < B3PW91 < B3LYP.

Age of Information for Single Buffer Systems With Vacation Server

In this research, we study the information freshness in M/G/1 queueing system with a single buffer and the server taking multiple vacations. This system has wide applications in communication systems. We aim to evaluate the information freshness in this system with both i.i.d. and non-i.i.d. vacations under three different scheduling policies, namely Conventional Buffer System (CBS), Buffer Relaxation System (BRS), and Conventional Buffer System with Preemption in Service (CBS-P). For the systems with i.i.d. vacations, we derive the closed-form expressions of information freshness metrics such as the expected Age of Information (AoI), the expected Peak Age of Information (PAoI), and the variance of peak age under each policy. For systems with non-i.i.d. vacations, we use the polling system as an example and provide the closed-form expression of its PAoI under each policy. We explore the conditions under which one of these policies has advantages over the others for each information freshness metric. We further perform numerical studies to validate our results and develop insights.

Stringent censorship and relaxed co-governance: understanding platform governance and user practices of queer social and dating apps

ABSTRACT Platform governance plays a key role in guiding and regulating user behaviors and helping the platforms grow healthily and has thus attracted growing scholarly attention. By deploying the walkthrough method and semi-structured in-depth interviews, this study examines the governance mechanisms of two queer social and dating platforms – Rela and HER – and users’ practices for engaging with their governance systems. The findings suggest that Rela developes a type of stringent governance culture, characterized by the highly strict and authoritative censorship stipulations and practices, particularly with respect to sexual and political content. HER, however, establishes a relatively relaxed governance system, showing higher tolerance toward a wider range of topics and foregrounding a co-governance approach by encouraging users’ self-regulation and mutual supervision. These differences in governance practices and cultures have been substantially shaped by the sociopolitical environments in which these two platforms have developed. Interviewees expressed diverse interpretations of the governance systems of Rela and HER based on their individual practices, for example, articulating their concerns and dissatisfaction while also emphasizing their positive experiences enabled by these two platforms’ governance practices. This study enriches the existing platform governance studies by offering insights into queer social platforms’ governance systems and their users’ practices.

Global Convergence to Compressible Full Navier–Stokes Equations by Approximation with Oldroyd-Type Constitutive Laws

We consider smooth solutions to a relaxed Euler system with Oldroyd-type constitutive laws. This system is derived from the one-dimensional compressible full Navier-Stokes equations for a Newtonian fluid by using the Cattaneo–Christov model and the Oldroyd-B model. In a neighborhood of equilibrium states, we construct an explicit symmetrizer and show that the system is symmetrizable hyperbolic with partial dissipation. Moreover, by establishing uniform estimates with respect to the relaxation times, we prove the uniform global existence of smooth solutions and the global-in-time convergence of the system towards the full Navier–Stokes equations.

On the Construction of Conservative Semi-Lagrangian IMEX Advection Schemes for Multiscale Time Dependent PDEs

This article is devoted to the construction of a new class of semi-Lagrangian (SL) schemes with implicit-explicit (IMEX) Runge-Kutta (RK) time stepping for PDEs involving multiple space-time scales. The semi-Lagrangian (SL) approach fully couples the space and time discretization, thus making the use of RK strategies particularly difficult to be combined with. First, a simple scalar advection-diffusion equation is considered as a prototype PDE for the development of a high order formulation of the semi-Lagrangian IMEX algorithms. The advection part of the PDE is discretized explicitly at the aid of a SL technique, while an implicit discretization is employed for the diffusion terms. In this way, an unconditionally stable numerical scheme is obtained, that does not suffer any CFL-type stability restriction on the maximum admissible time step. Second, the SL-IMEX approach is extended to deal with hyperbolic systems with multiple scales, including balance laws, that involve shock waves and other discontinuities. A conservative scheme is then crucial to properly capture the wave propagation speed and thus to locate the discontinuity and the plateau exhibited by the solution. A novel SL technique is proposed, which is based on the integration of the governing equations over the space-time control volume which arises from the motion of each grid point. High order of accuracy is ensured by the usage of IMEX RK schemes combined with a Cauchy–Kowalevskaya procedure that provides a predictor solution within each space-time element. The one-dimensional shallow water equations (SWE) are chosen to validate the new conservative SL-IMEX schemes, where convection and pressure fluxes are treated explicitly and implicitly, respectively. The asymptotic-preserving (AP) property of the novel schemes is also studied considering a relaxation PDE system for the SWE. A large suite of convergence studies for both the non-conservative and the conservative version of the novel class of methods demonstrates that the formal order of accuracy is achieved and numerical evidences about the conservation property are shown. The AP property for the corresponding relaxation system is also investigated.

