Characteristic Time Tau Research Articles

Microwave volt-impedance spectroscopy of semiconductor structure

Microwave voltage-impedance spectroscopy is used to study a semiconductor structure in the form of a doped n-GaAs film grown on a conducting n^+-GaAs substrate with a buffer sublayer. A system of concentric barrier contacts is formed on the structure surface. A technique has been developed for measuring complex impedance spectrum Z(f,U) of the sample as a function of DC bias voltage U. Spectra Z(f,U) were measured using a Cascade Microtech probe station in the frequency range 0.01-40 GHz with a lateral resolution of 15-30 μm at U=0-10 V. The main electrophysical characteristics of a semiconductor film were determined from the spectra: type, concentration and mobility of free charge carriers, electrical conductivity. An excess resistance was found in the range f=0.1-20 GHz. This effect is interpreted as the deep states (traps) recharging for two types of traps --- low-frequency l and high-frequency h with characteristic time tau_l=10-9 s, tau_h=4.2·10-11 s. A model description is proposed that explains the characteristic shape of the trap resistance spectrum, its dependence on the contact area and voltage U. Keywords: microwave band, near field, impedance, semiconductor, barier contact, deep states, electrophysical characteristics.

The Reissner\u2013Nordstr\xf6m black hole with the fastest relaxation rate

Numerous numerical investigations of the quasinormal resonant spectra of Kerr-Newman black holes have revealed the interesting fact that the characteristic relaxation times tau ({bar{a}},{bar{Q}}) of these canonical black-hole spacetimes can be described by a two-dimensional function {{bar{tau }}}equiv tau /M which increases monotonically with increasing values of the dimensionless angular-momentum parameter {bar{a}}equiv J/M^2 and, in addition, is characterized by a non-trivial (non-monotonic) functional dependence on the dimensionless charge parameter {bar{Q}}equiv Q/M. In particular, previous numerical investigations have indicated that, within the family of spherically symmetric charged Reissner–Nordström spacetimes, the black hole with {bar{Q}}simeq 0.7 has the fastest relaxation rate. In the present paper we use analytical techniques in order to investigate this intriguing non-monotonic functional dependence of the Reissner–Nordström black-hole relaxation rates on the dimensionless physical parameter {bar{Q}}. In particular, it is proved that, in the eikonal (geometric-optics) regime, the black hole with {bar{Q}}={{sqrt{51-3sqrt{33}}}over {8}}simeq 0.73 is characterized by the fastest relaxation rate (the smallest dimensionless relaxation time {{bar{tau }}}) within the family of charged Reissner–Nordström black-hole spacetimes.

CHARACTERIZING THE RADIO-X-RAY CONNECTION IN GRS 1915+105

We analyzed radio and X-ray observations of GRS 1915+105, between May 1995 and June 2006, focusing on the times characterized by radio flares and cycles of hard dips-soft spikes in the X-ray lightcurve. Assuming these flares to be discrete ejections, we applied a plasmon model to the radio data, with good agreement with the lightcurves. We fitted a total of 687 radio flares with a standard model of a plasmon. We found that the distribution of width is t_0=1160 s with an rms deviation of 360 s, while that of the amplitude is S_{max}=59 mJy with an rms deviation of 28 mJy. The distribution of width is thus rather peaked, while that of the amplitude not. Regarding radio and X-ray links, this study confirms previous observations on smaller datasets, namely that X-ray cycles of hard dips-soft spikes are always followed by radio flares. A strong correlation is found between the length of X-ray "dips" in the X-ray lightcurves, and the amplitude and fluence of the subsequent radio oscillations. A model of an exponential rise of the form L_{15 GHz}(Delta t) = L_{max} (1-exp(-(Delta t - Delta t_{min})/tau) is in good agreement with the observations, with the maximum fluence L_{max} of the order 70 Jy.s, and the characteristic time tau of the order 200-500 s. We discuss possible physical interpretations of this correlation, regarding the nature of the ejected material, and the physical process responsible for the ejection.

