Response of thermal source in a transversely isotropic thermoelastic half-space with mass diffusion by using a finite element method

The two-dimensional problem of generalized thermoelastic diffusion material with thermal and diffusion relaxation times is investigated in the context of the Lord-Shulman theory.As an application of the problem,a particular type of thermal source is considered and the problem is solved numerically by using a finite element method.The components of displacement,stress,temperature distribution,chemical potential,and mass concentration are obtained.The resulting quantities are depicted graphically for a special model.An appreciable effect of relaxation times is observed on various resulting quantities.     

Observation of size-dependent thermalization in CdSe nanocrystals using time-resolved photoluminescence spectroscopy

We report heat dissipation times in semiconductor nanocrystals of CdSe. Specifically, a previously unresolved, subnanosecond decay component in the low-temperature photoluminescence decay dynamics exhibits longer decay lifetimes (tens to hundreds of picoseconds) for larger nanocrystals as well as a size-independent, ~25-meV spectral shift. We attribute the fast relaxation to transient phonon-mediated relaxation arising from nonequilibrium acoustic phonons. Following acoustic phonon dissipation, the dark exciton state recombines more slowly via LO-phonon assistance resulting in the observed spectral shift. The measured relaxation time scales agree with classical calculations of thermal diffusion, indicating that interfacial thermal conductivity does not limit thermal transport in these semiconductor nanocrystal dispersions.     

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.     

Thermal and chemical diffusion in the rapid solidification of binary alloys

Solidification of binary alloys is characterized by the necessity to reject away from the advancing front two conserved quantities: the latent heat released at the solid-liquid interface and the solute atoms that cannot be accommodated in the solid phase. As thermal diffusion is much faster than chemical diffusion, the latter is generally assumed to be the rate limiting mechanism for the process, and the problem is addressed through the isothermal approximation. In the present paper we use the phase-field model to study the planar growth of a solid germ, nucleated in its undercooled melt. We focus on the effects of a noninstantaneous thermal relaxation. The steady growth predicted at large supersaturation in the isothermal limit is prevented. Depending on the value of the Lewis number the growth rate is limited by either mass or heat diffusion; in the latter case we observe a sharp transition between two different regimes, in which originates a nonmonotonic time dependence of the interface temperature. The effects of this transition reflect in the composition of the solidified alloy.     

A study of the polymerization of styrene by Rayleigh-Brillouin spectroscopy

The Rayleigh-Brillouin spectrum has been used to probe the kinetics of the thermal polymerization of styrene. The behaviour of the velocity and attenuation of hypersound in the medium is consistent with frequency-dependent bulk and shear viscosities. The characteristic relaxation times are dependent on the degree of polymerization.

The relaxation times continuously increase as the polymerization proceeds. In the initial stages of the experiment the measured sound velocity and absorption coefficients correspond to the zero frequency values, and as the polymerization proceeds these quantities go over to the infinite frequency values.     

Stabilization of thermal lattice Boltzmann models

A three-dimensional thermal lattice-Boltzmann model with two relaxation times to separately control viscosity and thermal diffusion is developed. Numerical stability of the model is significantly improved using Lax-Wendroff advection to provide and adjustable time step. Good agreement with a conventional fiitedifference Navier-Stokes solver is obtained in modeling compressible Rayleigh-Bénard convestion when boundary conditions are treated similarly.     

Field Free Relaxation of the Electron Component in the Temporally Decaying Molecular Gas Plasmas Hydrogen and Nitrogen

This paper deals with the temporal relaxation of the electron component of weakly ionized, anisothermal and collision dominated plasma in the molecular gases hydrogen and nitrogen after jump-like switching off of the electric field starting from stationary states. The investigation is based upon a solution of the non-stationary Boltzmann equation using a finite difference approach of the resulting partial differential equation. Besides the temporal development of the energy distribution and of some macroscopic quantities of the electrons especially the characteristic relaxation times and their physical nature are discussed and compared with former results on the relaxation in an inert gas plasma.     

The influence of measurement and relaxation time on flux jumps in high temperature superconductors

The influence of the magnetization and relaxation time on flux jumps in high temperature superconductors (HTSC) under varying magnetic field is studied using the fundamental electromagnetic field equations and the thermal diffusion equation; temperature variety corresponding to flux jump is also discussed. We find that for a low sweep rate of the applied magnetic field, the measurement and relaxation times can reduce flux jump and to constrain the number of flux jumps, even stabilizing the HTSC, since much heat produced by the motion of magnetic flux can transfer into coolant during the measurement and relaxation times. As high temperature superconductors are subjected to a high sweep rate or a strong pulsed magnetic field, magnetization undergoes from stability or oscillation to jump for different pause times. And the period of temperature oscillation is equal to the measurement and relaxation time.     

