Relaxation Of System Research Articles

Construction of boundary conditions for hyperbolic relaxation approximations I: The linearized Suliciu model

Starting with this paper, we intend to develop a program aiming at construction of boundary conditions (BCs) for hyperbolic relaxation systems. Physically, such BCs are not always available. The construction is based on the assumption that the relaxation systems and well-posed BCs for the corresponding equilibrium systems are given. This paper focuses on the linearized Suliciu model. We obtain strictly dissipative and compatible BCs for the linearized model with different non-characteristic boundaries. Moreover, the effectiveness of the constructed BCs is shown by resorting to formal asymptotic solutions and energy estimates.

A General Non-hydrostatic Hyperbolic Formulation for Boussinesq Dispersive Shallow Flows and Its Numerical Approximation

In this paper, we propose a novel first-order reformulation of the most well-known Boussinesq-type systems that are used in ocean engineering. This has the advantage of collecting in a general framework many of the well-known systems used for dispersive flows. Moreover, it avoids the use of high-order derivatives which are not easy to treat numerically, due to the large stencil usually needed. These first-order PDE dispersive systems are then approximated by a novel set of first-order hyperbolic equations. Our new hyperbolic approximation is based on a relaxed augmented system in which the divergence constraints of the velocity flow variables are coupled with the other conservation laws via an evolution equation for the depth-averaged non-hydrostatic pressures. The most important advantage of this new hyperbolic formulation is that it can be easily discretized with explicit and high-order accurate numerical schemes for hyperbolic conservation laws. There is no longer need of solving implicitly some linear system as it is usually done in many classical approaches of Boussinesq-type models. Here a third-order finite volume scheme based on a CWENO reconstruction has been used. The scheme is well-balanced and can treat correctly wet–dry areas and emerging topographies. Several numerical tests, which include idealized academic benchmarks and laboratory experiments are proposed, showing the advantage, efficiency and accuracy of the technique proposed here.

AI based control theory for interaction of ocean system

This paper deals with the problem of the global stabilization for a class of tension leg platform (TLP) nonlinear control systems. Problem and objective: Based on the relaxed method, the chaotic system can be stabilized by regulating appropriately the parameters of dither. Scope and method: If the frequency of dither is high enough, the trajectory of the closed-loop dithered chaotic system and that of its corresponding model the closed-loop fuzzy relaxed system can be made as close as desired. Results and conclusion: The behavior of the closed-loop dithered chaotic system can be rigorously predicted by establishing that of the closed-loop fuzzy relaxed system.

Pressure-induced gap modulation and topological transitions in twisted bilayer and twisted double bilayer graphene

We study the electronic and topological properties of fully relaxed twisted bilayer (TBG) and double bilayer (TDBG) graphene under perpendicular pressure. An approach has been proposed to obtain the equilibrium in-plane structural deformation and out-of-plane corrugation in moir\'{e} superlattices under pressure. We find that the in-plane relaxation becomes much stronger under higher pressure, while the corrugation height in each layer is maintained. The comparison between band structures of relaxed and rigid structures demonstrates that not only the gaps on the electron and hole sides ($\Delta_e$ and $\Delta_h$) are significantly underestimated without relaxation but also the detailed dispersions of the middle bands of rigid structures are rather different from those of relaxed systems. $\Delta_e$ and $\Delta_h$ in TBG reach maximum values around critical pressures with narrowest middle bands. Topological transitions occur in TDBG under pressure with the middle valence and conduction bands in one valley touching and their Chern numbers transferred to each other. The pressure can also tune the gap at the neutrality point of TDBG, which becomes closed for a pressure range and reopened under higher pressure. The behavior of electronic structure of supertlattices under pressure is sensitive to the twist angle $\theta$ with the critical pressures generally increase with $\theta$.

A Low Cost Semi-implicit Low-Mach Relaxation Scheme for the Full Euler Equations

We introduce a semi-implicit two-speed relaxation scheme to solve the compressible Euler equations in the low Mach regime. The scheme involves a relaxation system with two speeds, already introduced by Bouchut et al. (Numer Math, 2020. https://doi.org/10.1007/s00211-020-01111-5) in the barotropic case. It is entropy satisfying and has a numerical viscosity well-adapted to low Mach flows. This relaxation system is solved via a dynamical Mach number dependent splitting, similar to the one proposed by Iampietro et al. (J Comput Appl Math 340:122–150, 2018). Stability conditions are derived, they limit the range of admissible relaxation and splitting parameters. We resolve separately the advection part of the splitting by an explicit method, and the acoustic part by an implicit method. The relaxation speeds are chosen so that the implicit system fully linearizes the acoustics and requires just to invert an elliptic operator with constant coefficients. The scheme is shown to well capture with low cost the incompressible slow scale dynamics with a timestep adapted to the velocity field scale, and rather well the fast acoustic waves.