Concentration fluctuations in a binary glass former investigated by x-ray photon correlation spectroscopy

We investigate structure and dynamics of concentration fluctuations in the binary glass former methyl-tetrahydrofuran and oligomeric methyl metacrylate by photon correlation spectroscopy with partially coherent x-rays from a synchrotron source. Although the system is macroscopically well miscible and optically clear in the full temperature range, calorimetric and dielectric measurements reveal two distinct glass transition temperatures. The relaxation of long range concentration fluctuations turns out to be diffusive and exponential only well above the upper glass transition temperature. As the characteristic time tau(cf) for concentration fluctuations shows a much weaker temperature dependence than the alpha-relaxation both traces finally intersect upon lowering the temperature. Thus, close to T(g), the concentration fluctuations show pronounced features of out-of-equilibrium dynamics such as compressed relaxation functions and a crossover to a ballistic wave vector dependence of tau(cf), like previously observed in various soft matter systems. Moreover, the analysis of time-resolved correlation functions reveals that the relaxation of concentration fluctuations around T(g) involves pronounced dynamic heterogeneities.

Granular medium impacted by a projectile: Experiment and model

We present a minimal discrete model for the propagation of energy through a 3D granular medium impacted by a particulate projectile. In this model, energy is transferred from grain to grain via binary collision events. This description can be successfully applied to the analysis of the collision process of a single spherical particle (of diameter donto a half space of granular medium composed of similarly sized particles. The model reproduces remarkably well the experimental observations. Besides, the present model provides a clear picture of the mechanism of energy propagation. A continuum version of the model, where the energy propagation from bead to bead is characterized by a diffusion equation, is derived. The diffusion coefficient is found to be proportional to the ratio of d(2) to the characteristic collision time Tau(c) . The numerical value of the coefficient of proportionality is essentially governed by the geometry of the packing. This paper constitutes an extension of a previously published letter (J. Crassous, D. Beladjine, A. Valance, Phys. Rev. Lett. 99, 248001 (2007)).

Critical dynamics of lateral and transversal phase separations in bilayer biomembranes and surfactants

We consider bilayer biomembranes or surfactants made of two chemically incompatible amphiphile molecules, which may laterally or transversely phase separate into macrodomains, upon variation of some suitable parameter (temperature, lateral pressure, etc.). The purpose is an extensive study of the dynamics of both lateral and transverse phase separations, when the bilayer is suddenly cooled down from a high initial temperature towards a final one very close to the spinodal point. The critical dynamics are investigated through the partial dynamic structure factors of different species. Using a two-order parameter field theory, where the two fields are the composition fluctuations of one component in the leaflets of the bilayer, combined with an extended van Hove approach that is based on two coupled Langevin equations (with noise), we exactly compute these dynamic structure factors. We first find that the dynamics is governed by two time scales. The longest one, Tau, can be related to the thermal correlation length, Xi ~ Sigma|T - T(c)|(-1/2), by Tau ~ Xi(z), with the dynamic critical exponent z = 4, where Sigma is an atomic length scale, T the absolute temperature, and T(c) its critical value. The characteristic time Tau can be interpreted as the time required for the formation of the final macrophase domains. The second time scale is rather shorter, and can be viewed as the short time during which the unlike phospholipids execute local motion. Second, we demonstrate that the dynamic structure factors obey exact scaling laws, and depend on three lengths, namely the wavelength q(-1) (q is the wave vector modulus), the correlation length Xi, and a length scale R(t) ~ t(1/z) (z = 4) representing the size of macrophase domains at time t. Of course, the two lengths Xi and R(t) coincide at the final time Tau at which the bilayer reaches its final equilibrium state. Finally, the present work must be considered as a natural extension of our previously published one dealing with the study of lateral and transverse phase separations from a static point of view.

