Modeling phase transition for compressible two-phase flows applied to metastable liquids

The seven-equation model for two-phase flows is a full non-equilibrium model, each phase has its own pressure, velocity, temperature, etc. A single value for each property, an equilibrium value, can be achieved by relaxation methods. This model has better features than other reduced models of equilibrium pressure for the numerical approximations in the presence of non-conservative terms. In this paper we modify this model to include the heat and mass transfer. We insert the heat and mass transfer through temperature and Gibbs free energy relaxation effects. New relaxation terms are modeled and new procedures for the instantaneous temperature and Gibbs free energy relaxation toward equilibrium is proposed. For modeling such relaxation terms, our idea is to make use of the assumptions that the mechanical properties, the pressure and the velocity, relax much faster than the thermal properties, the temperature and the Gibbs free energy, and the ratio of the Gibbs free energy relaxation time to the temperature relaxation time is extremely high. All relaxation processes are assumed to be instantaneous, i.e. the relaxation times are very close to zero. The temperature and the Gibbs free energy relaxation are used only at the interfaces. By these modifications we get a new model which is able to deal with transition fronts, evaporation fronts, where heat and mass transfer occur. These fronts appear as extra waves in the system. We use the same test problems on metastable liquids as in Saurel et al. [R. Saurel, F. Petitpas, R. Abgrall, Modeling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607 (2008) 313–350]. We have almost similar results. Computed results are compared to the experimental ones of Simões-Moreira and Shepherd [J.R. Simões-Moreira, J.E. Shepherd, Evaporation waves in superheated dodecane, J. Fluid Mech. 382 (1999) 63–86]. A reasonable agreement is achieved. In addition we consider the six-equation model with a single velocity which is obtained from the seven-equation model in the asymptotic limit of zero velocity relaxation time. The same procedure for the heat and mass transfer is used with the six-equation model and a comparison is made between the results of this model with the results of the seven-equation model.     

Continuum model for low temperature relaxation of crystal steps

High and low temperature relaxation of crystal steps are described in a unified picture, using a continuum model based on a modified expression of the step-free energy. Results are in agreement with experiments and Monte Carlo simulations of step fluctuations and monolayer cluster diffusion and relaxation. In an extended model where mass exchange with neighboring terraces is allowed, step transparency and a low temperature regime for unstable step meandering are found.     

Rotational stretched exponential relaxation in random trap–barrier model

The relaxation behavior of complex-disordered systems, such as spin glasses, polymers, colloidal suspensions, structural glasses,and granular media, has not been clarified. Theoretical studies show that relaxation in these systems has a topological origin. In this paper, we focus on the rotational stretched exponential relaxation behavior in complex-disordered systems and introduce a simple phase space model to understand the mechanism of the non-exponential relaxation of these systems. By employing the Monte Carlo simulation method to the model, we obtain the rotational relaxation function as a function of temperature. We show that the relaxation function has a stretched exponential form under the critical temperature while it obeys the Debye law above the critical temperature.     

Hierarchical description for a non-Markoff relaxation process

A phenomenal model is proposed in this paper to describe a non-Markoff relaxation process. The main feature of the model is the fractal time concept introduced to take account of the coupling of a relaxation mode with a heat bath. The theoretical investigation indicates that a weakly non-Markoff relaxation process can be related to a set of hierarchically distributed Markoff relaxation processes and the fractal exponential law exp [?(t/τ)^1?σ] is the character of a non-Markoff relaxation process. Calculations about the temperature and time scale dependence of the exponent σ have been made, and comparison with recent experiments is also given.     

Estimation of temperature elevation generated by ultrasonic irradiation in biological tissues using the thermal wave method

In most previous models,simulation of the temperature generation in tissue is based on the Pennes bio-heat transfer equation,which implies an instantaneous thermal energy deposition in the medium.Due to the long thermal relaxation time τ(20 s-30 s) in biological tissues,the actual temperature elevation during clinical treatments could be different from the value predicted by the Pennes bioheat equation.The thermal wave model of bio-heat transfer(TWMBT) defines a thermal relaxation time to describe the tissue heating from ultrasound exposure.In this paper,COMSOL Multiphysics 3.5a,a finite element method software package,is used to simulate the temperature response in tissues based on Pennes and TWMBT equations.We further discuss different factors in the bio-heat transfer model on the influence of the temperature rising and it is found that the temperature response in tissue under ultrasound exposure is a rising process with a declining rate.The thermal relaxation time inhibits the temperature elevation at the beginning of ultrasonic heating.Besides,thermal relaxation in TWMBT leads to lower temperature estimation than that based on Pennes equation during the same period of time.The blood flow carrying heat dominates most to the decline of temperature rising rate and the influence increases with temperature rising.On the contrary,heat diffusion,which can be described by thermal conductivity,has little effect on the temperature rising.     

