Influence Of Relaxation Time Research Articles

Microwave absorption properties of β-type ferrites: Influence of Nd-loading percentage on structural, spectral, elemental, and electrical features

Hexagonal ferrites have drawn significant attention due to a broad range of telecommunication and stealth technology applications. β-Type hexagonal ferrites are rarely used in various technological applications. In the current work, Nd3+ substituted polycrystalline β-type hexagonal ferries with composition LiFe11-x NdxO17 (x = 0.0–0.04, ∇ x = 0.01) were prepared using the sol-gel method. All prepared samples were sintered at 1000 °C for 4 h. The influence of Neodymium (Nd3+) on its structural, electrical, and dielectric properties was investigated. Lattice parameters (a, c) and Vcell increased with varying Neodymium substitution levels. The crystallite size was measured in the range of 38–42 nm. Fourier Transform IR (Infrared) spectroscopy exposed the presence of two spectral bands at 416 to 449 cm−1 and 449 to 489 cm−1. XPS (x-ray photoelectron spectroscopy) analysis verified the presence of metal ions and their chemical states in all prepared samples. The dielectric constant, loss, tan δ, and σac (ac-conductivity) decreased by increasing Nd3+ content. Jonscher's power law explains the conduction mechanism of charge carriers in all fabricated samples. The influence of relaxation time and grain boundaries on the electrical characteristics of prepared nanomaterials was investigated by impedance analysis. SEM (scanning electron microscopy) confirms the successful formation of β-hexaferrite nanomaterials. A minimum reflection loss of −32.08 dB was observed at 1.5 GHz for the x = 0.04 sample. This minimum reflection loss evidenced the novelty of the research and suggested their usefulness in high-frequency microwave applications. All samples investigated in this research work are suitable for high-frequency applications, multilayer chip inductors, and EM interference shielding.

Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy.

The study of thermal therapy to tumors and the response of living cells to this therapy used to treat tumor is very important due to the complexity of heat transfer in biological tissues. In the past few years, there has been a growing interest among clinicians, mathematicians, and engineers regarding the use of computational and mathematical methods to simulate biological systems. Numerous medical proceedings also employ mathematical modeling and engineering techniques as a means to guarantee their safety and evaluate the associated risks effectively. This manuscript provides an analytical solution used for the first time to study the mechanism of biological thermal response during heat therapy on spheroidal skin tumor. The proposed method used a generalized thermoelasticity model with one relaxation time. The influence of relaxation times on the responses of diseased and healthy tissues is studied and interpreted graphically. Also, the impact of different laser irradiance on the thermal profile of the malignant tumor cells over a period of 2 minutes is interpreted graphically. To investigate the transfer of heat within biological tissues during the thermal therapy, the Laplace transform and inverse Laplace transform methods were applied. A comparison of the present generalized thermoelasticity model and different models based on Pennes bioheat transfer PBT shows that our proposed model yields more realistic and accurate predictions. The current model can be used to explain various therapeutic methods.

Nonlinear periodic response of viscoelastic laminated composite plates using shooting technique

The nonlinear periodic response of viscoelastic laminated composite plates subjected to harmonic excitation is carried out in time domain using the generalized Maxwell model in the form of a Boltzmann integral. The integral form of the viscoelastic constitutive relation is converted to the incremental form for the finite element formulation based on the Reissner–Mindlin plate theory incorporating von Karman geometric nonlinearity. The recursive relations are developed to compute the current time-step solution using only the previous time-step solution. The periodic response is obtained using shooting technique coupled with Newmark’s time integration and arc length continuation method. The implementation of the shooting technique for the Boltzmann Integral based viscoelasticity done for the first time in this study involves derivation of a number of additional recursive relations and initial conditions at the beginning of each shooting cycle. The nonlinear periodic vibration characteristics such as frequency response, damping factor, steady-state response history, phase plane plots, and frequency spectra are presented for viscoelastic plates with different boundary conditions and lamination schemes. Further, the influence of relaxation time and number of Maxwell elements on the frequency response characteristics are investigated. It is seen that the shooting technique is capable of predicting periodic responses of viscoelastic dynamical systems directly from the second-order equations of motion and is more efficient than the direct time integration method. The nonlinear response of viscoelastic plates predicted using the equivalent elastic model with Rayleigh proportional damping (having same linear frequency response) is found to be significantly different from the one predicted using viscoelastic constitutive model.

