Varying Relaxation Times Research Articles

Group analysis of the two‐dimensional two‐temperature gas dynamics equations

The two‐dimensional two‐temperature nonstationary gas dynamics equations with the relaxation Landau–Teller equation are considered in the paper. The group analysis method is applied to the study these equations. The admitted Lie groups are found for two modifications of relaxation time. Optimal systems of one‐ and two‐dimensional subalgebras are constructed for the group corresponding to the case of varying relaxation time which is closer to the case of ideal gas dynamics. Solutions with two and one independent invariant variables are derived using the optimal systems of admitted Lie algebras. The corresponding reduced systems were numerically calculated and compared with numerical solutions of analogous problems for classical gas dynamics equations. The differential conservation laws which present the fundamental properties of two‐temperature gas dynamics equations are also obtained.

Quantum dynamics of a nucleon in the Fermi accelerator

The quantum dynamics of a particle in a one-dimensional box with an oscillating wall (the Fermi accelerator) is investigated. The model is applied to the motion of a single nucleon in the mean-field potential of a heavy atomic nucleus whose surface vibrates. By directly solving the time-dependent Schrödinger equation, both the state of the particle and its mean-energy are studied. The effects of the frequency of the wall oscillation on the nucleon’s energy are addressed. Its energy oscillates in phase with the moving wall for all frequencies, showing no chaotic behaviour. There is a large initial peak of the nucleon’s energy as the particle adjusts to the sudden change in the size of the box and a varying relaxation time as it plateaus towards lower energy and a partial equilibrium. Small oscillations in energy continue, since there cannot be a true equilibrium while the wall is moving. The quantum coherence between the different parts of the nucleon’s wave-function in real space is very much preserved. This research lays the foundation for future investigations into quantum tunnelling in the Fermi accelerator.

Wealth distribution models with regulations: Dynamics and equilibria

Simple agent based exchange models are a commonplace in the study of wealth distribution in an artificial economy. Generally, in a system that is composed of many agents characterized by their wealth and risk-aversion factor, two agents are selected sequentially and randomly to exchange wealth, allowing its redistribution. Here we analyze how the effect of social protection policies, which favor agents of lower wealth during the exchange, influences the stability and some relevant economic indicators of the system. On the other hand, we study how periods of interruption of these policies produce, in the short and long term, changes in the system. In all cases, a steady state is reached, but with varying relaxation times. We conclude that regulations may improve economic mobility and reduce inequality. Moreover, our results indicate that the removal of social protection entails a high cost associated with the hysteresis of the distribution of wealth. Economic inequalities increase during the period without social protection and decrease when they are restored. But recovery to the initial equilibrium may take longer than it took to disturb it. In some extreme cases, inequality is irreversible.

Step scan T-cell Fourier-transform infrared photoacoustic spectroscopy (FTIR-PAS) for detection of ambient air contaminants

The theory of T-cells and their application in Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS) based on a commercial FTIR spectrometer are discussed. This work was undertaken with the view to develop portable compact instrumentation for monitoring air contaminants. A resonant T-cell was determined to be the most appropriate resonator in view of the requirement for the low frequency and the limited space available in the FTIR spectrometer sample compartment. A two dimensional analytical solution with a semi-empirical boundary condition was introduced for resonance frequency prediction. Carbon dioxide (CO2) gas was the chosen air contaminant. Linear amplitude response to CO2 concentrations from 1000 to 8000 ppmv was observed, leading to a theoretical detection limit of 4 ppmv. The FTIR-PA phase shift was correlated to varying relaxation times in a mixture of CO2 and nitrogen (N2) gases. The analytical solution showed excellent agreement with simulated and experimental data, providing a reliable means for estimating the resonance frequency of the system. The experimental results establish the feasibility of using step-scan T-cell FTIR-PAS for quantitative detection of ambient air pollutants.

Electroosmotic flows of viscoelastic fluids with asymmetric electrochemical boundary conditions

The electroosmotic flow of viscoelastic fluids is studied analytically by using the Phan-Thien Tannar (PTT) constitutive model. Unidirectional steady-state flow is formed in a two-dimensional microchannel bounded by two parallel plates with different zeta potentials or by a plane substrate and a free surface. The exact flow field is obtained based on first principles. Velocity profiles and flow rates are studied parametrically by varying relaxation time, extensibility parameter and slip parameter of the PTT model and the electrochemical properties of the liquid and the bounding plates. Comparisons are made with Newtonian fluids and previous non-Newtonian analyses.