An entropy satisfying two-speed relaxation system for the barotropic Euler equations: application to the numerical approximation of low Mach number flows

In the first part of this work, we introduce a new relaxation system in order to approximate the solutions to the barotropic Euler equations. We show that the solutions to this two-speed relaxation model can be understood as viscous approximations of the solutions to the barotropic Euler equations under appropriate sub-characteristic conditions. Our relaxation system is a generalization of the well-known Suliciu relaxation system, and it is entropy satisfying. A Godunov-type finite volume scheme based on the exact resolution of the Riemann problem associated with the relaxation system is deduced, as well as its stability properties. In the second part of this work, we show how the new relaxation approach can be successfully applied to the numerical approximation of low Mach number flows. We prove that the underlying scheme satisfies the well-known asymptotic-preserving property in the sense that it is uniformly (first-order) accurate with respect to the Mach number, and at the same time it satisfies a fully discrete entropy inequality. This discrete entropy inequality allows us to prove strong stability properties in the low Mach regime. At last, numerical experiments are given to illustrate the behaviour of our scheme.

Relaxation of the Cahn–Hilliard equation with singular single-well potential and degenerate mobility

The degenerate Cahn–Hilliard equation is a standard model to describe living tissues. It takes into account cell populations undergoing short-range attraction and long-range repulsion effects. In this framework, we consider the usual Cahn–Hilliard equation with a singular single-well potential and degenerate mobility. These degeneracy and singularity induce numerous difficulties, in particular for its numerical simulation. To overcome these issues, we propose a relaxation system formed of two second-order equations which can be solved with standard packages. This system is endowed with an energy and an entropy structure compatible with the limiting equation. Here, we study the theoretical properties of this system: global existence and convergence of the relaxed system to the degenerate Cahn–Hilliard equation. We also study the long-time asymptotics which interest relies on the numerous possible steady states with given mass.

“Let’s have a break”: An experimental comparison of work-break interventions and their impact on performance

Work breaks are known for positively influencing employees’ psychologically and physiologically. Thus far, only limited research regarding the importance of precise work-break activities has been conducted, which becomes crucial to an employer when deciding on investing in additional work-break activities. Therefore, in this study, we investigate whether performance effects induced by work breaks differ for different work-break interventions. Using a laboratory pre-test-post-test-design, the impact of three work-break interventions (namely, relaxation system, boxing, napping) on objective and subjective performance- and state-related determinants is investigated. It was found that the boxing and relaxation system interventions had significantly greater impacts on the performance variables as compared to napping. However, we did not find any significant differences between the two aforementioned interventions - boxing and the relaxation system.

Relative entropy in diffusive relaxation for a class of discrete velocities BGK models

We provide a general framework to extend the relative entropy method to a class of diffusive relaxation systems with discrete velocities. The methodology is detailed in the toy case of the 1D Jin-Xin model under the diffusive scaling, and provides a direct proof of convergence to the limit parabolic equation in any interval of time, in the regime where the solutions are smooth. Recently, the same approach has been successfully used to show the strong convergence of a vector-BGK model to the 2D incompressible Navier-Stokes equations.

Hyperbolic compressible Navier-Stokes equations

We consider the non-isentropic compressible Navier-Stokes equations with hyperbolic heat conduction and a law for the stress tensor which is modified correspondingly by Maxwell's law. These two relaxations, turning the whole system into a hyperbolic one, are not only treated simultaneously, but are also considered in a version having Galilean invariance. For this more complicated relaxed system, the global well-posedness is proved for small data. Moreover, for vanishing relaxation parameters the solutions are shown to converge to solutions of the classical system.