Particle migration induced by confinement of colloidal suspensions along the gravitational direction

We confine charged spheres in cells with the smallest dimension along the direction of gravity ĝ. The particles are density mismatched with the surrounding medium and sediment along ĝ with typical Péclet numbers of Pe approximately 10(-3). After a certain time, we find that the number of particles N increases near both upper and lower plates until a characteristic time tau is reached; above this time N plateaus. We attribute the observed phenomenology to collective particle motions driven by gravity and mediated by hydrodynamic interactions; these could yield formation of swirls made of particles with correlated velocities that could eventually drive the particles towards the upper plate. The characteristic time for these migrations scales with plate-to-plate separation Lz as tau approximately Lz1.2, exactly as the characteristic decay time of velocity fluctuations in sedimentation processes [S. Y. Tee, Phys. Rev. Lett. 89, 054501 (2002)], despite that in these experiments the smallest cell dimension is perpendicular to ĝ and 7<Pe<50. In the absence of gravitational field, the observed particle migrations disappear, emphasizing the key role played by gravity in these experiments.

Selective advantage for sexual reproduction

This paper develops a simplified model for sexual reproduction within the quasispecies formalism. The model assumes a diploid genome consisting of two chromosomes, where the fitness is determined by the number of chromosomes that are identical to a given master sequence. We also assume that there is a cost to sexual reproduction, given by a characteristic time tau(seek) during which haploid cells seek out a mate with which to recombine. If the mating strategy is such that only viable haploids can mate, then when tau(seek) = 0, it is possible to show that sexual reproduction will always out compete asexual reproduction. However, as tau(seek) increases, sexual reproduction only becomes advantageous at progressively higher mutation rates. Once the time cost for sex reaches a critical threshold, the selective advantage for sexual reproduction disappears entirely. The results of this paper suggest that sexual reproduction is not advantageous in small populations per se, but rather in populations with low replication rates. In this regime, the cost for sex is sufficiently low that the selective advantage obtained through recombination leads to the dominance of the strategy. In fact, at a given replication rate and for a fixed environment volume, sexual reproduction is selected for in high populations because of the reduced time spent finding a reproductive partner.

Source apportionment modeling of volatile organic compounds in streams

It often is of interest to understand the relative importance of the different sources contributing to the concentration c(w) of a contaminant in a stream; the portions related to sources 1, 2, 3, etc. are denoted c(w,1), c(w2), c(w3), etc. Like c(w), the fractions alpha1 = c(w,1)/c(w), alpha2 = c(w,2)/c(w), alpha3 = c(w,3)/c(w), etc. depend on location and time. Volatile organic compounds (VOCs) can undergo absorption from the atmosphere into stream water or loss from stream water to the atmosphere, causing complexities affecting the source apportionment (SA) of VOCs in streams. Two SA rules are elaborated. Rule 1: VOC entering a stream across the air/water interface exclusively is assigned to the atmospheric portion of c(w). Rule 2: VOC loss by volatilization, flow loss to groundwater, in-stream degradation, etc. is distributed over c(w,1), c(w,2), c(w3), etc. in proportion to their corresponding alpha values. How the two SA rules are applied, as well as the nature of the SA output for a given case, will depend on whether transport across the air/water interface is handled using the net flux F convention or using the individual fluxes J convention. Four hypothetical stream cases involving acetone, methyl-tert-butyl ether (MTBE), benzene, chloroform, and perchloroethylene (PCE) are considered. Acetone and MTBE are sufficiently water soluble from air for a domestic atmospheric source to be capable of yielding c(w) values approaching the common water quality guideline range of 1 to 10 microg/L. For most other VOCs, such levels cause net outgassing (F > 0). When F > 0 in a given section of stream, in the net flux convention, all of the alpha(j) for the compound remain unchanged over that section while c(w) decreases. A characteristic time tau(d) can be calculated to predict when there will be differences between SA results obtained by the net flux convention versus the individual fluxes convention. Source apportionment modeling provides the framework necessary for comparing different strategies for mitigating contamination at points of interest along a stream.