Elastic liquid jet impaction on a high‐speed moving surface

AbstractIn the railroad industry a friction‐modifying non‐Newtonian liquid, showing elastic behavior, may be applied to the rail in the form of a liquid jet. The interaction of this elastic liquid jet and the moving surface—specifically whether it splashes or adheres without splash—is important in this industrial application. Twelve different elastic liquids with widely varying relaxation times were tested to isolate the effect of elasticity from other fluid properties. Using high‐speed imaging, the interaction between the impinging jet and the moving surface could be captured and analyzed. Although similar to Newtonian jets, for which the Reynolds number plays a major role, the Deborah number was also salient to the splash of elastic liquids. At the elevated Weber numbers of the testing, the Weber number had a much smaller impact on splash than did the Reynolds or Deborah numbers. The ratio of the surface velocity to the jet velocity has only a small effect on the splash. © 2012 American Institute of Chemical Engineers AIChE J, 2012

A lattice Boltzmann approach for the non-Newtonian effect in the blood flow

A new lattice Boltzmann approach within the framework of D2Q9 lattice for simulating shear-thinning non-Newtonian blood flows described by the power-law, Carreau–Yasuda and Casson rheology models is proposed in this study. The essence of this method lies in splitting the complete non-Newtonian effect up into two portions: one as the Newtonian result and the other as an effective external source. This arrangement takes the advantage in remaining fixed relaxation time during the whole course of numerical simulation that can avoid the potential numerical instability caused by the relaxation time approaches to 1/2, an inherent difficulty in the conventional lattice Boltzmann methods using varying relaxation times for the non-Newtonian effect. Macroscopically, consistency of the proposed model with the equations of motion for the three target non-Newtonian models is demonstrated through the technique of Chapman–Enskog multi-scale expansion. The feasibility and accuracy of the method are examined by comparing with the analytical solutions of the two-dimensional Poiseuille flows based on the power-law and Casson models. The results show that the velocity profiles agree very well with those of analytical solutions and the error analyses demonstrate that the proposed scheme is with second-order accuracy. The present approach also demonstrates its superiority over the conventional lattice Boltzmann method in the extent of numerical stability for simulating the power-law-based shear-thinning flows. The straightforwardness in scheme derivation and implementation renders the present approach as a potential method for the complex non-Newtonian flows.

Investigation on Heat and Mass Transfer in a Evaporator of a Capillary-Pumped Loop with the Lattice Boltzmann Method: Pore Scale Simulation

A two-dimensional transient numerical model based on the lattice Boltzmann method (LBM) for the global evaporator of a capillary-pumped loop (CPL) is proposed to describe heat and mass transfer with evaporation in the porous wick, heat conduction in the cover plate, and heat transfer in the vapor groove. To indicate the stochastic phase distribution characteristics of most porous wick, the quartet structure generation set (QSGS) is introduced for generating more realistic microstructures of porous media. By using the present lattice Boltzmann algorithm along with the porous structure, the heat and mass transfer of an evaporator on pore scale can be predicted without resorting to any empirical parameters determined case by case. The energy equations for entire evaporator are solved as a conjugate problem, which are solved by means of a spatially varying relaxation time in the lattice Boltzmann model and the liquid flow is driven via the interfacial mass flux. A convective boundary condition considering the latent heat during the evaporation on the interface is introduced into the lattice Boltzmann model based on the nonequilibrium extrapolation rule. Especially, the bounce-back rule and the equilibrium rule of the LBM are, respectively, introduced to deal with the momentum boundary conditions inside the porous wick and on the evaporation interface in order to ensure the stability and the efficiency of the LBM model. Numerical results corresponding to different working conditions and different working fluids are presented, which provide guidance for the evaporator design of a CPL system.