A study of the parameterisation of the uniaxial model of superparamagnetic relaxation

Mössbauer spectra of the iron storage protein ferritin taken over a range of temperatures exhibit the characteristic behaviour of superparamagnetic relaxation, and can be used to investigate a model for the superparamagnetic relaxation of a sample of small magnetic particles. A computer program is used to calculate a series of Mössbauer spectra based on the relaxation model, and these theoretical spectra are then fitted simultaneously to all the variable temperature experimental spectra, with the parameters of the uniaxial anisotropy model as the only variables.     

Temperature dependence of proton relaxation times in vitro

Accurate measurement of tissue relaxation characteristics is dependent on many factors, including field strength and temperature. The purpose of this study was to evaluate the relationship between sample temperature, viscosity and proton spin-lattice relaxation time (T1) and spin-spin relaxation time (T2). A review of two basic models of relaxation the simple molecular motion model and the fast exchange two state model is given with reference to their thermal dependencies. The temperature dependence for both T1 and T2 was studied on a 0.15 Tesla whole body magnetic resonance imager. Thirteen samples comprising both simple and complex materials were investigated by using a standard spin-echo (SE) technique and a modified Carr-Purcell-Meiboom-Gill (CPMG) multi-echo sequence. A simple linear relationship between T1 and temperature was observed for all samples over the range of 20 degrees C to 50 degrees C. There is an inverse relationship between viscosity and T1 and T2. A quantity called the temperature dependence coefficient (TDC) is introduced and defined as the percent rate of change of the proton relaxation time referenced to a specific temperature. The large TDC found for T1 values, e.g. 2.37%/degrees C for CuSO4 solutions and 3.59%/degrees C for light vegetable oils at 22 degrees C, indicates that a temperature correction should be made when comparing in-vivo and in-vitro T1 times. The T2 temperature dependence is relatively small.     

Photoexcited electron dynamics in Kondo insulators and heavy fermions

We have studied the photoexcited carrier relaxation dynamics in the Kondo insulator SmB6 and the heavy fermion metal YbAgCu4 as a function of temperature and excitation level. The dynamic response is found to be both strongly temperature dependent and nonlinear. The data are analyzed with a Rothwarf-Taylor bottleneck model, where the dynamics are governed by the presence of a narrow gap in the density of states near the Fermi level. The remarkable agreement with the model suggests that carrier relaxation in a broad class of heavy electron systems (both metals and insulators) is governed by the presence of a (weakly temperature dependent) hybridization gap.     

Die Temperaturabhängigkeit des Halleffektes von Palladium und Silber und ihre Beeinflussung durch Zusatzmetalle im Temperaturbereich von 50° bis 300°K

Hall effect measurements in the temperature range between 50 and 300°K are presented for Pd-alloys with Rh, Ag, Ti, Fe and Ag-alloys with Cd, In, Sn, Sb, Mg, Li and for the pure metals Pd and Ag too. They are compared with former measurements by other authors. Using the two band model for the Pd-alloys and Zimans eight cone model for the Ag-alloys the temperature dependence of the Hall constant is connected with a temperature dependent anisotropy of the relaxation time. For the Pd-alloys we use the free electron approximation for the s-electrons, which are the main current carriers. Since the s-band is coupled with the nearly occupied d-band by scattering processes, the relaxation time for the s-electrons may get anisotropic. This effect is stronger the lower the temperature. An anisotropic relaxation time may occur for the Ag-alloys too caused by large distortions of the Fermi surface towards the Brillouin zone faces.     

Bifurcation phenomenon in spin relaxation

Spin relaxation in a strong-coupling regime (with respect to the spin system) is investigated in detail based on the spin-boson model in a stochastic limit. We find a bifurcation phenomenon in temperature dependence of relaxation constants, which is never observed in the weak-coupling regime. We also discuss inequalities among the relaxation constants in our model and show the well-known relation 2gamma(T)>or=gamma(L), for example, for a wider parameter region than before.     