Pulse electromagnetic flow of Jeffrey fluid in parallel plate microchannels

This paper investigates the pulse electromagnetic flow of a Jeffery fluid between parallel plate microchannels, where the pulse is considered as a relatively stable and common rectangular pulse. The Laplace transform and residue theorem are employed to derive the analytical solutions for the velocity and volumetric flow rate of the pulse electromagnetic flow. Graphical representations depict the effects of several important parameters, including the Hartmann number pulse width relaxation time and retardation time on them. The study findings demonstrate that the Hartmann number plays a vital role in the investigation of pulse electromagnetic flow. During the first half-cycle of the pulse electric field, the magnitude of the velocity amplitude increases and then decreases with the Hartmann number An interesting observation is that in the second half-cycle, larger Hartmann number values result in a decrease in velocity followed by a reverse increase. The profiles of velocity and volumetric flow rate exhibit oscillations over a relatively short period of time, then gradually reach a stable state with time and display periodic variation characteristics. Moreover, a larger pulse width leads to a longer variation period and more stable profiles of velocity and volumetric flow rate. For smaller Hartmann numbers the magnitude of the volumetric flow rate amplitude grows with the relaxation time and reduces with the retardation time However, as the Hartmann number increases, the influence of relaxation time and retardation time on the volumetric flow rate becomes significantly weakened, especially the retardation time

Analysis of pulse electromagnetic electroosmotic flow of Jeffrey fluid through parallel plate microchannels under a constant pressure gradient

The purpose of this work is to investigate the pulse electromagnetic electroosmotic flow (EOF) behavior of a Jeffrey fluid in parallel plate microchannels under a constant pressure gradient. Analytical solutions for the velocity and volumetric flow rate are derived by employing the Laplace transform method and the residue theorem. In particular, the electric double layer (EDL) effect is considered, and an analysis is conducted on both the near-center and near-wall velocities. The flow periodicity is also noted, and these velocities are evaluated during the first and second half-cycles, respectively. Moreover, both 3D and 2D graphics are simultaneously utilized to visualize the impact of relevant parameters on velocity and volumetric flow rate. Our analysis yielded the following key findings: The effects of relevant parameters, such as pulse width a¯, pressure gradient Ω, Hartmann number Ha, electric field strength β, electrokinetic width K, relaxation time λ¯1 and retardation time λ¯2, on the near-center velocity during the first half-cycle align with the results of previous studies. During the second half-cycle, higher values of variables Ha and β lead to reduced velocities. Interestingly, during any half-cycle, the near-wall velocity demonstrates similar characteristics to the near-center velocity in response to variations in certain parameters, including Hartmann number Ha, electric field strength β, relaxation time λ¯1 and retardation time λ¯2. It is worth mentioning that the influence of relaxation time λ¯1 and retardation time λ¯2 on the near-wall velocity is largely independent of the Hartmann number, especially for the retardation time. Regardless of the values of the parameters λ¯1 and λ¯2, a higher volumetric flow rate is observed with an increased electrokinetic width K. Additionally, the volumetric flow rate profile of the Jeffrey fluid exhibits a comparatively smoother trend over time compared to that of the Maxwell fluid. The remarkable similarity between Jeffrey fluid and blood suggests that the results presented in this paper hold immense potential as a crucial reference for studying blood transport within the field of microfluidics.