High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge--Kutta Methods with Asymptotic Preserving Properties

In this work we present a class of high order unconditionally strong stability preserving (SSP) implicit two-derivative Runge--Kutta schemes and SSP implicit-explicit (IMEX) multi-derivative Runge--Kutta schemes where the time-step restriction is independent of the stiff term. The unconditional SSP property for a method of order $p>2$ is unique among SSP methods and depends on a backward-in-time assumption on the derivative of the operator. We show that this backward derivative condition is satisfied in many relevant cases where SSP IMEX schemes are desired. We devise unconditionally SSP implicit Runge--Kutta schemes of order up to $p=4$ and IMEX Runge--Kutta schemes of order up to $p=3$. For the multiderivative IMEX schemes, we also derive and present the order conditions, which have not appeared previously. The unconditional SSP condition ensures that these methods are positivity preserving, and we present sufficient conditions under which such methods are also asymptotic preserving when applied to a range of problems, including a hyperbolic relaxation system, the Broadwell model, and the Bhatnagar--Gross--Krook kinetic equation. We present numerical results to support the theoretical results on a variety of problems.

Galaxy cluster mass density profile derived using the submillimetre galaxies magnification bias

Context. The magnification bias is a gravitational lensing effect that produces an increase or decrease in the detection probability of background sources near the position of a lense. The special properties of the submillimetre galaxies (SMGs; steep source number counts, high redshift, and a very low cross-contamination with respect to the optical band) makes them the optimal background sample for magnification bias studies. Aims. We want to study the average mass density profile of tens to hundreds of clusters of galaxies acting as lenses that produce a magnification bias on the SMGs, and to estimate their associated masses and concentrations for different richness ranges. The cluster richness is defined as R = L200/L* with L200 as the total r-band luminosity within the radius r200. Methods. The background sample is composed of SMGs observed by Herschel with 1.2 < z < 4.0 (mean redshift at ∼2.3) while the foreground sample is made up of galaxy clusters extracted from the Sloan Digital Sky Survey III with photometric redshifts of 0.05 < z < 0.8 (mean redshift at ∼0.38). Measurements are obtained by stacking the SMG–cluster pairs to estimate the cross-correlation function using the Davis-Peebles estimator. This methodology allows us to derive the mass density profile for a wide range of angular scales, ∼2 − 250 arcsec or ∼10 − 1300 kpc for z = 0.38, with a high radial resolution, and in particular to study the inner part of the dark matter halo (< 100 kpc). In addition, we also divide the cluster sample into five bins of richness and we analyse the estimated cross-correlation data using different combinations of the most common theoretical mass density profiles. Results. It is impossible to fit the data with a single mass density profile at all scales: in the inner part there is a clear excess in the mass density profile with respect to the outer part that we interpret as the galactic halo of the big central galaxy. As for the outer part, the estimated average masses increase with richness from M200c = 5.8 × 1013 M⊙ to M200c = 51.5 × 1013 M⊙ (M200c = 7.1 × 1013 M⊙ for the total sample). With respect to the concentration parameter, its average also increases with richness from C = 0.74 to C = 1.74 (C = 1.72 for the total sample). In the small-scale regions, the obtained average masses fluctuate around M200c = 3 − 4 × 1013 M⊙ with average concentration values of around C ∼ 4. Conclusions. The total average masses are in perfect agreement with the mass–richness relationship estimated from the cluster catalogue. In the bins of lowest richness, the central galactic halo constitutes ∼40% of the total mass of the cluster and its relevance decreases for higher richness values. While the estimated average concentration values of the central galactic halos are in agreement with traditional mass–concentration relationships, we find low concentrations for the outer part. Moreover, the concentrations decrease for lower richness values, probably indicating that the group of galaxies cannot be considered to be relaxed systems. Finally, we notice a systematic lack of signal at the transition between the dominance of the cluster halo and the central galactic halo (∼100 kpc). This feature is also present in previous studies using different catalogues and/or methodologies, but is never discussed.