Hole growth in freely standing polystyrene films probed using a differential pressure experiment

We have probed the whole chain mobility of polymer molecules confined to freely standing films by measuring the flow of gas through holes growing in the films at elevated temperatures using a differential pressure experiment. Freely standing polystyrene films were measured for the temperature range 92 degrees C<T<105 degrees C for films with two different molecular weights Mw=717 x 10(3) and 2240 x 10(3) , with thicknesses 51 nm<h<97 nm . This range of film thicknesses is of particular interest because large reductions in the glass transition temperature Tg have been measured previously for freely standing PS films in this thickness range. We find that hole formation and growth, and therefore substantial chain mobility, does not occur until temperatures close to the bulk value of the glass transition temperature T(bulk)g. The characteristic growth times tau for the thinnest films, which have reduced values of Tg, are not substantially less than those for thicker films, and we find that these small differences in tau can be understood in terms of the bulk phenomenon of shear thinning. We also show that the viscosity at the edge of the hole inferred from the characteristic growth times obtained in this and previous studies exhibit shear thinning with reduced shear strain rates beta that span twelve orders of magnitude.

The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T(0) only affects the relaxation up to T(0)+T(Lag), where T(Lag) is proportional to the logarithm of the annealing time t(A). A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E=(317+1.17xi)x10(3) J/mol, and therefore must have a characteristic relaxation time tau which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t)=[Formula: see text]N(xi)e(-t/tau(T,xi))dxi, in which both the relaxation time tau(T,xi) and the distribution function N(xi) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.

Dynamical scaling of single chains on adsorbing substrates: Diffusion processes

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time tau of the fluctuations of a free chain in a good solvent grows as tau approximately N(a), where the coefficient a obeys a=2nu+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state tau(perpendicular), the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; tau(perpendicular) is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by tau(parallel) approximately N(2nu(2)+1)L(-2Delta(nu/nu)), where nu(2) is the Flory exponent in two dimensions, nu is the Flory exponent in three dimensions, and Deltanu=nu(2)-nu. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time.

NMR as a Probe of the Relaxation of the Magnetization in Magnetic Molecules

We investigate the time autocorrelation of the molecular magnetization M(t) for three classes of magnetic molecules (antiferromagnetic rings, grids, and nanomagnets), in contact with the phonon heat bath. For all three classes, we find that the exponential decay of the fluctuations of M(t) is characterized by a single characteristic time tau(T,B) for not too high temperature T and field B. This is reflected in a nearly single-Lorentzian shape of the spectral density of the fluctuations. We show that such fluctuations are effectively probed by NMR, and that our theory explains the recent phenomenological observation by Baek et al. [Phys. Rev. B 70, 134434 (2004)] that the Larmor-frequency dependence of 1/T(1) data in a large number of AFM rings fits to a single-Lorentzian form.

NMR polarization echoes in a nematic liquid crystal.

We have modified the polarization echo (PE) sequence through the incorporation of Lee-Goldburg cross polarization steps to quench the 1H-1H dipolar dynamics. In this way, the 13C becomes an ideal local probe to inject and detect polarization in the proton system. This improvement made possible the observation of the local polarization P(00)(t) and polarization echoes in the interphenyl proton of the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline. The decay of P(00)(t) was well fitted to an exponential law with a characteristic time tau(C) approximately 310 micros. The hierarchy of the intramolecular dipolar couplings determines a dynamical bottleneck that justifies the use of the Fermi Golden Rule to obtain a spectral density consistent with the structural parameters. The time evolution of P(00)(t) was reversed by the PE sequence generating echoes at the time expected by the scaling of the dipolar Hamiltonian. This indicates that the reversible 1H-1H dipolar interaction is the main contribution to the local polarization decrease and that the exponential decay for P(00)(t) does not imply irreversibility. The attenuation of the echoes follows a Gaussian law with a characteristic time tau(phi) approximately 527 micros. The shape and magnitude of the characteristic time of the PE decay suggest that it is dominated by the unperturbed homonuclear dipolar Hamiltonian. This means that tau(phi) is an intrinsic property of the dipolar coupled network and not of other degrees of freedom. In this case, one cannot unambiguously identify the mechanism that produces the decoherence of the dipolar order. This is because even weak interactions are able to break the fragile multiple coherences originated on the dipolar evolution, hindering its reversal. Other schemes to investigate these underlying mechanisms are proposed.

