Time scales for transitions between free-energy minima of a dense hard-sphere system

Time scales associated with activated transitions between glassy metastable states of a free-energy functional appropriate for a dense hard-sphere system are calculated by using a new Monte Carlo method for the local density variables. In particular, we calculate the time the system, initially placed in a shallow glassy minimum of the free-energy, spends in the neighborhood of this minimum before making a transition to the basin of attraction of another free-energy minimum. This time scale is found to increase as the average density is increased. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This time scale does not show any evidence of increasing with sample size

Dynamo models of grand minima

Since a universally accepted dynamo model of grand minima does not exist at the present time, we concentrate on the physical processes which may be behind the grand minima. After summarizing the relevant observational data, we make the point that, while the usual sources of irregularities of solar cycles may be sufficient to cause a grand minimum, the solar dynamo has to operate somewhat differently from the normal to bring the Sun out of the grand minimum. We then consider three possible sources of irregularities in the solar dynamo: (i) nonlinear effects; (ii) fluctuations in the poloidal field generation process; (iii) fluctuations in the meridional circulation. We conclude that (i) is unlikely to be the cause behind grand minima, but a combination of (ii) and (iii) may cause them. If fluctuations make the poloidal field fall much below the average or make the meridional circulation significantly weaker, then the Sun may be pushed into a grand minimum.

Origin of grand minima in Sunspot cycles

One of the most striking aspects of the 11-year sunspot cycle is that there have been times in the past when some cycles went missing, a most well-known example of this being the Maunder minimum during 1645-1715. Analyses of cosmogenic isotopes (C-14 and Be-10) indicated that there were about 27 grand minima in the last 11 000 yrs, implying that about 2.7% of the solar cycles had conditions appropriate for forcing the Sun into grand minima. We address the question of how grand minima are produced and specifically calculate the frequency of occurrence of grand minima from a theoretical dynamo model. We assume that fluctuations in the poloidal field generation mechanism and in the meridional circulation produce irregularities of sunspot cycles. Taking these fluctuations to be Gaussian and estimating the values of important parameters from the data of the last 28 solar cycles, we show from our flux transport dynamo model that about 1-4% of the sunspot cycles may have conditions suitable for inducing grand minima.

Fluctuations in the alpha-effect and grand solar minima

The parameters of a special type of alpha-effect known in dynamo theory as the Babcock-Leighton mechanism are estimated using the data of sunspot catalogs. The estimates support the presence of the Babcock-Leighton alpha-effect on the Sun. Fluctuations of the alpha-effect are also estimated. The fluctuation amplitude appreciably exceeds themean value, and the characteristic time for the fluctuations is comparable to the period of the solar rotation. Fluctuations with the parameters found are included in a numericalmodel for the solar dynamo. Computations show irregular changes in the amplitudes of the magnetic cycles on time scales of centuries and millennia. The calculated statistical characteristics of the grand solar minima and maxima agree with the data on solar activity over the Holocene.

Studies of grand minima in sunspot cycles by using a flux transport solar dynamo model

We propose that grand minima in solar activity are caused by simultaneous fluctuations in the meridional circulation and the Babcock-Leighton mechanism for the poloidal field generation in the flux transport dynamo model. We present the following results: (a) fluctuations in the meridional circulation are more effective in producing grand minima; (b) both sudden and gradual initiations of grand minima are possible; (c) distributions of durations and waiting times between grand minima seem to be exponential; (d) the coherence time of the meridional circulation has an effect on the number and the average duration of grand minima, with a coherence time of about 30 yr being consistent with observational data. We also study the occurrence of grand maxima and find that the distributions of durations and waiting times between grand maxima are also exponential, like the grand minima. Finally we address the question of whether the Babcock-Leighton mechanism can be operative during grand minima when there are no sunspots. We show that an alpha-effect restricted to the upper portions of the convection zone can pull the dynamo out of the grand minima and can match various observational requirements if the amplitude of this alpha-effect is suitably fine-tuned.

Free energy landscape of a dense hard-sphere system

The topography of the free energy landscape in phase space of a dense hard-sphere system characterized by a discretized free energy functional of the Ramakishnan-Yussouff form is investigated numerically using a specially devised Monte Carlo procedure. We locate a considerable number of glassy local minima of the free energy and analyze the distributions of the free energy at a minimum and an appropriately defined phase-space "distance" between different minima. We find evidence for the existence of pairs of closely related glassy minima("two-level systems"). We also investigate the way the system makes transitions as it moves from the basin of attraction of a minimum to that of another one after a start under nonequilibrium conditions. This allows us to determine the effective height of free energy barriers that separate a glassy minimum from the others. The dependence of the height of free energy barriers on the density is investigated in detail. The general appearance of the free energy landscape resembles that of a putting green: relatively deep minima separated by a fairly flat structure. We discuss the connection of our results with the Vogel-Fulcher law and relate our observations to other work on the glass transition.

