Relaxation Damping Research Articles

Effects of thermal treatment and temperature on domain wall dynamics in magnetic microwire

Investigation of the influence of thermal treatment and temperature on domain wall (DW) dynamics in bi-stable magnetic microwire with strong unidirectional effect on DW propagation is presented. Measurements of remanent magnetic flux allowed to use in our consideration the force acting on the DW during propagation instead of applied driving field. Then the DW damping coefficient was determined for two values of force acting on the propagating DW for the same sample, but under different conditions (effects of annealing and temperature). Experimental and model temperature dependences of normalized damping coefficient were compared. The theoretical model used takes into account possible changes in DW length caused by mechanical stress and applied force. Experimental and model dependences are in qualitative agreement and show that changes in mechanical stress with temperature are the dominant mechanism responsible for changes in damping coefficient with temperature. Additional analysis shows that the ratio between spin relaxation and eddy current damping is not a constant parameter, but probably increases with increasing DW velocity (applied field).

Limits of the phonon quasi-particle picture at the cubic-to-tetragonal phase transition in halide perovskites

The soft modes associated with continuous-order phase transitions are associated with strong anharmonicity. This leads to the overdamped limit where the phonon quasi-particle picture can break down. However, this limit is commonly restricted to a narrow temperature range, making it difficult to observe its signature feature, namely the breakdown of the inverse relationship between the relaxation time and damping. Here we present a physically intuitive picture based on the relaxation times of the mode coordinate and its conjugate momentum, which at the instability approach infinity and the inverse damping factor, respectively. We demonstrate this behavior for the cubic-to-tetragonal phase transition of the inorganic halide perovskite CsPbBr3 via molecular dynamics simulations, and show that the overdamped region extends almost 200 K above the transition temperature. Further, we investigate how the dynamics of these soft phonon modes change when crossing the phase transition.

Partially dissipative systems in the critical regularity setting, and strong relaxation limit

Many physical phenomena may be modeled by first order hyperbolic equations with degenerate dissipative or diffusive terms. This is the case for example in gas dynamics, where the mass is conserved during the evolution, but the momentum balance includes a diffusion (viscosity) or damping (relaxation) term, or, in numerical simulations, of conservation laws by relaxation schemes. Such so-called partially dissipative systems have been first pointed out by S. K. Godunov in a short note in 1961. Much later, in 1984, S. Kawashima highlighted in his PhD thesis a simple criterion ensuring the existence of global strong solutions in the vicinity of a linearly stable constant state. This criterion has been revisited in a number of research works. In particular, K. Beauchard and E. Zuazua proposed in 2010 an explicit method for constructing a Lyapunov functional allowing to refine Kawashima’s results and to establish global existence results in some situations that were not covered before. These notes originate essentially from the PhD thesis of T. Crin-Barat that was initially motivated by an earlier observation of the author in a chapter of the handbook edited by Y. Giga and A. Novotný. Our main aim is to adapt the method of Beauchard and Zuazua to a class of symmetrizable quasilinear hyperbolic systems (containing the compressible Euler equations), in a critical regularity setting that allows to keep track of the dependence with respect to e.g. the relaxation parameter. Compared to Beauchard and Zuazua’s work, we exhibit a ‘damped mode’ that will have a key role in the construction of global solutions with critical regularity, in the proof of optimal time-decay estimates and, last but not least, in the study of the strong relaxation limit. For simplicity, we here focus on a simple class of partially dissipative systems, but the overall strategy is rather flexible, and adaptable to much more general situations.

Discontinuous precipitation in a Cu-10Ni-1Si alloy with ultra-high strength, high shock absorption, and good stress relaxation resistance

The discontinuous precipitation in a Cu-10Ni-1Si alloy aged at 500 °C and 550 °C was studied to clarify the types of discontinuous precipitates, and the crystal relationships between precipitates and the matrix. The continuous δ-Ni2Si precipitates were detected in the initial aging stage, then discontinuous β-Ni3Si and continuous δ-Ni2Si precipitates were detected simultaneously. The crystal relationship between discontinuous β-Ni3Si precipitates and the copper matrix at the beginning of aging was that: (1̅11̅)Cu//(111̅)β, [011]Cu//[011]β. The lamellar discontinuous β-Ni3Si precipitates significantly improve stress relaxation resistance and damping properties, which are attributed to the interaction between lamellar structure and dislocation motion. These findings indicated that the formation of the lamellar discontinuous precipitates tends to prevent dislocation slip and promote precipitation, resulting in enhanced mechanical properties and conductivity properties simultaneously.