Origin of pulsars with 0.1 s &lt; P &lt; 0.3 s and 5 × 105years &lt; τ &lt; 107years after the second supernova explosion in high-mass X-ray binaries

The origin of a part of the single pulsars with relatively low magnetic fields B < 1E12 G and with characteristic times Tau < 1E7 yr is established. Such pulsars occur as a result of the disruption of High Mass X-ray Binary Systems after a second Supernova explosion. In these binaries mass accretion onto the surface of X-ray pulsars leads to the decrease of the magnetic field from its initial value B ~ 1E12-1E13 G down to B < 1E12 G similar to the processes in Low Mass X-ray Binaries.

Critical exponents of isotropic-hexatic phase transition in the hard-disk system.

The hard-disk system is studied by observing the nonequilibrium relaxation behavior of a bond-orientational order parameter. The density dependence of characteristic relaxation time tau is estimated from the finite-time scaling analysis. The critical point between the fluid and the hexatic phase is refined to be 0.899 (1) by assuming the divergence behavior of the Kosterlitz-Thouless transition. The value of the critical exponent eta is also studied by analyzing the fluctuation of the order parameter at the criticality and estimated as eta=0.25 (2). These results are consistent with the prediction by the Kosterlitz-Thouless-Halperin-Nelson-Young theory.

Critical behavior of thermal relaxation near a breakdown point.

At a composition far above the percolation threshold, the resistance of a composite sample increases with time due to Joule heating as a constant current of a sufficiently large value is passed through the sample. If the current is less than a certain breakdown current (I(b)) the resistance eventually reaches a steady value with a characteristic relaxation time tau(h). The latter diverges with current I as tau(h) approximately (1-I(2)/I(2)(b))(-z). The value of the exponent z displays large fluctuations leading to unusual scaling of the relaxation time. It is shown that the results lead to important conclusions about the nature of breakdown phenomena.

Granular friction, Coulomb failure, and the fluid-solid transition for horizontally shaken granular materials.

We present the results of an extensive series of experiments, molecular dynamics simulations, and models that address horizontal shaking of a layer of granular material. The goal of this work was to better understand the transition between the "fluid" and "solid" states of granular materials. In the experiments, the material-consisting of glass spheres, smooth and rough sand-was contained in a container of rectangular cross section, and subjected to horizontal shaking of the form x=A sin(omega(t)). The base of the container was porous, so that it was possible to reduce the effective weight of the sample by means of a vertical gas flow. The acceleration of the shaking could be precisely controlled by means of an accelerometer mounted onboard the shaker, plus feedback control and lockin detection. The relevant control parameter for this system was the dimensionless acceleration, Gamma=Aomega(2)/g, where g was the acceleration of gravity. As Gamma was varied, the layer underwent a backward bifurcation between a solidlike state that was stationary in the frame of the shaker and a fluidlike state that typically consisted of a sloshing layer of maximum depth H riding on top of a solid layer. That is, with increasing Gamma, the solid state made a transition to the fluid state at Gamma(cu) and once the system was in the fluid state, a decrease in Gamma left the system in the fluidized state until Gamma reached Gamma(cd)<Gamma(cu). In the fluidized state, the flow consisted of back and forth sloshing at the shaker frequency, plus a slower convective flow along the shaking direction and additionally in the horizontal direction transverse to the shaking direction. Molecular dynamics simulations show that the last of these flows is associated with shear and dilation at the vertical sidewalls. For Gamma<Gamma(cu) and in the solid state, there was a "gas" of free particles sliding on the surface of the material. These constituted much less than one layer's worth of particles in all cases. If these "sliders" were suppressed by placing a thin strip of plastic on the surface, the hysteresis was removed, and the transition to fluidization occurred at a slightly lower value than Gamma(cd) for the free surface case. The hysteresis was also suppressed if a vertical gas flow from the base was sufficient to support roughly 40% of the weight of the sample. Both the transition to the fluid state from the solid and the reverse transition from the fluid to the solid were characterized by similar divergent time scales. If Gamma was increased above Gamma(cu) by a fractional amount epsilon=(Gamma-Gamma(cu))/Gamma(cu), where epsilon was small, there was a characteristic time tau=Aepsilon(-beta) for the transition from solid to fluid to occur, where beta is 1.00+/-0.06. Similarly, if Gamma was decreased below Gamma(cd) in the fluidized state by an amount epsilon=(Gamma-Gamma(cd))/Gamma(cd), there was also a transient time tau=Bepsilon(-beta), where beta is again indistinguishable from 1.00. In addition, the amplitudes A and B are essentially identical. By placing a small "impurity" on top of the layer, consisting of a heavier particle, we found that the exponent beta varied as the impurity mass squared and changed by a factor of 3. A simple Coulomb friction model with friction coefficients mu(k)<mu(s) for the fluid and solid states predicts a reversible rather than hysteretic transition to the fluid state, similar to what we observe with the addition of the small overload from a plastic strip. In an improved model, we provide a relaxational mechanism that allows the friction coefficient to change continuously between the low and high values. This model produces the hysteresis seen in experiments.