Ground and Excited State Intramolecular Proton Transfer in Salicylic Acid: an Ab Initio Electronic Structure Investigation

Energetics of the ground and excited state intramolecular proton transfer in salicylic acid have been studied by ab initio molecular orbital calculations using the 6-31G** basis set at the restricted Hartree-Fock (RHF) and configuration interaction-single excitation (CIS) levels and also using the semiempirical method AM1 at the RHF level as well as with single and pair doubles excitation configuration interaction spanning eight frontier orbitals (PECI = 8). The ab initio potential energy profile for intramolecular proton transfer in the ground state reveals a single minimum corresponding to the primary form, in the first excited singlet state, however, there are two minima corresponding to the primary and tautomeric forms, separated by a barrier of similar to 6 kcal/mol, thus accounting for dual emission in salicylic acid. Electron density changes with electronic excitation and tautomerism indicate no zwitterion formation. Changes in spectral characteristics with change in pH, due to protonation and deprotonation of salicylic acid, are also accounted for, qualitatively. Although the AM1 calculations suggest a substantial barrier for proton transfer in the ground as well as the first excited state of SA, it predicts the transition wavelength in near quantitative accord with the experimental results for salicylic acid and its protonated and deprotonated forms.

The hemispheric asymmetry of solar activity during the last century and the solar dynamo

We believe the Babcock-Leighton process of poloidal field generation to be the main source of irregularity in the solar cycle. The random nature of this process may make the poloidal field in one hemisphere stronger than that in the other hemisphere at the end of a cycle. We expect this to induce an asymmetry in the next sunspot cycle. We look for evidence of this in the observational data and then model it theoretically with our dynamo code. Since actual polar field measurements exist only from the 1970s, we use the polar faculae number data recorded by Sheeley (1991, 2008) as a proxy of the polar field and estimate the hemispheric asymmetry of the polar field in different solar minima during the major part of the twentieth century. This asymmetry is found to have a reasonable correlation with the asymmetry of the next cycle. We then run our dynamo code by feeding information about this asymmetry at the successive minima and compare the results with observational data. We find that the theoretically computed asymmetries of different cycles compare favorably with the observational data, with the correlation coefficient being 0.73. Due to the coupling between the two hemispheres, any hemispheric asymmetry tends to get attenuated with time. The hemispheric asymmetry of a cycle either from observational data or from theoretical calculations statistically tends to be less than the asymmetry in the polar field (as inferred from the faculae data) in the preceding minimum. This reduction factor turns out to be 0.43 and 0.51 respectively in observational data and theoretical simulations.

Structure of 7-methyl-1(2)a,1(6)a,3(4)a-trihomocubane-1(6)a,3(4)a-dione,star-c12h12o2- a case of enantiomeric and rotational disorder

M r = 188.22, monoclinic, P21/n, a = 6.219 (2), b= 10.508 (2), c=7.339 (1)A, t= 107.64 (2) °, V= 457 ,/k 3, Z = 2, D m - - 1.360 (3), D x = 1.366 (2)Mgm -3, ~,(MoKa) = 0.7107/~, #= 0.053 mm -I, F(000) = 200, T= 293 K. Final R = 5.8% for 614 significant reflections. The molecule, which does not possess a centre of symmetry, occupies a crystallographic centre of symmetry because of the statistical enantiomeric and rotational disorder. Latticeenergy calculations, based on van der Waals attractive and repulsive potentials, clearly show minima at the observed disordered positions.

Stereochemical studies on cyclic peptides. XIII. Energy minimization studies on cyclic hexapeptides having hydrogen bonds

The basic cyclic hexapeptide conformations which accommodate hydrogen bonded β and γ turns in the backbone have been worked out using stereochemical criteria and energy minimization procedures. It was found that cyclic hexapeptides can be made up of all possible combinations of 4 ± 1 hydrogen bonded types I, I', II and II' β turns, giving rise to symmetric conformations having twofold and inversion symmetries as well as nonsymmetric structures. Conformations having exclusive features of 3 ± 1 hydrogen bonded γ turns were found to be possible in threefold and S6 symmetric cyclic hexapeptides. The results show that the cyclic hexapeptides formed by the linking of two β turn tripeptide fragments differ mainly in (a) the hydrogen bonding scheme present in the β turn tripeptides and (b) the conformation at the α-carbon atoms where the two tripeptide fragments link. The different hydrogen bonding schemes found in the component β turns are: 1) a β turn with only a 4 ± 1 hydrogen bond, 2) a type I or I' β turn with 4 ± 1 and 3 ± 1 hydrogen bonds occurring in a bifurcated form and 3) a type II or II' β turn having both the 4 ± 1 and the 3 ± 1 hydrogen bonds with the same acceptor oxygen atom. The conformation at the linking α-carbon atoms was found to lie either in the extended region or in the 3 ± 1 hydrogen bonded γ turn or inverse γ turn regions. Further, the threefold and the S6 symmetric conformations have three γ turns interleaved by three extended regions or three inverse γ turns, respectively. The feasibility of accommodating alanyl residues of both isomeric forms in the CHP minima has been explored. Finally, the available experimental data are reviewed in the light of the present results.

