Showing papers by "Pawan Kumar published in 1994"

Femtosecond solvation dynamics of water

Abstract: THE timescale of the response of solvent molecules to electronic rearrangement of solute molecules has a critical influence on the rates of chemical reactions in liquids1–10. In particular, if the solvent cannot adapt quickly enough to this rearrangement as the reactants pass through the transition state, the evolving products may recross the free-energy barrier, reducing the reaction rate. Computer simulations have shown11–18 that the response of a solvent to a change in solute charge distribution is strongly bimodal: there is an initial ultrafast response owing to inertial (mainly libra-tional) motions of the solvent molecules, followed by a slow component owing to diffusive motions. Water seems to be by far the 'fastest' solvent studied so far: simulations predict that well over half of the solvation response for atomic solutes is inertial, happening on a timescale of about 20 femtoseconds12,13. The presence of this ultrafast component implies that solvent friction plays an important role in many aqueous charge-transfer processes9,10,19–21. Experimental verification of this prediction has been lacking, however, in part because of the difficulty of obtaining sufficient time resolution. Here we present experimental measurements of the ultrafast solvation dynamics of a coumarin salt in water. When considered in conjunction with computer simulations, our results demonstrate that a solvent response on a timescale faster than 50 fs can dominate aqueous solvation dynamics.

Excitation of solar p-modes

Abstract: We investigate the rates at which energy is supplied to individual p-modes as a function of their frequencies v and angular degrees l. The observationally determined rates are compared with those calculated on the hypothesis that the modes are stochastically excited by turbulent convection. The observationally determined excitation rate is assumed to be equal to the product of the mode's energy E and its (radian) line width Г. We obtain E from the mode's mean square surface velocity with the aid of its velocity eigenfunction. We assume that Г measures the mode's energy decay rate, even though quasi-elastic scattering may dominate true absorption. At fixed l, EГ rises as v^7 at low v, reaches a peak at v ≈ 3.5 mHz, and then declines as v^(-4•4) at higher v. At fixed v, EГ exhibits a slow decline with increasing l. To calculate energy input rates, P_ α, we rely on the mixing-length model of turbulent convection. We find entropy fluctuations to be about an order of magnitude more effective than the Reynolds stress in exciting p-modes. The calculated P_ α mimic the v^7 dependence of EГ at low v and the v^(-4•4) dependence at high v. The break of 11.4 powers in the v-dependence of EГ across its peak is attributed to a combination of (1) the reflection of high-frequency acoustic waves just below the photosphere where the scale height drops precipitously and (2) the absence of energy-bearing eddies with short enough correlation times to excite high-frequency modes. Two parameters associated with the eddy correlation time are required to match the location and shape of the break. The appropriate values of these parameters, while not unnatural, are poorly constrained by theory. The calculated P_ α can also be made to fit the magnitude of EГ with a reasonable value for the eddy aspect ratio. Our results suggest a possible explanation for the decline of mode energy with increasing l at fixed v. Entropy fluctuations couple to changes in volume associated with the oscillation mode. These decrease with decreasing n at fixed v, becoming almost zero for the ƒ-mode.

Properties of acoustic sources in the Sun

Abstract: The power spectrum of solar acoustic oscillations shows peaks extending out to frequencies much greater than the acoustic cutoff frequency of approximately 5.3 mHz, where waves are no longer trapped. Kumar & Lu (1991) proposed that these peaks arise from the interference of traveling waves which are generated by turbulent convection. According to this model, the frequencies of the peaks in the power spectrum depend on the static structure of the Sun as well as the radial location of the sources. Kumar & Lu used this idea to determine the depth of the acoustic sources. However, they ignored dissipative effects and found that the theoretically computed power spectrum was falling off much more rapidly than the observed spectrum. In this paper, we include the interaction of radiation with acoustic waves in the computation of the power spectrum. We find that the theoretically calculated power spectra, when radiative damping is included are in excellent agreement with the observed power spectra over the entire observed frequency range of 5.3 to 7.5 mHz above the acoustic cutoff frequency. Moreover, by matching the peak frequencies in the observed and theoretical spectra we find the mean depth of acoustic sources to be 140 +/- 60 km below the photosphere. We show that the spectrum of solar turbulence near the top of the solar convection zone is consistent with the Kolmogorov spectrum, and that the observed high frequency power spectrum provides strong evidence that the acoustic sources in the Sun are quadrupolar. The data, in fact, rules out dipole sources as significant contributors to acoustic wave generation in the Sun. The radial extent of the sources is poorly determined and is estimated to be less than about 550 km.