Dielectric investigation of the temperature dependence of the nonexponentiality of the dynamics of polymer melts

Using broad band dielectric spectroscopy (10(-5)-10(9) Hz), combining time domain and frequency domain techniques, we study the temperature dependence of the non-Debye character of the alpha relaxation of polymer melts in the glass transition temperature T(g) range. The alpha relaxation process is described in terms of the Kohlrausch-Williams-Watts relaxation function which has a single parameter beta to characterize the nonexponentiality of the relaxation. At high temperatures, beta remains nearly insensitive to temperature changes, whereas in the vicinity of T(g) a nearly linear increasing of beta with temperature is found. The temperature range where the change of the beta(T) behavior occurs is located for all the polymers investigated around 1.2T(g). Moreover, our results indicate a common value of beta approximately equal to 1/3 at the temperature where the relaxation time diverges. The beta(T) behavior near T(g) is discussed in terms of a "rugged landscape" phase space which allows us to rationalize both the beta(T) behavior observed as well as the similarities of our findings near T(g) with the results reported in simulations on Ising spin glasses and other model systems.     

The kinetics of the structural relaxation process in PHEMA-silica nanocomposites based on an equation for the configurational entropy

The enthalpy relaxation of polymer-silica nanocomposites prepared by simultaneous polymerization of poly(2-hydroxyethyl methacrylate) (PHEMA) and tetraethyloxysilane, TEOS, a silica precursor, is investigated. Both the glass transition temperature, T_g, and the temperature interval of the glass transition, ΔT _g , increase as the silica content in the sample does. Structural relaxation experiments show that the temperature interval in which conformational motions take place broadens as the silica content in the hybrid increases. A phenomenological model based on the evolution of the configurational entropy during the structural relaxation process, the SC model, has been used for determining the temperature dependence of the relaxation times during the process. The results show an increase of the fragility of the polymer as the silica content increases, a feature that can be related to the broadening of the distribution of relaxation times characterized by the β parameter of the stretched exponential distribution. On another hand the silica content increase produces a significant change of the relaxation times in the glassy state.     

Evidence of glass transition in thin films of maleic anhydride derivatives: Effect of the surfactant coadsorption

The glass transition temperature of poly (maleic anhydride-alt-1-octadecen) and poly (styreneco-maleic anhydride) cumene-terminated thin films has been measured by mechanical relaxation of Langmuir films of these polymers. The dynamical properties show glass-like features (non-Arrhenius relaxation times and non-Debye mechanical response) interpreted by the coupling model. The glass transition temperature values determined by a mechanical relaxation experiment (step-compression) agree very well with those obtained by surface potential measurements. It is found that the glass transition temperature values in thin films decrease by about 100K as compared with those corresponding to the bulk polymers. The coadsorption of the water-insoluble surfactant DODAB decreases the glass transition temperature.     

A simulation study of vibrational relaxation of I− 3 in liquids

The temperature dependence of the vibrational relaxation of a flexible model of triiodide in a Lennard-Jones solvent (xenon) has been studied using equilibrium molecular dynamics simulations. The internal dynamics of the ion is calculated from a previously published semi-empirical valence bond model with a limited number of basis states. Vibrational decorrelation rates of the symmetric and antisymmetric stretching modes were found from the time correlation functions of the normal coordinate velocities and the vibrational energy relaxation rates from the time correlation functions of the kinetic energy in each mode. The vibrational dephasing rates and the energy relaxation rates decrease slowly as the temperature is lowered and do not show a discontinuity when the fluid solidifies, although the reorientational diffusion rates change rapidly at low temperatures. In order to interpret the results, perturbation theory expressions for the relaxation rates were evaluated for simulations of a rigid model of the ion and found to agree well with the direct observations. These showed that, unusually, both the solvent force and its derivative, the solvent potential curvature, contribute to the dephasing of the symmetric mode. The relevant fluctuation correlation times are very short, which may explain the insensitivity of the vibrational relaxation to the state of the solvent.     

Determination of the Maier-Saupe strength parameter from dielectric relaxation experiments: a molecular dynamics simulation study

Molecular dynamics simulations have been performed to investigate the rotational motion in the nematic and isotropic phases of a model mesogenic system in which the interactions between the molecules are represented by the Gay-Berne potential. First-rank end-over-end rotational relaxation times, analogous to those measured using dielectric relaxation spectroscopy for real mesogens with a longitudinal electric dipole, have been determined as a function of temperature and density. The relaxation times at temperatures throughout the nematic region are found to be larger than the values extrapolated from the isotropic phase to the same temperature. The simulation results are compared with the extended Debye theory for dielectric relaxation in the nematic phase. This relates the reduction in the relaxation rate to the retardation factor which depends on the Maier-Saupe strength parameter, and in turn is defined uniquely by the second-rank orientational order parameter. The simulations indicate that the retardation factor at constant strength parameter is density dependent, a feature neglected in the relaxation theory. We compare the simulation results where possible with experiment.     