Experimental investigation of dynamic characteristics of material applied to reduced scale physical models in the elastic state

Dynamic and vibration difficulties have begun to play a major part in structural analysis as a result of the increasing complexity and slimness of bridges. Nonetheless, creating numerical models that accurately capture the true behaviour of structures remains a challenge. It can be caused by the lack of references that characterise the dynamic and vibration properties of the material. For that reason, the main goal of this work is to investigate experimental methods to characterise materials that are commonly used to build reduced scale physical models. We tested four types of materials in order to achieve this goal, as well as evaluating the major influence of reinforcement on the material’s elastic stiffness. That presents a novel approach to support engineers to suitably select scaled physical models materials. In addition to identifying the basic static properties of the studied materials, material damping and material relaxation were also characterised through the following: General logarithmic decrement method, Half-power band, modal damping and random decrement. In order to evaluate the material damping, we analysed the acceleration and displacement of cantilever specimens using a data acquisition module. As a result, the confidence level of each approach in contrast to the experimental data could be determined. Finally, the material behaviour of each material was examined in order to determine the best material for producing reduced scaled models of reinforced concrete bridges. As a result, it was easy to see that modal damping indicates higher confidence, whereas logarithmic decrement indicates lower confidence. It is also important to keep in mind that most methods for determining damping ratios are based on viscous damping. As a result, non-linear regression and modal damping were deemed the best methods for characterising vibration and dynamic responses of materials.

Modulation of plasmonic relaxation damping by surface phonons

We experimentally study the effect of amplitude-varying surface acoustic waves on a localized surface plasmon (LSP), which unveils exceptional properties of plasmon-phonon interaction with promising applications in future tunable photonic devices. Gold nanoparticles are deposited on X-cut LiNbO 3 to generate plasmonic oscillation, and an interdigital transducer is fabricated to create surface acoustic wave pulses. The interaction between an amplitude-varying mechanical wave and a plasmonic oscillation affects different plasmon dynamics and relaxation gradients, leading to a systematic change in LSP absorption. We also demonstrated the effect of polarized light on the device, providing a unique characteristic to explore the manipulation process effectively.

Improved multispecies Dougherty collisions

The Dougherty model Fokker–Planck operator is extended to describe nonlinear full- $f$ ( f is the distribution function) collisions between multiple species in plasmas. Simple relations for cross-species primitive moments are developed which obey conservation laws, and reproduce familiar velocity and temperature relaxation rates. This treatment of multispecies Dougherty collisions, valid for arbitrary mass ratios, avoids unphysical temperatures and satisfies the $H$ -theorem (H is related to the entropy) unlike an analogous Bhatnagar–Gross–Krook operator. Formulas for both a Cartesian velocity space and a gyroaveraged operator are provided for use in Vlasov as well as long-wavelength gyrokinetic models. We present an algorithm for the discontinuous Galerkin discretization of this operator, and provide results from relaxation and Landau damping benchmarks.

Microresonators and Microantennas—Tools to Explore Magnetization Dynamics in Single Nanostructures

The phenomenon of magnetic resonance and its detection via microwave spectroscopy provide insight into the magnetization dynamics of bulk or thin film materials. This allows for direct access to fundamental properties, such as the effective magnetization, g-factor, magnetic anisotropy, and the various damping (relaxation) channels that govern the decay of magnetic excitations. Cavity-based and broadband ferromagnetic resonance techniques that detect the microwave absorption of spin systems require a minimum magnetic volume to obtain a sufficient signal-to-noise ratio (S/N). Therefore, conventional techniques typically do not offer the sensitivity to detect individual micro- or nanostructures. A solution to this sensitivity problem is the so-called planar microresonator, which is able to detect even the small absorption signals of magnetic nanostructures, including spin-wave or edge resonance modes. As an example, we describe the microresonator-based detection of spin-wave modes within microscopic strips of ferromagnetic A2 Fe60Al40 that are imprinted into a paramagnetic B2 Fe60Al40-matrix via focused ion-beam irradiation. While microresonators operate at a fixed microwave frequency, a reliable quantification of the key magnetic parameters like the g-factor or spin relaxation times requires investigations within a broad range of frequencies. Furthermore, we introduce and describe the step from microresonators towards a broadband microantenna approach. Broadband magnetic resonance experiments on single nanostructured magnetic objects in a frequency range of 2–18 GHz are demonstrated. The broadband approach has been employed to explore the influence of lateral structuring on the magnetization dynamics of a Permalloy (Ni80Fe20) microstrip.