Causality in Strong Shear Flows

Abstract: It is well known that the standard transport equations violate causality when gradients are large or when temporal variations are rapid. We derive a modified set of transport equations that satisfy causality. These equations are obtained from the underlying Boltzmann equation. We use a simple model for particle collisions which enables us to derive moment equations non-perturbatively, i.e. without making the usual assumption that the distribution function deviates only slightly from its equilibrium value. We apply the model to two problems: particle diffusion and viscous transport. In both cases we show that signals propagate at a finite speed and therefore that the formalism obeys causality. When the velocity gradient is large on the scale of a mean free path, the viscous shear stress is suppressed relative to the prediction of the standard diffusion approximation. The shear stress reaches a maximum at a finite value of the shear amplitude and then decreases as the velocity gradient increases. In the case of a steady Keplerian accretion disk with hydrodynamic turbulent viscosity, the stress-limit translates to an upper bound on the Shakura-Sunyaev $\alpha$-parameter, namely $\alpha<0.07$. The limit on $\alpha$ is much stronger in narrow boundary layers where the velocity shear is larger than Keplerian.

Causality in Strong Shear Flows

Abstract: It is well known that the standard transport equations violate causality when gradients are large or when temporal variations are rapid. We derive a modified set of transport equations that satisfy causality. These equations are obtained from the underlying Boltzmann equation. We use a simple model for particle collisions which enables us to derive moment equations non-perturbatively, i.e. without making the usual assumption that the distribution function deviates only slightly from its equilibrium value. We apply the model to two problems: particle diffusion and viscous transport. In both cases we show that signals propagate at a finite speed and therefore that the formalism obeys causality. When the velocity gradient is large on the scale of a mean free path, the viscous shear stress is suppressed relative to the prediction of the standard diffusion approximation. The shear stress reaches a maximum at a finite value of the shear amplitude and then decreases as the velocity gradient increases. In the case of a steady Keplerian accretion disk with hydrodynamic turbulent viscosity, the stress-limit translates to an upper bound on the Shakura-Sunyaev $\alpha$-parameter, namely $\alpha<0.07$. The limit on $\alpha$ is much stronger in narrow boundary layers where the velocity shear is larger than Keplerian.

Effect of nonlinear interactions on p-mode frequencies and line widths

Abstract: We calculate the effect of nonlinear interactions among solar acoustic modes upon the modal frequencies and energy loss rates (or line widths). The frequency shift for a radial p-mode of frequency 3 mHz is found to be about -0.5 µHz. The magnitude of nonlinear frequency shift increases more rapidly with frequency than the inverse mode mass (mode mass is defined as the ratio of energy in the mode to its surface velocity amplitude squared). This frequency shift is primarily due to nonresonant three-mode interactions and is dominated by high l surface gravity waves (ƒ-modes) and p-modes. The line width of a radial p-mode of frequency 3 mHz, due to resonant nonlinear interactions, is about 0.3 µHz. This result is consistent with that of Kumar & Goldreich (1989). We also find, in agreement with these authors, that the most important nonlinear interactions of trapped p-modes involve ƒ-modes and high-frequency p-modes (frequency greater than about 5 mHz) which propagate in the solar photosphere. Thus, using the arguments advanced by Kumar & Goldreich (1989), we conclude that nonlinear couplings cannot saturate the overstable solar p-modes at their small observed amplitudes. Both the nonlinear frequency shifts and line widths, at a fixed frequency, are proportional to the inverse of mode mass which for modes of degree greater than about 100 is ~ l^(0.8). Therefore, the frequency of an ƒ-mode of l = 1000, due to nonlinear interactions, is decreased by approximately 0.4%.

Limits on coronal reflection using high-frequency solar oscillations

Abstract: Acoustic waves in the Sun with frequencies above about 5.3 mHz can propagate in the chromosphere. We examine imaged solar intensity data for evidence of reflection of these waves in the upper chromosphere, where the temperature increases by a large factor over a short distance. Our method is to compare the observed and theoretically derived frequency spacings between peaks in the power spectrum. We find that our theoretical frequencies provide the best fit to the data when the reflection in the upper atmosphere is eliminated. In particular, the model of Kumar (1993b), which includes the source depth, and radiative damping, in the calculation of power spectra but ignores chromospheric reflection, gives peak frequencies that are in good agreement with the observations. For acoustic waves of frequency greater than 6 mHz we put an upper limit to the reflectivity of chromosphere and corona, using our method, of about 10%. At a given spherical harmonic degree, the frequency spacing between peaks in the data generally decreases with increasing frequency, because the lower turning point of the waves is moving inward. However, between 5 and 5.5 mHz the frequency spacing increases slightly. This feature is probably associated with the acoustic cutoff frequency in the solar atmosphere, i.e., it indicates a transition from trapped waves to propagating waves. We are able to reproduce the observed behavior by a crude modeling of the solar atmosphere. Further study of these peaks should provide an independent way of exploring the mean structure of the solar atmosphere, particularly around the temperature minimum region.