A decomposition method by interaction prediction for the optimization of maintenance scheduling

Optimizing maintenance scheduling is a major issue to improve the performance of hydropower plants. We study a system of several physical components of the same family: either a set of turbines, a set of transformers or a set of generators. The components share a common stock of spare parts and experience random failures that occur according to known failure distributions. We seek a deterministic preventive maintenance strategy that minimizes an expected cost depending on maintenance and forced outages of the system. The Auxiliary Problem Principle is used to decompose the original large-scale optimization problem into a sequence of independent subproblems of smaller dimension while ensuring their coordination. Each subproblem consists in optimizing the maintenance on a single component. Decomposition-coordination techniques are based on variational techniques but the maintenance optimization problem is a mixed-integer problem. Therefore, we relax the dynamics and the cost functions of the system. The resulting algorithm iteratively solves the subproblems on the relaxed system with a blackbox method and coordinates the components. Relaxation parameters have an important influence on the optimization and must be appropriately chosen. An admissible maintenance strategy is then derived from the resolution of the relaxed problem. We apply the decomposition algorithm on a system with 80 components. It outperforms the reference blackbox method applied directly on the original problem.

Model-order reduction for hyperbolic relaxation systems

Abstract We propose a novel framework for model-order reduction of hyperbolic differential equations. The approach combines a relaxation formulation of the hyperbolic equations with a discretization using shifted base functions. Model-order reduction techniques are then applied to the resulting system of coupled ordinary differential equations. On computational examples including in particular the case of shock waves we show the validity of the approach and the performance of the reduced system.

Degenerate Cahn–Hilliard and incompressible limit of a Keller–Segel model

The Keller-Segel model is a well-known system representing chemotaxis in living organisms. We study the convergence of a generalized nonlinear variant of the Keller-Segel to the degenerate Cahn-Hilliard system. This analysis is made possible from the observation that the Keller-Segel system is equivalent to a relaxed version of the Cahn-Hilliard system. Furthermore, this latter equivalent system has an interesting application in the modelling of living tissues. Indeed, compressible and incompressible porous medium type equations are widely used to describe the mechanical properties of living tissues. The relaxed degenerate Cahn-Hilliard system, can be viewed as a compressible living tissue model for which the movement is driven by Darcy's law and takes into account the effects of the viscosity as well as surface tension at the surface of the tissue. We study the convergence of the Keller-Segel system to the Cahn-Hilliard equation and some of the analytical properties of the model such as the incompressible limit of our model. Our analysis relies on a priori estimates, compactness properties, and on the equivalence between the Keller-Segel system and the relaxed degenerate Cahn-Hilliard system.

Applying Visual-Motor Training Combined with an Eye Relaxation System Based on Far-Infrared Nanomaterials in Pseudomyopia.

To explore the effect of far-infrared nanomaterial eye relaxation system combined with visual-motor training in pseudomyopia, 120 patients with pseudomyopia were included in the experiment and randomly divided into nanomaterial and control groups. The control group received visual-motor training, and the nanomaterial group was treated with an eye relaxation system. This study found that nanozirconia and nanotitanium dioxide used in eye relaxation systems could maintain good stability in acidic and alkaline conditions. Additionally, nanozirconia could produce a warm effect, and nanotitanium dioxide had a clear sterilization effect. Moreover, the two abovementioned nanoparticles could be closely combined with fiberoptic materials. After treatment, the eye adjustment function, visual acuity, and diopter of the two groups were significantly improved, especially in the nanomaterial group. Additionally, using the nanomaterial eye relaxation system could better control intraocular pressure, reduce lens thickness, and improve the symptoms of eye fatigue. Furthermore, anxiety and depression were better reduced in the nanomaterial group, and their quality of life was greatly improved. Therefore, the far-infrared nanomaterial eye relaxation system combined with visual-motor training can be used as a new and effective scheme for pseudomyopia.