Retraction Note: Investigation of the key factors influencing cavity collapse using molecular dynamics simulation

Cavitation greatly affects the safe and stable operation of hydraulic machineries and thus has been key challenge in this field. Cavity collapse caused by cavitation can form transient characteristics such as high temperature, high pressure, strong shock wave, and high-speed micro-jet, which may cause serious damage to nearby solids. Cavitation can be affected by many intercoupled factors during the collapse transition. However, existing research rarely focuses on the analysis of its influencing factors. This research aims to reveal the collapse mechanism of cavitation, the parameters of each factor, and the influencing rules of the cavity collapse process. Molecular dynamics method was employed to analyze the evolution process of cavity collapse in the computational domain of liquid argon under different conditions. The influences of relaxation time, system temperature, and cavity size on cavity collapse were investigated. These simulation results showed that when the relaxation time was within 1 ns, the longer the relaxation time, the more likely the system molecules formed a stable state, and the more easily the cavities collapsed. When the relaxation time was greater than 0.2 ns, the difference in the process of collapse was smaller. When the temperature of the system was within 80 K, as the temperature increased, the thermal motion of the molecules intensified to increase the kinetic energy and weaken the intermolecular gravitation, shortening the time for cavities to reach the collapse point. When the temperature reached 80 K, as the temperature continued to increase, the time of collapse point and the process basically unchanged. When the initial cavity size was within 15 A, the larger the initial cavity size, the less likely the cavities tended to collapse. When the cavity size was larger than 15 A, the cavities were further less likely to collapse as the cavity size increased. The research results can provide theoretical support for the study of cavitation characteristics.

Second harmonic generation in the tilted type-I Dirac metals under terahertz frequency regime

Abstract In this work, we theoretically demonstrate that the second order response can survive in a two-dimensional (2D) tilted type-I Dirac metal due to the time reversal symmetry (TRS) breaking. We find that, in the terahertz regime, the second harmonic generation (SHG) is appreciably strong and is widely depending on the tilting parameter, temperature, excitation frequency and the applied electric field, respectively. By comparing with the first and third order optical response, we also note that each of the three modes of optical response dominates in different frequency intervals in accordance with the strength of the applied electric field. With the help of the ω − E c diagram (with ω and E c being the excitation frequency and the critical electric field, respectively), we are able to engineer the desired nonlinear response by varying the excitation frequency and the strength of the applied electric field. Finally, we briefly discuss on the influences of relaxation time on SHG by considering four types of k-dependent scattering mechanisms.

Talk about Several Time Periodic Pulse Electroosmotic Flow of Maxwell Fluid in a Circular Microchannel

Using the method of Laplace transform, analytical expressions are derived for the time periodic pulse electroosmotic flow (EOF) velocity of the triangle and sawtooth of Maxwell fluid in circular microchannel. The solution involves analytically solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations of inverse Laplace transform, the effects of electrokinetic width K, relaxation time and pulse width a on the above several pulse EOF velocities are investigated. In addition, we focused on the comparison and analysis of the formulas and graphs between the triangle and sawtooth pulse EOF with the rectangle pulse EOF. The study found that there are obvious differences in formulas and graphs between triangle and sawtooth pulse EOF with rectangle pulse EOF, and the difference mainly depends on the different definitions of the three kinds of time periodic pulse waves. Finally, we also studied the stability of the above three kinds of pulse EOF and the influence of relaxation time on pulse EOF velocity under different pulse widths is discussed. We find that the rectangle pulse EOF is more stable than the triangle and sawtooth pulse EOF. For any pulse, as the pulse width a increases, the influence of the relaxation time on the pulse EOF velocity will be weakened.

Instability of single-walled carbon nanotubes conveying Jeffrey fluid* *Project supported by the National Natural Science Foundation of China (Grant No. 11772162), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 2019BS01004), and the Inner Mongolia Grassland Talent, China (Grant No. 12000-12102408).