Growth and characterization of glycinium oxalate (GOX) single crystals

Glycinium oxalate (GOX) single crystals were grown by slow cooling solution growth method. The X-ray diffraction and Fourier transform infra red studies confirm the grown crystal. The hardness values of GOX are found to be higher than glycine. The increase in hardness may be due to the C–H---O bonding. The UV–Visible studies show that GOX crystals can be used for nonlinear applications. The dielectric measurement indicates that the GOX crystals have domains of varying sizes and varying relaxation time. The SHG output of GOX was 210 mV at given pulse energy of 5 mJ/s and KDP was 240 mV.

Experimental Investigation of Rate-Dependent Inner Hysteresis Loops in PZT

AbstractThe rate-dependence of piezoelectric materials resulting from the kinetics of domain switching is an important factor that needs to be included in realistic modeling attempts. This paper provides a systematic study of the rate-dependent hysteresis behavior of a commercially available PZT stack actuator. Experiments covering full as well as minor loops are conducted at different loading rates with polarization and strain recorded. In addition, the creep behavior at different constant levels of the electric field is observed. This provides evidence of kinetics being characterized by strongly varying relaxation times that can be associated with different switching mechanisms.

A hybrid kinetic–fluid model for solving the Vlasov–BGK equation

Our purpose is to derive a model for charged particles which combines a kinetic description of the fast particles with a fluid description of the slow ones. In a previous paper, a similar model was derived from a kinetic BGK equation that uses a constant relaxation time and does not include the effect of an electric field. In this paper, we consider a more general kinetic equation including an electric field and a varying relaxation time. Fast particles will be described through a collisional kinetic equation of Vlasov–BGK type while thermal particles will be modeled by a hydrodynamic model. Then, we construct a numerical scheme for this model and validate the approach by presenting various numerical tests.

Field-induced reorientation dynamics of a surface stabilized ferroelectric liquid crystal mixture

Time-resolved measurements of electro-optical response and Fourier-transform infrared absorption have been employed to study the submolecular motion of a surface stabilized ferroelectric liquid crystal (SSFLC) mixture during a field-induced reorientation process. All observed submolecular groups were found to rotate in unison about the layer normal in a steady d.c. field. In a transient situation, the FLC director can respond rapidly to a pulsed driving field. However, the orientation distribution was found to spread at first and then slowly converge to the new direction of the FLC director. When the field is switched off, all the core groups relax to a steady-state direction with varying relaxation times. The results reveal that submolecular fragments of different molecular species in the FLC mixture move correlatively in a steady d.c. field and during a field-induced reorientation process.

Orientational relaxation in cross-linked nonlinear optical polymers

Stability of the electro-optic coefficient of a poled and cross-linked nonlinear optical polymer is reported at 85, 100, and 110 °C. The observed decay, which is due to orientational relaxation of the nonlinear optical dyes in the films, is discussed in terms of several proposed models. The introduction of a continuously varying relaxation time, which occurs when considering physical aging during the stability tests, is observed to account for orientational relaxation over a long time period.

Interligand electron transfer and transition state dynamics in Ru(II)trisbipyridine

The interligand electron transfer (ILET) dynamics in the excited metal-to-ligand charge transfer state of RuIItrisbipyridine have been studied using picosecond time-resolved absorption polarization spectroscopy. The ILET dynamics have been studied in several solvents with widely varying relaxation times, and over the temperature range of −85 °C to room temperature. The solvents studied include acetonitrile, propanol, ethylene glycol, and glycerol. The results show that ILET is relatively fast in acetonitrile (∼47 ps), slower and nonexponential in propanol and ethylene glycol (∼30–200 ps), and fast in glycerol (∼30 ps). The glycerol results are roughly temperature independent. These results can be understood in terms of a model in which photoexcitation places the system near the ILET transition state and solvent relaxation competes with ILET in the nascent distribution. Following solvent relaxation a slower, steady state (probably transition state theory) rate is obtained.

Q switching and mode locking the Nd3+-glass laser with the nickel dithienes

Measurement of the relaxation time for transient bleaching of solutions of bis-(4-dimethylaminodithiobenzil)-nickel (BDN) explains observed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> -switch and mode-locking behavior. A pronounced solvent effect permits varying relaxation time by a factor of 5 down to times short enough to be considered for mode locking in special circumstances.