Frequency dependence of electron spin relaxation for threeS = 1/2 species doped into diamagnetic solid hosts

Electron spin lattice relaxation rates (1/T₁) were measured as a function of temperature at two or three microwave frequencies for threeS = 1/2 species in temperature ranges with different dominant relaxation processes. Between 10 and 50 K the contribution from the direct process to the relaxation rate was substantially greater at 94 than at 9.5 GHz for a vanadyl porphyrin doped into zinc tetratolylporphyrin. For bis(diethyldithiocarbamato)copper(II) doped into the diamagnetic Ni(II) analog the relaxation rate between 25 and 100 K is dominated by the Raman process and exhibits little frequency dependence between 9.2 and 94 GHz. For 4-hydroxy-2,2,6,6-tetramethylpiperidinoloxy (tempol) doped into a diamagnetic host the relaxation rate between about 40 and 100 K is dominated by the Raman process. In this temperature range, relaxation rates at 3.2, 9.2, and 94 GHz exhibit little frequency dependence. Above about 130 K, the relaxation rate for tempol decreases in the order S-band s> X-band > W-band. The relaxation rates in this temperature range fit a model in which 1/T₁ is dominated by a thermally activated process that is assigned as rotation of the methyl groups on the nitroxyl ring.     

Relaxation model of the orientational phase transition in fullerite C60

The model of thermal behavior of a thermoelastic medium is developed in the context of the Landau theory of phase transitions. In the framework of this model, two different problems are considered with allowance for order parameter relaxation: the problem of relatively slow uniform heating (cooling) of the medium under external hydrostatic pressure and the problem of order parameter relaxation at thermal isolation. A finite value of the relaxation constant τ of the order parameter is demonstrated to bring about the heating (cooling) rate dependence of the physical quantities, such as specific heat. The relaxation time of the order parameter is shown to be twice larger than the temperature relaxation time, as a consequence of the Landau expansion of the free energy.     

Electron paramagnetic resonance and relaxation of amorphous silicon below 1 K

Amorphous silicon, generated within crystalline Si by ²⁸Si⁺ ion implantation, exhibits an electron spin relaxation rate which varies with temperature as T^2.37 between 0.3 and 4.2 K. These results exclude the current model of a phonon-limited, direct relaxation mechanism in a-Si. A relaxation process, consistent with the known temperature variation, is outlined. EPR signal strengths, relative to a known paramagnet at temperatures near 1.2 and 0.4 K, put limits on an antiferromagnetic Curie-Weiss temperature of 0?θ?0.06 K.     

Internal dynamics of hydroxymethyl rotation from CH2 cross-correlated dipolar relaxation in methyl-beta-D-glucopyranoside

Conventional relaxation parameters (T1(-1), T2(-1), and NOE), obtained at different temperatures and magnetic fields, are reported for the hydroxymethyl (C6) carbon in methyl-beta-D-glucopyranoside in a D2O/DMSO cryosolvent. These data are interpreted with the Lipari-Szabo model. In addition, two-field measurements of longitudinal and spin-locked relaxation rates related to the cross-correlated carbon-proton dipole-dipole interactions for the same carbon are reported. The complete data set consisting the conventional and cross-correlated relaxation parameters is interpreted using a new "hybrid" approach, in which the Lipari-Szabo model for the auto-correlated spectral densities is combined with the two-site jump model for the cross-correlated spectral densities, with the global correlation time as a common parameter. The two-site jump rates thus obtained are in reasonable agreement with the ultrasonic relaxation measurements, and have reasonable temperature dependence.     

Effect of Pulse Width and Fluence of Femtosecond Laser on Electron--Phonon Relaxation Time

The electron phonon relaxation time as functions of pulse width and fluence of femtosecond laser is studied based on the two-temperature model. The two-temperature model is solved using a finite difference method for copper target. The temperature distribution of the electron and the lattice along with space and time for a certain laser fluence is presented. The time-dependence of lattice and electron temperature of the surface for different pulse width and different laser fluence are also performed, respectively. Moreover, the variation of heat-affected zone per pulse with laser Auence is obtained. The satisfactory agreement between our numerical results and experimental data indicates that the electron-phonon relaxation time is reasonably accurate with the influences of pulse width and Auence of femtosecond laser.