We report instability of the single-walled carbon nanotubes (SWCNT) filled with non-Newtonian Jeffrey fluid. Our objective is to get the influences of relaxation time and retardation time of the Jeffrey fluid on the vibration frequency and the decaying rate of the amplitude of carbon nanotubes. An elastic Euler–Bernoulli beam model is used to describe vibrations and structural instability of the carbon nanotubes. A new vibration equation of an SWCNT conveying Jeffrey fluid is first derived by employing Euler–Bernoulli beam equation and Cauchy momentum equation taking constitutive relation of Jeffrey fluid into account. The complex vibrating frequencies of the SWCNT are computed by solving a cubic eigenvalue problem based upon differential quadrature method (DQM). It is interesting to find from computational results that retardation time has significant influences on the vibration frequency and the decaying rate of the amplitude. Especially, the vibration frequency decreases and critical velocity increases with the retardation time. That is to say, longer retardation time makes the SWCNT more stable.

Anomalous diffusion on Archimedean spiral structure with Cattaneo flux model

In this paper, we study the properties of anomalous diffusion on a specific Archimedean spiral backbone with radial fingers. The partial differential equation with Cattaneo flux model is derived using spiral transformation and solved numerically. The influence of relaxation time and geometrical parameter on particle distribution and MSD is discussed graphically. Our results show that there is a transition between two types of diffusions. The super-diffusion (MSD ~tα; α > 1) starts for a short time then changes to sub-diffusion (MSD ~tα; 0 < α < 1) for a long time. This phenomenon is due to the length variation of radial fingers with the spiral geometrical structure. Our model can be used to study a class of specific anomalous diffusion, such as the search of DNA-binding proteins for their binding sites.

RETRACTED ARTICLE: Investigation of the key factors influencing cavity collapse using molecular dynamics simulation

Cavitation greatly affects the safe and stable operation of hydraulic machineries and thus has been key challenge in this field. Cavity collapse caused by cavitation can form transient characteristics such as high temperature, high pressure, strong shock wave, and high-speed micro-jet, which may cause serious damage to nearby solids. Cavitation can be affected by many intercoupled factors during the collapse transition. However, existing research rarely focuses on the analysis of its influencing factors. This research aims to reveal the collapse mechanism of cavitation, the parameters of each factor, and the influencing rules of the cavity collapse process. Molecular dynamics method was employed to analyze the evolution process of cavity collapse in the computational domain of liquid argon under different conditions. The influences of relaxation time, system temperature, and cavity size on cavity collapse were investigated. These simulation results showed that when the relaxation time was within 1 ns, the longer the relaxation time, the more likely the system molecules formed a stable state, and the more easily the cavities collapsed. When the relaxation time was greater than 0.2 ns, the difference in the process of collapse was smaller. When the temperature of the system was within 80 K, as the temperature increased, the thermal motion of the molecules intensified to increase the kinetic energy and weaken the intermolecular gravitation, shortening the time for cavities to reach the collapse point. When the temperature reached 80 K, as the temperature continued to increase, the time of collapse point and the process basically unchanged. When the initial cavity size was within 15 A, the larger the initial cavity size, the less likely the cavities tended to collapse. When the cavity size was larger than 15 A, the cavities were further less likely to collapse as the cavity size increased. The research results can provide theoretical support for the study of cavitation characteristics.

A normal contact force approach for viscoelastic spheres of the same material

This paper presents a normal contact force approach for viscoelastic spheres of the same material based on the theory of viscoelasticity. The approach treats the normal contact force as an elastic component superposed with a dissipative component based on which to derive a reduced expression, and is numerically analyzed for the viscoelastic spheres modelled by the standard linear solid with the sinusoidal displacement history. The influences of relaxation time and viscosity upon the approach are discussed. An application of the approach with the collinear impact of viscoelastic balls is carried out and its adequacy to reality is validated by the comparison of the numerical solution against the impact experiment of Golf and Superball, to conclude that the suggested approach is applicable to build the kinematic equation describing the normal contact of viscoelastic bodies.