Robust Stability Analysis and Feedback Control for Uncertain Systems with Time-Delay and External Disturbance

This paper addresses the delay-dependent Takagi-Sugeno (T-S) fuzzy state feedback control and exponential admissibility analysis for a class of T-S fuzzy singular uncertain systems. Firstly, the T-S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input and unmatched disturbance. Secondly, the delay-dependent T-S fuzzy state feedback controller is designed by employing the T-S fuzzy model. Thirdly, the free-weighting matrices and delay-dependent Lyapunov-Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T-S fuzzy state feedback controller is designed for the T-S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods.

Central schemes for networked scalar conservation laws

<abstract><p>We propose a novel scheme to numerically solve scalar conservation laws on networks without the necessity to solve Riemann problems at the junction. The scheme is derived using the relaxation system introduced in [Jin and Xin, <italic>Comm. Pure. Appl. Math.</italic> <bold>48</bold> (1995), 235-276] and taking the relaxation limit also at the nodes of the network. The scheme is mass conservative and yields well defined and easy-to-compute coupling conditions even for general networks. We discuss higher order extension of the scheme and applications to traffic flow and two-phase flow. In the former we compare with results obtained in literature.</p></abstract>

Effect of Nanoindentation Temperature on Plastic Deformation of 3C‐SiC Based on the Molecular Dynamics Method

To explore the effect of nanoindentation temperature on the plastic deformation of 3C‐SiC, it is possible to analyze the 3C‐SiC load‐displacement changes at different temperatures and the dislocation propagation in the plastic deformation stage. The 3C‐SiC nanoindentation model is established on the basis of molecular dynamics interatomic interaction potential. The model combines the 3C‐SiC crystal structure to optimize the Vashishta potential function and modifies the relaxation system, system boundary, and other simulated environmental factors. The plastic deformation process of 3C‐SiC at different temperatures is analyzed from multiple angles such as the load‐displacement curve, the stress distribution during the plastic deformation stage of the matrix, and the formation and growth of specimen dislocations. During the pressing process, intermolecular dislocations and stress are concentrated in the elastic‐plastic deformation zone. The load value of the elastic‐plastic deformation zone under high temperature environment is generally higher, and the energy of the dislocation loop will be released. In the plastic deformation zone, the dislocation loop will break under the action of high temperature environmental load. The premature release of energy will cause the load value to drop. During the pressing process, the bearing capacity of 3C‐SiC polycrystalline will decrease as the temperature rises. Plastic deformation occurs inside the material, and dislocations nucleate and expand from the grain boundary to the crystal and finally form a U‐shaped dislocation ring.

Tracing the non-thermal pressure and hydrostatic bias in galaxy clusters

We present a modelization of the non-thermal pressure, PNT, and we apply it to the X-ray (and Sunayev-Zel’dovich) derived radial profiles of the X-COP galaxy clusters. We relate the amount of non-thermal pressure support to the hydrostatic bias, b, and speculate on how we can interpret this PNT in terms of the expected levels of turbulent velocity and magnetic fields. Current upper limits on the turbulent velocity in the intracluster plasma are used to build a distribution 𝒩(< b)−b, from which we infer that 50 per cent of local galaxy clusters should have b < 0.2 (b < 0.33 in 80 per cent of the population). The measured bias in the X-COP sample that includes relaxed massive nearby systems is 0.03 in 50% of the objects and 0.17 in 80% of them. All these values are below the amount of bias required to reconcile the observed cluster number count in the cosmological framework set from Planck.

Variation diminishing linear time-invariant systems

This paper studies the variation diminishing property of k-positive linear time-invariant (LTI) systems, which diminish the number of sign changes (variation) from input to output, if the input variation is at most k−1. We characterize this property for the discrete-time Toeplitz and Hankel operators of finite-dimensional causal systems. Our main result is that these operators have a dominant approximation in the form of series or parallel interconnections of k first order positive systems. This is shown by expressing the k-positivity of a LTI system as the external positivity (that is, 1-positivity) of kcompound LTI systems. Our characterization generalizes well known properties of externally positive systems (k=1) and totally positive systems (k=∞; also known as relaxation systems in case of the Hankel operator). All results readily extend to continuous-time systems by considering sampled impulse responses.