Magnetic Field Induced Instabilities In Localized Two-Dimensional Electron Systems

The results of extensive transport studies in localized regime of mesoscopic two-dimensional electron systems (2DES) with varying disorder are presented. A quick overview of previously achieved result is given. The main focus is on the observation of density dependent instabilities manifested by strong resistance oscillations induced by high perpendicular magnetic fields B-perpendicular to. While the amplitude of the oscillations is strongly enhanced with increasing B-perpendicular to, their position in electron density remains unaffected. The temperature dependence of resistivity shows a transition from an activated behaviour at high temperature to a saturated behaviour at low T. In the positions of resistance minima, the T dependence can even become metal-like (d rho/dT > 0). The activation energies obtained from the high T behaviour exhibit a formation of plateaux in connection with the resistance oscillations when analyzed as a function of electron density. We suggest the interplay between a strongly interacting electron phase and the background disorder as a possible explanation for our observation.

An accurate method for the experimental evaluation of the acoustical impedance of a black box

Among different methods, the transmission-line or the impedance tube method has been most popular for the experimental evaluation of the acoustical impedance of any termination. The current state of method involves extrapolation of the measured data to the reflecting surface or exact locations of the pressure maxima, both of which are known to be rather tricky. The present paper discusses a method which makes use of the positions of the pressure minima and the values of the standing-wave ratio at these points. Lippert's concept of enveloping curves has been extended. The use of Smith or Beranek charts, with their inherent inaccuracy, has been altogether avoided. The existing formulas for the impedance have been corrected. Incidentally, certain other errors in the current literature have also been brought to light.Subject Classification: 85.20.

Conformational analysis of cyclo (l-cystine

Conformational analysis of cyclo(L-cystine) shows that the diketopiperazine ring has to exist only in the boat form. With this geometry, the molecule can adopt two distinct forms differing mainly in the chirality of the disulphide bridge. In both the P- and M-models, corresponding to dihedral angles of nearly + 90° and —90° respectively about the S-S bond, the molecule displays an approximate two-fold symmetry. According to our semi-empirical energy calculations, the minimum energy of the M-model is —9.2 kcal/mol, only 0.3 kcal/mol lower than that of the P-model. Because the difference between the two minima is so small, neither form is clearly superior to the other. However, the number of low energy conformations of the M-model in the allowed conformational space is significantly larger than that of the P-model by a ratio of 3 to 1, and therefore the former is likely to be thermodynamically favoured.

Measurement of the acoustical impedance of a black box at low frequencies using a shorter impedance tube

For the experimental evaluation of the acoustical impedance of a termination by the impedance-tube method at low frequencies, the length of the impedance tube is a problem. In the present paper, the method of exact analysis of standing waves developed by the authors for the stationary medium as well as for mean flow, has been extended for measurement of the acoustical impedance of a termination at low frequencies. The values of the tube attenuation factor and the wave number at the low frequency of interest are established from the experiment conducted, with the given impedance tube, at a higher frequency. Then, exciting the tube at the desired low frequency it is sufficient to measure sound pressure at three differenct locations (not necessarily the minima) in order to evaluate reflection coefficient and hence the impedance of the termination at that frequency.

Method for evaluation of the acoustical impedance of a black box, with or without mean flow, measuring pressures at fixed positions

The transmission-line or the impedance-tube method for the measurement of the acoustic impedance of any termination involves a search for various minima and maxima of pressure. For this purpose, arrangement has to be made for the microphone to travel along the length of the impedance tube, and this complicates the design of the tube considerably. The present paper discusses a method which consists in evaluating the tube attenuation factor at any convenient frequency by making use of measured SPL's at two (or more) fixed locations with a rigid termination, calculating the tube attenuation factor and wave number at the required frequency of interest with or without mean flow (as applicable), and finally evaluating the impedance of the given termination by measuring and using SPL's at three (or more) fixed locations. Thus, the required impedance tube is considerably smaller in length, simpler in design, easier to manufacture, cheaper in cost and more convenient to use. The design of the tube is also discussed. Incidentally, it is also possible to evaluate the impedance at any low frequency without having to use a larger impedance tube.