Measurement of thermal diffusivity by magnetic resonance imaging

Nuclear magnetic resonance (NMR) may be used for monitoring temperature changes within samples based on measurements of relaxation times, the diffusion coefficient of liquids, proton resonance frequency or phase shifts. Such methods may be extended to the explicit measurement of the thermal diffusivity of materials by NMR imaging. A method based on measuring nuclear spin phase shifts or changes in the equilibrium nuclear magnetization has been developed for measuring transient thermal diffusion effects and thermal diffusivity with potential applications in NMR thermotherapy and materials science. In this method, a thermal pulse is applied to a medium, and the resultant temporal variations of the nuclear spin phase or of the magnitude of the nuclear magnetization produced by the thermal pulse are monitored at a spatial distance. The results obtained on common fluids agree well with the data from other methods.     

Deuterium NMR lineshape and relaxation study of a hydrated cross-linked polymer

A combined study of²H nuclear magnetic resonance lineshape and spin-lattice and spin-spin relaxation times as functions of temperature and the amount of hydration water in a cross-linked copolymer of sucrose and 1,4-butadienol diglycidyl ether in the hydrogel phase is reported. The results show strong evidence that the onset of the relaxation mechanisms is driven by anomalous water molecule diffusion depending on both temperature and the hydration degree of the hydrogel. In addition, these results are correlated with the transitions observed by differential thermal analysis.     

Photon correlation spectroscopy in micellar solutions of sodium and potassium oleate

Photon correlation spectroscopy was applied to concentrated micellar solutions of sodium and potassium oleate. In rod-like micellar phases the relaxation times of the concentration fluctuation were measured as a function of temperature. A remarkable temperature dependence of the relaxation time was found in the isotropic phase of rod-like micelles. This suggests that the rotational diffusion is strongly reduced by the entanglement effect. The thermal expansion coefficient of rod-like micelles was determined.     

Hamiltonian and Brownian systems with long-range interactions: IV. General kinetic equations from the quasilinear theory

We develop the kinetic theory of Hamiltonian systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a general kinetic equation that can be applied to spatially inhomogeneous systems and that takes into account memory effects. This equation is valid at order 1/N in a proper thermodynamic limit and it coincides with the kinetic equation obtained from the BBGKY hierarchy. For N→+∞, it reduces to the Vlasov equation governing collisionless systems. We describe the process of phase mixing and violent relaxation leading to the formation of a quasistationary state (QSS) on the coarse-grained scale. We interpret the physical nature of the QSS in relation to Lynden-Bell’s statistical theory and discuss the problem of incomplete relaxation. In the second part of the paper, we consider the relaxation of a test particle in a thermal bath. We derive a Fokker-Planck equation by directly calculating the diffusion tensor and the friction force from the Klimontovich equation. We give general expressions of these quantities that are valid for possibly spatially inhomogeneous systems with long correlation time. We show that the diffusion and friction terms have a very similar structure given by a sort of generalized Kubo formula. We also obtain non-Markovian kinetic equations that can be relevant when the auto-correlation function of the force decreases slowly with time. An interesting factor in our approach is the development of a formalism that remains in physical space (instead of Fourier space) and that can deal with spatially inhomogeneous systems.     

Measuring pore connectivity by pulsed field gradient diffusion editing with hydrocarbon gases

Measurements of time-dependent diffusion are performed on a rock sample saturated first with water, then methane and finally ethane. The gases were selected because their increased diffusivities and relaxation times allow probing greater length scales than water and because of their practical relevance. The nuclear magnetic resonance measurements employed pulse field gradient diffusion editing pulse sequences, allowing analysis of D(t) as a function of relaxation time. Very different D(t) behaviors are observed for different relaxation times, including indications of connected pore networks at moderate relaxation times.     

Nonlinear diffusion and Nelson-Brown movement

The nonlinear diffusion process, which can be described as the Nelson-Brown motion, is considered. The obtained equation becomes the classical linear diffusion equation for small relaxation times, and for long relaxation times it is transferred into the Schrödinger-like equation. The possible nonequilibrium stationary states are discussed.     

