Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Concentration-dependent NMR and conductivity studies of (PEG)(x)NH4ClO4

Films of (PEG)(x)NH4ClO4 (x = 5 to 1000) were prepared and characterized. The physical properties are observed to be a sensitive function of concentration. Hygroscopicity increases as salt content increases. Conductivity peaks (sigma = 2.7 x 10(-6) S/cm) at x = 46. The H-1 NMR line width has a minimum at x = 46, while that of Cl-35 monotonically increases with salt concentration, indicating that the complex is essentially a protonic conductor.

Resonance de-enhancement in the 2(1)A(g) state of trans-azobenzene

We analyze the origin of de-enhancement for a number of vibrational modes in the 2(1)A(g) excited state of trans-azobenzene. We have used the time-dependent wave packet analysis of the RR intensities by including the multimode damping effects in the calculation. This avoids the use of unrealistically large values for the damping parameter. It is concluded that the de-enhancement is caused by the interference between the two uncoupled electronic states, and that the intensities observed under the so-called symmetry forbidden 2(1)A(g) <-- 1(1)A(g) transition are purely due to resonance excitation. It is also observed that the use of the time-dependent approach to study the de-enhancement effects caused by multiple electronic states on the RR intensities is not necessarily useful if one is interested in the structural dynamics.

Temperature-dependent valence-band photoemission spectra of La1-xSrxMnO3

We have studied the temperature dependence of the photoemission spectra of La1-xSrxMnO3 (x=0.0, 0.2, and 0.4) and found that the spectral line shape dramatically changes in the entire valence-band region, particularly for x=0.2 and 0.4. By contrast, the spectra of La0.6Sr0.4CoO3 show no significant temperature dependence. From comparison between the temperature-and composition-(x) dependent spectral changes and the temperature-composition phase diagram of La1-xSrxMnO3, we suggest that the changes are related to the degree of hole localization on oxygen p orbitals, which is influenced by electron-lattice coupling and magnetic correlations.

Drug-drug co-crystals: Temperature-dependent proton mobility in the molecular complex of isoniazid with 4-aminosalicylic acid

Two drug-drug co-crystals of the anti-tuberculosis drugs isoniazid (INH), pyrazinamide (PYR) and 4-aminosalicylic acid (PAS) are reported. The first is the 1 : 1 molecular complex of INH and PAS. The second is the monohydrate of the 1 : 1 complex of PYR and PAS. The crystal structures of both co-crystals are characterized by a number of hydrogen bonded synthons. Hydrogen bonding of the COOH center dot center dot center dot N-pyridine type is found in both cases. In the INH : PAS co-crystal, there are two symmetry independent COOH center dot center dot center dot center dot N-pyridine hydrogen bonds. In one of these, the H-atom is located on the carboxylic group and is indicative of a co-crystal. In the second case, partial proton transfer occurs across the hydrogen bond, and the extent of proton transfer depends on the temperature. This is more indicative of a salt. Drug-drug co-crystals may have some bearing in the treatment of tuberculosis.

Excited state structure and dynamics of p-benzoquinone and bromanil from time-resolved resonance Raman spectra and simulation

p-Benzoquinone and its halogen substituted derivatives are known to have differing reactivities in the triplet excited state. While bromanil catalyzes the reduction of octaethylporphyrin most efficiently among the halogenated p-benzoquinones, the reaction does not take place in presence of the unsubstituted p-benzoquinone (T. Nakano and Y. Mori, Bull. Chem. Soc. Jpn., 67, 2627 (1994)). Understanding of such differences requires a detailed knowledge of the triplet state structures, normal mode compositions and excited state dynamics. In this paper, we apply a recently presented scheme (M. Puranik, S. Umapathy, J. G. Snijders, and J. Chandrasekhar, J. Chem, Phys., 115, 6106 (2001)) that combines parameters from experiment and computation in a wave packet dynamics simulation to the triplet states of p-benzoquinone and bromanil. The absorption and resonance Raman spectra of both the molecules have been simulated. The normal mode compositions and mode specific excited state displacements have been presented and compared. Time-dependent evolution of the absorption and Raman overlaps for all the observed modes has been discussed in detail. In p-benzoquinone, the initial dynamics is along the C=C stretching and C-H bending modes whereas in bromanil nearly equal displacements are observed along all the stretching coordinates.

On the Magnetic Ground State of La(0.85)Sr(0.15)CoO(3) Single Crystals

We present an extensive study on magnetic and transport properties of La(0.85)Sr(0.15)CoO(3) single crystals grown by a float zone method to address the issue of phase separation versus spin-glass (SG) behavior. The dc magnetization study reveals a kink in field-cooled magnetization, and the peak in the zero-field-cooling curve shifts to lower temperature at modest dc fields, indicating the SG magnetic phase. The ac susceptibility study exhibits a considerable frequency-dependent peak shift (similar to 4 K) and a time-dependent memory effect below the freezing temperature. In addition, the characteristic time scale tau(0) estimated from the frequency-dependent ac susceptibility measurement is found to be similar to 10(-13) s, which matches well with typical values observed in canonical SG systems. The transport relaxation study evidently demonstrates the time-dependent glassy phenomena. In essence, all our experimental results corroborate the existence of SG behavior in La(0.85)Sr(0.15)CoO(3) single crystals.