Two-photon excitation and photolysis by pulsed laser illumination modelled by spatially non-uniform reactions with simultaneous diffusion.

Two-photon absorption in the focus of a pulsed laser has the potential for localized photolysis of caged compounds, generating high concentrations of neurotransmitters, hormones and messengers. The concentrations of cage, intermediates and products in the femtolitre focal volume depend on reaction rates and diffusional exchange with the external volume. This problem of reaction with diffusion was analysed with analytical and numerical methods to determine simple relations between parameters useful in the design and interpretation of experiments. The diffraction-limited laser spot is approximated well by a sphere, radius A, in diffusional exchange with either an infinite uniform medium, representing extracellular photolysis, or within a non-permeable sphere, a "cell" of radius B, representing intracellular photolysis. Photolysis is modelled as sequential irreversible reactions, with either the excitation step alone, rate constant k(e), or with a subsequent "dark" reaction, rate constant k(p). For extracellular photolysis, steady-state depletion of a cage averaged in a spherical spot increases hyperbolically with k(e) with half-maximum depletion at k(e) = K0.5 = 2.5 D/A2, where D is the diffusion coefficient. With measured parameters for spot size A = 0.3 microm and diffusion D = 800 microm2/s, K0.5 = 22,200 s(-1). The optimal exposure for localized photolysis is the characteristic diffusion time tau = A2/D, 113 micros in this example, and is the time taken to reach 57% of steady state in the diffusion-limited case. In the two-step model, with excitation and "dark" reaction steps, rate constants both exceeding K0.5 are necessary to generate 50% of maximal product concentration in the illuminated volume. High concentrations of photolysis products depend particularly on a high excitation rate constant (k(e) > K0.5), and localization of the products requires fast dark reactions (k(p) > K0.5). If products diffuse faster than the cage, their steady-state concentrations are decreased, and concentration transients may occur. For localized intracellular photolysis, the duration of exposure that generates product concentration at the cell boundary, B, less than 10% of the spot concentration should be shorter than 0.043(B/A)3tau, and is determined by diffusion.

Diffusion as a mixing mechanism in granular materials.

We present several numerical results on granular mixtures. In particular, we examine the efficiency of diffusion as a mixing mechanism in these systems. The collisions are inelastic and to compensate the energy loss, we thermalize the grains by adding a random force. Starting with a segregated system, we show that uniform agitation (heating) leads to a uniform mixture of grains of different sizes. We define a characteristic mixing time tau(mix), and study theoretically and numerically its dependence on other parameters like the density. We examine a model for bidisperse systems for which we can calculate some physical quantities. We also examine the effect of a temperature gradient and demonstrate the appearance of an expected segregation.