Measurement of the Relaxation Rates ofH Longitudinal Modes

Accurate decay rate measurements for longitudinal modes are essential for many of the methods proposed for investigating molecular dynamics by NMR. However, the effects of cross relaxation often make it impossible to determine accurate values for these quantities. A method is presented that enables the effects of cross relaxation to be largely eliminated from such measurements. Its reliability is assessed by comparing the values for internuclear distances that can be determined from the resulting relaxation rates with values obtained using other methods. Other consequences of using this technique include an increased robustness of experiments to short (i.e., <5T₁) relaxation times and the ability to make multiple “selective” relaxation measurements simultaneously.     

Thermal Lens Phenomenon Studied by the Z-Scan Technique: Measurement of the Thermal Conductivity of Highly Absorbing Colloidal Solutions

We discuss the thermal lens phenomenon in high-absorbing colloidal systems, studied by using the Z-scan technique. The characteristics of the experimental setup to avoid undesirable effects are presented, in particular when pulsed laser beam is used. We show that a cumulative effect may appear in the experiment with chopped laser beams and compromise the results obtained with this technique. This artefact is more significative when colloidal suspensions are investigated. These materials have different characteristic times of heat and mass diffusion, which must be carefully considered to choose the appropriate time interval for the laser pulse and the time between pulses. Two experimental cases with a chopped laser beam, with and without a shutter, are discussed. The sample employed is a magnetic colloidal suspension (a ferrofluid). This sample has magnetic nanoparticles electrically charged in an aqueous solution with free ions and counter ions. Besides the thermal lens effect, charge and mass diffusion may take place when the sample is illuminated by the Gaussian beam, which imposes a thermal gradient on it. The results show that, with the experimental setup without a shutter, the sample does not achieve a complete relaxation between two laser pulses. This generates a measurable cumulative effect after the sample is illuminated during a relatively long period of time. A time modulation with longer time interval between chopped pulses allows the complete relaxation of the sample. This procedure is important for the correct analysis of the thermal lens effect. Reliable values of the thermal conductivity of the sample in different temperatures are obtained and discussed.     

Solution to the Glarum model with a finite relaxation rate

The one-dimensional version of the Glarum model of target relaxation by diffusing defects is generalized by considering a finite relaxation rate upon an encounter defect-target. This eliminates the difficulties associated with the instantaneous relaxation of the targets initially occupied by a defect. The diffusion and relaxation processes are described in terms of the master equation for a continuous-time random walk. An exact solution valid for all times and relaxation rates is obtained by the use of the van Kampen-Oppenheim method. The transition from exponential relaxation at short times to fractional exponential behaviour at long times is described in detail.     

Nuclear magnetic spin-rotational relaxation times for symmetric molecules

It is shown that the problem of calculating times related to nuclear magnetic spin-rotational interactions may be solved for the symmetric rotator model of a molecule by employing the method already proposed in a general manner for asymmetric molecules that undergo rotational thermal motion. Expressions are derived for the spin-rotational correlation time and for the contributions arising from spin-rotational interactions to the longitudinal and transverse relaxation times.     

Non-Markovian Diffusion Over a Saddle with a Generalized Langevin Equation

The diffusion over a simple parabolic barrier is exactly solved with a non-Markovian Generalized Langevin Equation. For a short relaxation time, the problem is shown to be similar to a Markovian one, with a smaller effective friction. But for longer relaxation time, the average trajectory starts to oscillate and the system can have a very fast first passage over the barrier. For very long relaxation times, the solution tends to a zero-friction limit. PACS: 02.50.EY, 05.40.−a, 25.70.Jj     

Nonlinear dielectric response and thermodynamic heterogeneity in liquids

If large amplitude time-dependent fields (e.g., dielectric, magnetic, mechanical) are applied to a sample that displays relaxational modes, some energy of the external field is absorbed by the slow degrees of freedom. The weak coupling of these modes to the phonon bath leads to long persistence times of the resulting higher fictive temperature. Assuming heterogeneities regarding dielectric and thermal relaxation times, extremely strong nonlinear dielectric effects are predicted and experimentally verified. For glycerol at T = 213 K, the dielectric loss measured at 280 kV/cm increases by more than 6% over its low-field value. This nonlinearity shows a characteristic frequency dependence and implies that dielectric and thermal time constants are locally correlated in viscous liquids.