Large time behavior of solutions to a nonlinear hyperbolic relaxation system with slowly decaying data

We consider the large time asymptotic behavior of the global solutions to the initial value problem for the nonlinear damped wave equation with slowly decaying initial data. When the initial data decay fast enough, it is known that the solution to this problem converges to the self‐similar solution to the Burgers equation called a nonlinear diffusion wave, and its optimal asymptotic rate is obtained. In this paper, we focus on the case that the initial data decay more slowly than previous works and derive the corresponding asymptotic profile. Moreover, we investigate how the change of the decay rate of the initial values affect its asymptotic rate.

Band structure, effective mass, and carrier mobility of few-layer h-AlN under layer and strain engineering

Wide bandgap two-dimensional semiconductors are of paramount importance for developing van der Waals heterostructure electronics. This work reports the use of layer and strain engineering to introduce the feasibility of two-dimensional hexagonal (h)-AlN to fill the scientific and application gap. We show that such one- to five-layer h-AlN has an indirect bandgap, tunable from 2.9 eV for a monolayer to ∼3.5 eV for multilayer structures, along with isotropic effective masses and carrier mobilities between zigzag and armchair directions. With an increase in the layer number to bulk AlN, the bandgap will experience a transition from an indirect gap to direct gap. Surprisingly, high room-temperature mobilities of electrons and holes (of the order of 1000 cm2 V−1 s−1) in a relaxed monolayer h-AlN system and widely adjustable effective masses and carrier mobilities in a different layer h-AlN are observed. In the presence of strain engineering, the bandgap decreases obviously with an increase in tensile strain; meanwhile, the isotropy and value of effective mass or carrier mobility in monolayer h-AlN can also be modulated effectively; the hole mobilities in the armchair direction, especially, will be enhanced dramatically. With a tunable bandgap, high carrier mobilities, and modifiable isotropy, our results indicate that few-layer h-AlN has potential applications in future mechano-electronic devices.

A DESCRIPTIVE STUDY OF MR DEFECOGRAPHY FOR EVALUATION OF OBSTRUCTED DEFECATION SYNDROME

Objective:-This study aims to ascertain the role of MR Defecography in the evaluation of obstructed defecation syndrome (ODS) with objective to describe spectrum of MR Defecography findings in obstructed defecation syndrome (ODS) and describe a number of reference lines and measurement points used to diagnose and grade pelvic floor disorders and Document the MRI appearance of disorders associated with ano-rectal dysfunction. MR Defecography demonstrated the profile of obstructed defecation syndrome on the basis of MR defecography and demonstrate its utility in simultaneous & objective evaluation of all three pelvic compartments. This diagnostic modalities provide a detailed pelvic floor anatomy and functional evaluation, as well as their respective abnormalities, making a precise diagnosis and provides valuable information on treatment planning & decrease chance of postoperative recurrence.
 Subjects and Methods: It was Cross-sectional and prospective (quantitative) hospital based descriptive type of observational study carried out at a tertiary hospital SMS hospital, jaipur. Chosen the patients diagnosed with ODS as per Rome criteria (III) whose colonoscopy or rectosigmoidoscopy, had been done to rule out other findings from Feb 2018 to September 2019.MR defecography (static and dynamic) with 3 T (PHILIPS INGENIA) MRI system having tunnel configuration. After written and informed consent, patient was positioned supine in MR machine gantry . Static imaging performed in the axial T1WI high resolution, axial, coronal and sagittal T2WI high resolution images at rest for anatomical evaluation. Following this,after ultrasound gel instilled in the patient’s rectum and intravaginaly ,dynamic imaging were taken in the midsagittal plane through the anal canal using a T2 weighted sequence. This sequence was ran for almost 2 min, while the patient performs various maneuvers (Kegel (squeeze), valsalva menuvere (strain), and defecation). MR defecography structurally and functionally evaluated in all 3 pelvic floor compartments and associated defects noted and grading of specific findings like organ specific prolapse, pelvic floor relaxiation and descent were measured.
 Results: In our study most common findings were pelvic floor descent and anorectal junction descent in 92.68% cases each followed by rectocele in 82.93% cases. Among the females, vaginal/uterine prolapse were observed in 65.31% cases. Least common findings were paradoxical contraction (8.54%) and sigmoidocele (0%). Significant difference was observed in MRI functional parameters in resting state and during defecation/maximal strain position, utilising HMO system for pelvic floor relaxation and descent, as significant difference (p <0.001S) was observed in all parameters including H line, M line, bladder base descent, cervical/vaginal and anorectal junction descent during resting state and during defecation/maximal strain position. Out of 82 conservative biofeedback therapy was given to 79.27 % patients, surgical management was done in (7.32%) and combination of both therapies was given in 13.41% of cases. Out of 82 patients 68.29% showed benefit from management and showed improvement on follow and 31.71% patients were not improved on follow up.
 Conclusion: As complete survey of the entire pelvis is necessary before surgical repair Magnetic resonance imaging permits evaluation of all three pelvic compartments and as we demonstrated in our study more than one compartment are frequently affected in obstructed defecation syndrome. Static MR Imaging can be also useful to identify the defects responsible for pelvic organ prolapse and stress urinary incontinence, and so help perform site specific repair in surgery, to avoid the high recurrence rates.Findings reported at dynamic MR imaging of the pelvic floor are valuable for selecting candidates for surgical treatment and for indicating the most appropriate surgical approach as detection rate of pathologies increased during defecation / maximal straning as concluded by our study.