Model Updating for Systems with General Proportional Damping Using Complex FRFs

In this paper, we propose a model updating method for systems with nonviscous proportional damping. In comparison to the traditional viscous damping model, the introduction of nonviscous damping will not only reduce the vibration of the system but also change the resonance frequencies. Therefore, most of the existing updating methods cannot be directly applied to systems with nonviscous damping. In many works, for simplicity, the Rayleigh damping model has been applied in the model updating procedure. However, the assumption of Rayleigh damping may result in large errors of damping for higher modes. To capture the variation of modal damping ratio with frequency in a more general way, the diagonal elements of the modal damping matrix and relaxation parameter are updated to characterize the damping energy dissipation of the structure by the proposed method. Spatial and modal incompleteness are both discussed for the updating procedure. Numerical simulations and experimental examples are adopted to validate the effectiveness of the proposed method. The results show that the systems with general proportional damping can be predicted more accurately by the proposed updating method.

Описание кратковременного процесса уравнением теплопроводности с дробными производными

The thermal conductivity models of Fourier, Cattaneo-Vernotte, Maxwell-Cattaneo-Luikov and models with fractional time derivatives of temperature and heat flux are considered. An algorithm for the numerical solution of the generalized problem of one-dimensional heat conduction is constructed. The algorithm comprises all the models listed above applying boundary conditions of the third kind and difference analogs of differential operators of the second order of accuracy in coordinate and time. The parameters (Biot number, time of thermal relaxation and thermal damping, indicators of fractional derivatives) that describe experimental transient processes are determined using the listed models applied for both in the center and on the surface of a low heat-conducting body.

Picosecond laser ultrasonic measurements of interlayer elastic properties of 2H-MoSe2 and 2H-WSe2

We have used the ultrafast pump-probe technique known as picosecond ultrasonics to generate and detect coherent acoustic phonon pulses with frequencies reaching 40 GHz in exfoliated crystals of MoSe2 and WSe2 on Si and sapphire substrates. We report picosecond time-resolved reflectivity data from samples ranging from 180 nm to 920 nm in thickness and compare our results to a 1D simulation of strain-induced changes in the optical reflectivity. We find the longitudinal sound velocity along the c-axis (the interlayer direction) to be 2800 m/s ± 40 m/s for MoSe2 and 2510 m/s ± 60 m/s for WSe2. We also report the measured lifetime of longitudinal acoustic phonons approaching 40 GHz to be 0.85 ± 0.2 ns and compare this value with predictions of relaxation damping and 3-phonon models, as well as discuss its relationship to the predicted thermal conductivity of MoSe2.

Performance of different techniques of generation and absorption of free-surface waves in Computational Fluid Dynamics

In wave-structure interaction problems, the minimization of wave reflection at boundaries is important for achieving accurate results and limiting the disturbances on the air/water interface. The present study compares a set of existing wave outlet techniques which are commonly applied in free surface simulations using a viscous flow solver. These techniques are stretched mesh, linear damping source, increased viscosity, and relaxation schemes. The comparisons are performed for test conditions which include propagation of regular incident waves and damping of radiation waves.

Programmable microwire composites: from functional units to material design

Microwire composites possess a wide range of functionalities that can be actively manipulated by magnetic field/stress stimuli or hybridization. Beyond those strategies, here we focus on programming microwave response by designing the wire functional units and assembling them in a specific arrangement. The programming was based on a code type defined by structural relaxation and electromagnetic damping and on a code pattern by wave attenuation, effective conductivity and near-field interaction effects. Structural relaxation was achieved by current annealing the wires, which was reflected in changes in Curie temperature, structural, magnetic and electrical properties. The wave propagation mapped by the transmission coefficient was manipulated by the wire concentration and periodicity and by arrangement of as-cast and annealed wires in their array. Increasing the wire concentration blueshifted the transmission band of the wire composites due to larger conductivity, while decreasing the wire periodicity redshifted the band owing to stronger inter-wire coupling. A larger blueshift was obtained by alternating as-cast and annealed wires due to an overlapped flow closure of fields from the same type of wire in the array. Our strategy demonstrates that macroscopic properties of wire composites can be effectively programmed from a material structure/unit arrangement perspective. This concept promotes deeper understanding of high-frequency properties and further expands the applications of fiber-reinforced composites in fields such as information, energy and security technologies.

Bio-Heat Models Revisited: Concepts, Derivations, Nondimensalization and Fractionalization Approaches

The heat transfer in living tissues is an evergreen problem in mathematical modelling with great practical importance starting from the Pennes equation postulation. This study focuses on concept in model building, the correct scaling of the bio-heat equation (one-dimensional) by appropriate choice of time and length scales, and consequently order of magnitude analysis of effects, as well as fractionalization approaches. Fractionalization by different constitutive approaches, leading to application of different fractional differential operators, modelling the finite speed of the heat wave, is one of the principle problems discussed in the study. The correct choice of the damping (relaxation) function of the heat flux is of primarily importance in the formulation of the bio-heat equation with memory. Moreover, this affects the consequent scaling, order of magnitude analysis and solutions.