Law of Distribution and Variation of Electrostatic Potential in Oil Tanks during Filling Process

Electrostatic potential is a critical factor to evaluate the severity of electrostatic hazard during filling oil tanks. A novel model is proposed for calculating electrostatic potential in tanks during filling process. In the model, the nonuniform electrostatic charge distribution is solved by considering the diffusion, convection, conduction, and dissipation forces acting on the electrostatic charge. Additionally, an experiment was carried out for measuring electrostatic potential, and the maximum surface potential from the experiment coincided with that of calculation well. By applying the model, the distribution of electrostatic potential is explored, and the influences of relaxation time and some other factors on the electrostatic potential are analyzed. The results show that the peak value of the maximum surface potential calculated by the proposed model occurs much later in the filling than the existed model with the assumption of uniform electrostatic charge distribution. The relaxation time is a key factor to influence the electrostatic potential, and it also affects the filling fraction at which surface potential reaches the peak value. The maximum surface potential increases with the increase of the diffusion coefficient of the ion, the dynamic viscosity of the oil and the filling rate, respectively. © 2018 American Institute of Chemical Engineers Process Saf Prog: e12035 2019

Modeling approach to describe fouling removal during relaxation

Abstract Filtration tests were designed with fixed filtration durations and varying relaxation lengths to study the influence of relaxation time on flux recovery and fouling removal. A mathematical model was used to estimate the development and removal of fouling during the filtration and relaxation phases. During the relaxation phases, a relaxation-time dependent back transport constant was introduced to properly simulate removal of the cake layer. It was found that the rate of removal of cake was highest in the beginning of relaxation period and decreased during relaxation. This shows that the rate of removal depends on the amount of cake to be removed, but can also be explained by cake not being removed as single flocs or colloids, but as fragments of flocs released in the beginning or relaxation, followed by release of colloids more strongly adhered to the surface or due to an initial swelling of the cake layer during the relaxation. Based on this, a model was proposed to simulate the development in amount of cake during filtration and removed during relaxation. With this, the development in amount of cake and permeability could be simulated for different filtration and relaxation times to identify the setting with the highest net flux.

Low threshold optical bistability at terahertz frequencies with graphene surface plasmons.

We propose a modified Kretschmann-Raether configuration to realize the low threshold optical bistable devices at the terahertz frequencies. The metal layer is replaced by the dielectric sandwich structure with the insertion of graphene, and this configuration can support TM-polarization surface electromagnetic wave. The surface plasmon resonance is strongly dependent on the Fermi-level of graphene and the thickness of the sandwich structure. It is found that the switching-up and switching-down intensities required to observe the optical bistable behavior are lowered markedly due to the excitation of the graphene surface plasmons, thus making this configuration a prime candidate for experimental investigation at the terahertz range. And the switching threshold value can be further reduced by decreasing the Fermi-level or increasing the thickness of sandwich structure, hence providing a new way for realizing tunable optical bistable devices. Finally, the optical bistability at higher terahertz frequency and the influence of relaxation time under the actual experimental condition on Fermi-level are discussed.

EFFECT OF RELAXATION TIME ON MHD PULSATILE FLOW OF BLOOD THROUGH POROUS MEDIUM IN AN ARTERY UNDER THE EFFECT OF PERIODIC BODY ACCELERATION

In this investigation, the influence of relaxation time on magnetohydrodynamic (MHD) pulsatile flow of blood through porous medium in an artery under the effect of periodic body acceleration is investigated. The applied magnetic field is assumed to be constant and perpendicular to the blood flow in the artery, and blood is considered as an incompressible electrically conducting fluid. An analytical solution of the equation of motion is obtained by applying the Laplace Transform. With a view of illustrating the applicability of the mathematical model developed here, the analytic explicit expressions of axial velocity and wall shear stress are given. The results show that the values of the axial velocity and shear stress are affected by the relaxation time. Numerical results are reported for different values of the physical parameters of interest.