The magnetic properties of multiferroic Sr3Fe2F12

Pure phase Sr3Fe2F12 powders were prepared by solid state reaction, which has been confirmed by the X-ray diffraction pattern. The morphology was studied by scanning electron microscope which shows the layered growth. The Fe ions are in +3 valence state from X-ray photoelectron spectroscopy. Two kinks can be observed from temperature dependent magnetization measurements, suggesting two antiferromagnetic transitions. A bifurcation between field cooling and zero field cooling temperature dependent magnetization curves happens below Néel temperature (TN1) of 47 K, suggesting a magnetic relax system. The field dependent magnetization curves show clear hysteresis below TN1, indicating the occurrence of weak ferromagnetism. This is related to the spin canting due to the Dzyaloshinskii-Moriya (DM) interaction. The two antiferromagnetic transitions with magnetic relaxation below TN1 are related to the complicated arrangements of FeF6 octahedra, leading to the complicated exchange interaction between Fe3+ ions.

Simultaneous Heterogeneous Sensor Localization, Joint Tracking, and Upper Extremity Modeling for Stroke Rehabilitation

In stroke rehabilitation systems and applications, reliability, accuracy, and occlusion should be taken into consideration. Unfortunately, most existing approaches focus primarily on the first two issues. However, during the stroke rehabilitation process, occlusion leads to incorrect judgements even for medical staff. In order to tackle these three important issues simultaneously, we propose a heterogeneous sensor fusion framework composed of an RGB-D camera and a wearable device to consider occlusion and provide robust joint locations for rehabilitation. To fuse multiple sensor measurements when compensating for occlusion, we apply heterogeneous sensor simultaneous localization, tracking, and modeling to estimate the locations of joints and sensors and construct an upper extremity model for occlusion situation. Virtual measurements based on this model are used to estimate the joint's location during occlusion, and a virtual relative orientation technique is applied to relax system limitations regarding orientation. Experimental results using the proposed approach with synthetic data and data collected from ten subjects show a 4.6 cm error on average and about 15 cm error on average during occlusion. This constitutes a more robust approach for stroke patients which takes into account these three important issues.

Spectral stability of hydraulic shock profiles

By reduction to a generalized Sturm–Liouville problem, we establish spectral stability of hydraulic shock profiles of the Saint-Venant equations for inclined shallow-water flow, over the full parameter range of their existence, for both smooth-type profiles and discontinuous-type profiles containing subshocks. Together with work of Mascia–Zumbrun and Yang–Zumbrun, this yields linear and nonlinear H2∩L1→H2 stability with sharp rates of decay in Lp, p≥2, the first complete stability results for large-amplitude shock profiles of a hyperbolic relaxation system.

Sub-Sampling Direct RF-to-Digital Converter With 1024-APSK Modulation for High Throughput Polar Receiver

This article presents a direct RF-to-digital converter (RDC) for polar receivers, in which the amplitude information of the received signal is detected by a reconfigurable analog-to-digital converter (ADC) and its phase is digitized using a time-to-digital converter (TDC). The RDC prototype also includes a multi-phase reference generator and an ADC sampling position adjustment unit realizing the sub-sampling technique. Unlike conventional direct-RF sampling receivers, the proposed RDC samples the input RF signal at the baseband rate. The RDC is capable of digitizing a variety of modulation waveforms, such as quadrature amplitude modulation (QAM), phase shift keying (PSK), and amplitude phase shift keying (APSK). When comparing QAM to APSK, the later has advantages of relaxed system requirements on phase noise and linearity. The proposed direct RF-to-digital polar converter IC achieves a maximum data rate of 1.94 GB/s with a 1024-APSK modulation at a carrier frequency of 6 GHz, while consumes only 3.8 mW power under 1.1 V supply.