Properties of a domain wall in a bi-stable magnetic microwire

Abstract The properties of a domain wall between axial domains in a bi-stable microwire are studied in this paper. The axial dimension of a long planar static domain wall is calculated using a simple theoretical model. The obtained value of a few millimetres is in good agreement with known experimental values. The dynamic properties of the domain wall were analysed using wall velocity versus applied field dependences v(H). Based on a simple model which includes standard damping mechanisms (eddy current damping and spin relaxation damping), the experimentally observed decrease in wall mobility in v ( H ) can be caused by decrease in the wall axial dimension, its length. This should be accompanied by changes in the voltage peaks induced in the pick-up coil in the Sixtus–Tonks experiment which was, however, not observed. Taking into account a stray field around the moving wall, the voltage peaks were calculated for the situation when the pick-up coil radius was much larger than the wire radius. The calculated peaks are relatively wide also for very short domain walls, and they are only slightly influenced by the wall length. This indicates that obtaining information on the wall length and changes in its length and shape from the induced voltage peaks is very difficult.

Analytical Model of Cyclic Heat Exchange of the Plate of Finite Sizes Adjusted for the Thermal Relaxation

The hyperbolic boundary value problem of heat conduction in a two-dimensional rectangular plate with the third kind boundary conditions was formulated. The model of transient thermal processes in the body takes into account changes in time and along the flow direction of the ambient temperature. An analytical solution was obtained for the temperature field in the plate, adjusted for the phenomena of thermal relaxation and thermal damping.

The influence of thermal relaxation and thermal damping on transient processes with cyclic boundary conditions

Variants of the differential equation of heat conduction in a solid body, which follow from the Fourier and Cattaneo–Vernotte hypotheses and the Lykov equation, are considered. A boundary value problem describing temperature fields in a body (cylinder) upon cyclic heat transfer with cold and hot media is formulated. An analytical solution to the boundary value problem with a hyperbolic differential equation of heat conduction with allowance for thermal relaxation and temperature damping with cyclic boundary conditions of the third kind is given. The thermal transient processes calculated by the classical heat conductance equation and hyperbolic equation of heat conduction on the axis of the cylinder at different values of factors such as the ratio of the thermal damping time to the thermal relaxation time, the duration of cyclic periods, the Fourier relaxation number, and the Biot number are compared. A conclusion is made that the theory of regenerative air heater should be improved by taking into account thermal relaxation and thermal damping in the nozzle and measurements of the thermal relaxation and thermal damping times of the corresponding materials.

Relaxation damping and friction

Recent research has shown that energy losses named as ‘relaxation damping’ can occur even with an infinite coefficient of friction using the method of dimensional reduction (MDR) which is strictly applicable to axis-symmetric elastic contact problems. If the solution with infinite coefficient of friction is regarded as a limiting case of ‘very large’ friction, this limiting solution is often useful because it will typically be much simpler than that obtained assuming a finite coefficient of friction, and it is likely to give reasonable estimates for the actual dissipation in cases that are far from the gross slip (sliding) limit. Using the advantage of relaxation damping, we shall give a generalized proof that is independent of the MDR. We shall also extend the proof to problems in which the applied loads follow a general trajectory in three-dimensional vector space. Further, we shall demonstrate how the energy dissipation per cycle varies with an increasing normal force, showing that relaxation damping could be useful as a limit in cases where there is significant variation in a normal force.

Bulk plasmon-phonon polaritons in n-GaN

We studied theoretically and experimentally plasmon-phonon polaritons and longitudinal plasmon-phonon oscillations in n-GaN epitaxial layers. The studies were carried out on the epitaxial layers with various doping levels. Simulation of the reflectivity spectra and dispersion relations of plasmon-phonon polaritons was performed in a wide frequency range. Reflectivity spectra transformation associated with phonon damping and electron relaxation processes has been revealed. Experimental studies of the reflectivity spectra have been performed in the spectral range of 8–80 meV. The experimental spectra are well fitted by the simulated ones. Results of the study can be used for contactless determination of the electron concentration and mobility in GaN epitaxal layers.

Measurement of thermal relaxation and temperature damping time in a solid

Differential equations of heat conductance of solid body are presented, a result of Fourier, Cattaneo–Vernotte, and two-phase delay hypotheses. The experimental set-up and automated measuring system is described for the study of transient thermal processes in solid. The solution of the boundary problem of the third kind is given with differential equations of heat conductance of parabolic and hyperbolic types. The results of experimental and theoretical study of transient thermal processes in the plate center are given in the sudden immersion into a hot environment. Based on the comparison of theoretical transient processes with recorded automated measuring system, the adequacy of hypotheses and corresponding differential equations of heat conductance are concluded with respect to short-term transient processes. Thermal relaxation and temperature damping constants for polymethyl methacrylate are measured.