Pyrochlore ``dynamic spin-ice'' Pr(2)Sn(2)O(7) and monoclinic Pr(2)Ti(2)O(7): A comparative temperature-dependent Raman study

Here we report a temperature-dependent Raman study of the pyrochlore ``dynamic spin-ice'' compound Pr(2)Sn(2)O(7) and compare the results with its non-pyrochlore (monoclinic) counterpart Pr(2)Ti(2)O(7). In addition to phonon modes, we observe two bands associated with electronic Raman scattering involving crystal field transitions in Pr(2)Sn(2)O(7) at similar to 135 and 460 cm(-1) which couple strongly to phonons. Anomalous temperature dependence of phonon frequencies that are observed in Pyrochlore Pr(2)Sn(2)O(7) are absent in monoclinic Pr(2)Ti(2)O(7). This, therefore, confirms that the strong phonon-phonon anharmonic interactions, responsible for the temperature-dependent anomalous behavior of phonons, arise due to the inherent vacant sites in the pyrochlore structure. (C) 2011 Elsevier Inc. All rights reserved.

Size dependent microstructure for Ag-Ni nanoparticles

The Ag-Ni system is characterized by large differences in atomic sizes (14%) and a positive heat of mixing (+23 kJ mol(-1)). The binary equilibrium diagram for this system therefore exhibits a large miscibility gap in both solid and liquid state. This paper explores the size-dependent changes in microstructure and the suppression of the miscibility gap which occurs when free alloy particles of nanometer size are synthesized by co-reduction of Ag and Ni metal precursors. The paper reports that complete mixing between Ag and Ni atoms could be achieved for smaller nanoparticles (<7 nm). These particles exhibit a single-phase solid solution with face-centered cubic (fcc) structure. With increase in size, the nanoparticles revealed two distinct regions. One of the regions is composed of pure Ag. This region partially surrounds a region of fcc solid solution at an early stage of decomposition. Experimental observations were compared with the results obtained from the thermodynamic calculations, which compared the free energies corresponding to a physical mixture of pure Ag and Ni phases and a fcc Ag-Ni solid solution for different particle sizes. Results from the theoretical calculations revealed that, for the Ag-Ni system, solid solution was energetically preferred over the physical mixture configuration for particle sizes of 7 nm and below. The experimentally observed two-phase microstructure for larger particles was thus primarily due to the growth of Ag-rich regions epitaxially on initially formed small fcc Ag-Ni nanoparticles. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Usefulness of in Situ Single Crystal to Single Crystal Transformation (SCSC) Studies in Understanding the Temperature-Dependent Dimensionality Cross-over and Structural Reorganization in Copper-Containing Metal-Organic Frameworks (MOFs)

Two copper-containing compounds [Cu(3)(mu(3)-OH)(2)-(H(2)O)(2){(SO(3))-C(6)H(3)-(COO)(2)}(CH(3)COO)] , I, and [Cu(5)(mu(3)-OH)(2)(H(2)O)(6){(NO(2))-C(6)H(3)-(COO)(2)}(4)]center dot 5H(2)O, II, were prepared using sulphoisophthalic and nitroisophthalic acids. The removal of the coordinated water molecules in the compounds was investigated using in situ single crystal to single crystal (SCSC) transformation studies, temperature-dependent powder X-ray diffraction (PXRD), and thermogravimetric analysis (TGA). The efficacy of SCSC transformation studies were established by the observation of dimensionality cross-over from a two-dimensional (I) to a three-dimensional structure, Cu(6)(mu(3)-OH)(4){(SO(3))-C(6)H(3)-(COO)(2)}(2)(CH(3)COO)(2), Ia, during the removal of the coordinated water molecules. Compound H exhibited a structural reorganization forming Cu(5)(mu(2)-OH)(2){(NO(2))C(6)H(3)-(COO)(2))(4)], Ha, possessing trimeric (Cu(3)O(12)) and dimeric (Cu(2)O(8)) copper clusters. The PXRD studies indicate that the three-dimensional structure (Ia) is transient and unstable, reverting back to the more stable two-dimensional structure (I) on cooling to room temperature. Compound Ha appears to be more stable at room temperature. The rehydration/dehydration studies using a modified TGA setup suggest complete rehydration of the water molecules, indicating that the water molecules in both compounds are labile. A possible model for the observed changes in the structures has been proposed. Magnetic studies indicate changes in the exchanges between the copper centers in Ha, whereas no such behavior was observed in Ia.