Boundary conditions for hyperbolic relaxation systems with characteristic boundaries of type II

This paper is a continuation of our preceding work on hyperbolic relaxation systems with characteristic boundaries of type I. Here we focus on the characteristic boundaries of type II, where the boundary is characteristic for the equilibrium system and is non-characteristic for the relaxation system. For this kind of characteristic initial-boundary-value problems (IBVPs), we introduce a three-scale asymptotic expansion to analyze the boundary-layer behaviors of the general multi-dimensional linear relaxation systems. Moreover, we derive the reduced boundary condition under the Generalized Kreiss Condition by resorting to some subtle matrix transformations and the perturbation theory of linear operators. The reduced boundary condition is proved to satisfy the Uniform Kreiss Condition for characteristic IBVPs. Its validity is shown through an error estimate involving the Fourier-Laplace transformation and an energy method based on the structural stability condition.

Parameter identification for nonlocal phase field models for tumor growth via optimal control and asymptotic analysis

In this paper, we introduce the problem of parameter identification for a coupled nonlocal Cahn–Hilliard-reaction-diffusion PDE system stemming from a recently introduced tumor growth model. The inverse problem of identifying relevant parameters is studied here by relying on techniques from optimal control theory of PDE systems. The parameters to be identified play the role of controls, and a suitable cost functional of tracking-type is introduced to account for the discrepancy between some a priori knowledge of the parameters and the controls themselves. The analysis is carried out for several classes of models, each one depending on a specific relaxation (of parabolic or viscous type) performed on the original system. First-order necessary optimality conditions are obtained on the fully relaxed system, in both the two- and three-dimensional cases. Then, the optimal control problem on the non-relaxed models is tackled by means of asymptotic arguments, by showing convergence of the respective adjoint systems and the minimization problems as each one of the relaxing coefficients vanishes. This allows obtaining the desired necessary optimality conditions, hence to solve the parameter identification problem, for the original PDE system in case of physically relevant double-well potentials.

The ultra-steep diffuse radio emission observed in the cool-core cluster RX J1720.1+2638 with LOFAR at 54 MHz

ABSTRACT Diffuse radio emission at the centre of galaxy clusters has been observed both in merging clusters on scales of Mpc, called giant radio haloes, and in relaxed systems with a cool-core on smaller scales, named mini haloes. Giant radio haloes and mini haloes are thought to be distinct classes of sources. However, recent observations have revealed the presence of diffuse radio emission on Mpc scales in clusters that do not show strong dynamical activity. RX J1720.1+2638 is a cool-core cluster, presenting both a bright central mini halo and a fainter diffuse, steep-spectrum emission extending beyond the cluster core that resembles giant radio halo emission. In this paper, we present new observations performed with the LOw Frequency ARray Low Band Antennas (LBA) at 54 MHz. These observations, combined with data at higher frequencies, allow us to constrain the spectral properties of the radio emission. The large-scale emission presents an ultrasteep spectrum with $\alpha _{54}^{144}\sim 3.2$. The radio emission inside and outside the cluster core have strictly different properties, as there is a net change in spectral index and they follow different radio-X-ray surface brightness correlations. We argue that the large-scale diffuse emission is generated by particles re-acceleration after a minor merger. While for the central mini halo, we suggest that it could be generated by secondary electrons and positrons from hadronic interactions of relativistic nuclei with the dense cool-core gas, as an alternative to re-acceleration models.

Time-resolved thermal lens investigation of glassy dynamics in supercooled liquids: Theory and experiments.

This work reports results on the simultaneous spectroscopy of the specific heat and thermal expansivity of glycerol by making use of a wideband time-resolved thermal lens (TL) technique. An analytical model is presented which describes TL transients in a relaxing system subjected to impulsive laser heating. Experimentally, a set of TL waveforms, from 1ns to 20ms, has been recorded for a glycerol sample upon supercooling, from 300 to 200K. The satisfactory fitting of the TL signals to the model allows the assessment of relaxation strength and relaxation frequency of the two quantities up to sub-100MHz, extending the specific heat and thermal expansion spectroscopy by nearly three and eight decades, respectively. Fragility values, extracted from the relaxation behavior of the specific heat and the thermal expansion coefficient, are found to be similar, despite a substantial difference in relaxation strength.