Influence of relaxation time on the lifetime of commercial lithium-ion cells

The influence of rest periods on the lifetime of lithium-ion cells is investigated. The investigations focus on commercially available cells (type 18650) with a lithium–nickel–manganese–cobalt-dioxide (NMC)/lithium–cobalt-dioxide (LCO) blend and lithium–iron–phosphate (LFP) as cathode material and graphite as anode material. The above test cells are subjected to different cycle tests. Important influence factors in addition to the relaxation time are: the current, the temperature and the state of charge (SOC).We were able to detect an increase of capacity (e.g. 0.1% of the nominal cell capacity for LFP test cells) after a rest period of 120 min in our measurements, the so called relaxation effect.Further, the question is answered, whether relaxation affects battery lifetime. This was achieved by cycling cells with and without different rest periods at different temperatures and C-rates with a total of 50 test cells. However, no observable differences between cells with and without rest periods (≤2 h) were found. Moreover, experiments with many small breaks or one larger break showed that the duration of one continuous relaxation time is more important for the aging behavior, than the sum of rest periods. In addition, also impedance spectra were evaluated.

Influence of Relaxation Time on the Lifetime of Commercial Lithium-Ion Cells

not Available.

Temperature Prediction for Tumor Hyperthermia with the Behavior of Thermal Wave

In magnetic nanoparticle hyperthermia for cancer treatment, controlling the heat distribution and temperature elevations is an immense challenge in clinical applications. It is expected for treatment quality to understand the heat transport occurring in biological tissue. The non-Fourier thermal behavior in biological tissue has been experimentally observed. This work uses the thermal wave model to predict the temperature excess occurring in a two-layer concentric spherical tissue with the heat source of Gaussian distribution. The solutions to the hyperbolic bio-heat equation with the space-dependent source term in the spherical coordinate system are presented. The influences of relaxation time, blood perfusion rate, and heating strength on the thermal response in tumor and normal tissue are discussed.

Modeling deposition of particles in typical horizontal ventilation duct flows

Particles carried by airflows through ventilation ducts in heating, ventilation and air-conditioning (HVAC) systems have adverse effects on human health. Knowledge of particle deposition rates in ventilation ducts is useful for modeling exposures to particles within buildings and more completely understanding particle fates. To meet these objectives, deposition rates of particles to various internal surfaces in a smooth horizontal square ventilation duct are predicted by Reynolds-Averaged Navier-Stokes (RANS)-Lagrangian simulation at all three air speeds of 3.0 m/s, 7.0 m/s and 9.0 m/s. Drag, lift force, gravity, inertial force and turbulent diffusions are considered in the computation of particle motion. The influences of relaxation time, particle size, air speed, turbulent flow development profiles and surface orientations on predicted deposition rates (dimensionless deposition velocities) of particles is discussed. For particles larger than 10 μm, it is shown that vertical wall deposition rates in a smooth horizontal square ventilation duct where the turbulent flow profiles is fully developed first increase with dimensionless relaxation time increase and then slightly decrease with dimensionless relaxation time increasing at three different air speeds. The maximum of the sidewall deposition rates is 0.12. Floor deposition rates increase with dimensionless relaxing time increase and attain the maximum value of 9.6. Ceiling deposition rates firstly gradually decrease and then rapidly decrease to zero with dimensionless relaxing time increasing at different air speeds. The maximum of the ceiling deposition rates is 0.054. Particle deposition rates to the ceiling, wall and floor in the horizontal duct with a fully developed turbulent flow profile are all lower than that in the horizontal duct with a developing turbulent flow profile. Particle deposition rates are mainly dependent on friction velocity (air speed) and particle size. The differences in deposition rates to the duct floor, wall and ceiling decrease with increasing air speed. The results of Lagrangian simulations in this work are valuable for more accurately predicting and understanding particle deposition in typical ventilation ducts.