Time-dependent transitions with time-space noncommutativity and its implications in quantum optics

We study the time-dependent transitions of a quantum-forced harmonic oscillator in noncommutative R(1,1) perturbatively to linear order in the noncommutativity theta. We show that the Poisson distribution gets modified, and that the vacuum state evolves into a `squeezed' state rather than a coherent state. The time evolutions of uncertainties in position and momentum in vacuum are also studied and imply interesting consequences for modeling nonlinear phenomena in quantum optics.

Effect of dimerization on dynamics of spin-charge separation in Pariser-Parr-Pople model: A time-dependent density matrix renormalization group study

We investigate the effect of static electron-phonon coupling on real-time dynamics of spin and charge transport in pi-conjugated polyene chains. The polyene chain is modeled by the Pariser-Parr-Pople Hamiltonian with dimerized nearest-neighbor parameter t(0)(1 + delta) for short bonds and t(0)(1 - delta) for long bonds, and long-range electron-electron interactions. We follow the time evolution of the spin and charge using time-dependent density matrix renormalization group technique when a hole is injected at one end of the chain in its ground state. We find that spin and charge dynamics followed through spin and charge velocities depend both on chain length and extent of dimerization delta. Analysis of the results requires focusing on physical quantities such as average spin and charge polarizations, particularly in the large dimerization limit. In the dimerization range 0.0 <= delta <= 0.15, spin-charge dynamics is found to have a well-defined behavior, with spin-charge separation (measured as the ratio of charge velocity to spin velocity) as well as the total amount of charge and spin transported in a given time along the chain decreasing as dimerization increases. However, in the range 0.3 <= delta <= 0.5, it is observed that the dynamics of spin and charge transport becomes complicated. It is observed that, for large delta values, spin-charge separation is suppressed and the injected hole fails to travel the entire length of the chain.

Temperature dependent photoemission spectroscopy on lightly-doped sodium tungsten bronze

Temperature dependent photoemission studies on lightly doped (x = 0.025) sodium tungsten bronzes, NaxWO3 have been investigated by high-resolution photoemission spectroscopy. The experimental results show evidence for polaron formation at the valence band edge and the photoemission spectra taken in different modes of the electron analyzer suggest that the density of states at the valence band edge gradually moves to other k-points in the Brillouin zone with increasing temperature and explain the dynamics of polarons in the insulating disordered sodium tungsten bronzes. (C) 2012 Elsevier Ltd. All rights reserved.

Structural and phase dependent thermo and photoluminescent properties of Dy(OH)(3) and Dy2O3 nanorods

Hexagonal Dy(OH)(3) and cubic Dy2O3 nanorods were prepared by hydrothermal method. Dy(OH)(3) nanorods was directly obtained at 180 degrees C for 20 h after hydrothermal treatment whereas subsequently heat treatment at 750 degrees C for 2 h gives pure cubic Dy2O3. SEM micrographs reveal that needle shaped rods with different sizes were observed in both the phases. TEM results also confirm this. The TL response of hexagonal Dy(OH)(3) and cubic Dy2O3 nanorods have been analyzed for gamma-irradiation over a wide range of exposures (1-5 kGy). TL glow peak intensity increases with gamma dose in both the phases. The activation energy (E), order of kinetics (6), and frequency factor (s) for both the phases have been determined using Chen's peak shape method. The simple glow curve shape, structure and linear response to gamma-irradiation over a large span of exposures makes the cubic Dy2O3 as a useful dosimetric material to estimate high exposures of gamma-rays. (c) 2012 Elsevier Ltd. All rights reserved.

Non-monotonic, distance-dependent relaxation of water in reverse micelles: Propagation of surface induced frustration along hydrogen bond networks

Layer-wise, distance-dependent orientational relaxation of water confined in reverse micelles (RM) is studied using theoretical and computational tools. We use both a newly constructed ``spins on a ring'' (SOR) Ising-type model (with Shore-Zwanzig rotational dynamics) and atomistic simulations with explicit water. Our study explores the effect of reverse micelle size and role of intermolecular correlations, compromised by the presence of a highly polar surface, on the distance (from the interface) dependence of water relaxation. The ``spins on a ring'' model can capture some aspects of distance dependence of relaxation, such as acceleration of orientational relaxation at intermediate layers. In atomistic simulations, layer-wise decomposition of hydrogen bond formation pattern clearly reveals that hydrogen bond arrangement of water at a certain distance away from the surface can remain frustrated due to the interaction with the polar surface head groups. This layer-wise analysis also reveals the presence of a non-monotonic slow relaxation component which can be attributed to this frustration effect and which is accentuated in small to intermediate size RMs. For large size RMs, the long time component decreases monotonically from the interface to the interior of the RMs with slowest relaxation observed at the interface. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4732095]