Measuring bulk flows of the intracluster medium in the Perseus and Coma galaxy clusters usingXMM-Newton

We demonstrate a novel technique for calibrating the energy scale of the EPIC-pn detector onXMM-Newton, which allows us to measure bulk flows in the intracluster medium (ICM) of the Perseus and Coma galaxy clusters. The procedure uses the fluorescent instrumental background lines present in all observations, in particular, Cu-Kα. By studying their spatial and temporal variations, in addition to incorporating calibration observations, we refined the absolute energy scale of the detector to better than 150 km s−1at the Fe-K line, a large improvement over the nominal calibration accuracy of 550 km s−1. With our calibration, we mapped the bulk motions over much of the central 1200 and 800 kpc of Perseus and Coma, respectively, in spatial regions down to 65 and 140 kpc size. We cross-checked our procedure by comparing our measurements with those found in Perseus byHitomifor an overlapping 65 kpc square region, finding consistent results. For Perseus, there is a relative line-of-sight velocity increase of 480 ± 210 km s−1(1σ) at a radius of 250 kpc east of the nucleus. This region is associated with a cold front, providing direct evidence of the ICM sloshing in the cluster potential well. Assuming the intrinsic distribution of bulk motions is Gaussian, its width is 214 ± 85 km s−1, excluding systematic uncertainties. Removing the sloshing region, this is reduced to 20–150 km s−1, which is similar in magnitude to theHitomiline width measurements in undisturbed regions. In Coma, the line-of-sight velocity of the ICM varies between the velocities of the two central galaxies. Maps of the gas velocity and metallicity provide clues about the merger history of the Coma, with material to the north and east of the cluster core having a velocity similar toNGC 4874, while that to the south and west has velocities close toNGC 4889. Our results highlight the difference between a merging system, such as Coma, where we observe a ∼1000 km s−1range in velocity, and a relatively relaxed system, such as Perseus, with much weaker bulk motions.

From Nonlocal to Classical Shigesada--Kawasaki--Teramoto Systems: Triangular Case with Bounded Coefficients

This paper solves partially a question suggested by Fontbona and Meleard. The issue is to obtain rigorously cross-diffusion systems a la Shigesada--Kawasaki--Teramoto as the limit of relaxed system...

Uso de la técnica de relajación térmica para la medición de calor específico de láminas recubiertas con TiO2

El calor específico (Cp) es un parámetro térmico necesario para la descripción de fenómenos de transporte de calor, relacionado con la adaptación a cambios de temperatura. Por esta razón es importante en la industria de la construcción, de pegantes, de aislantes térmicos y de dispositivos electrónicos. En este trabajo, se utilizó un sistema de relajación térmica para determinar el Cp de láminas de Ti, recubiertas con S-TiO2 por Oxidación Electrolítica con Plasma (OEP). Cada muestra se ubicó dentro de una cámara de vacío que alcanza alrededor de 10-2 Torr y fue calentada por la incidencia de un haz de luz láser de 450 nm de longitud de onda; se ubicó un termómetro infrarrojo (IR) en la parte inferior de la muestra y los datos obtenidos se enviaron a un computador, usando una tarjeta de desarrollo programable. La validación del sistema se hizo comparando los resultados con los reportados por otros autores para zinc, wolframio, titanio y acero. El Cp de las muestras de Ti recubiertas por OEP, que fueron obtenidas usando un electrolito con dos concentraciones de tiourea (CH4N2S) y con tensión aplicada entre los electrodos a 2 kHz con ciclos útiles de 10 %, 20 %, y 30 %, se midió y se comparó con el fin de estudiar la influencia de los parámetros de crecimiento en las características térmicas del material. Los resultados del análisis de varianza de los datos llevaron a encontrar diferencias significativas, con un nivel de confianza del 95 %, relacionadas con la variación en la concentración de CH4N2S. Esto es un indicio del potencial uso de la técnica de relajación térmica para determinar particularidades de este tipo de recubrimientos.