Groups with exponent six

Burnside asked questions about periodic groups in his influential paper of 1902. The study of groups with exponent six is a special case of the study of the Burnside questions on which there has been significant progress. It has contributed a number of worthwhile aspects to the theory of groups and in particular to computation related to groups. Finitely generated groups with exponent six are finite. We investigate the nature of relations required to provide proofs of finiteness for some groups with exponent six. We give upper and lower bounds for the number of sixth powers needed to define the largest 2-generator group with exponent six. We solve related questions about other groups with exponent sis using substantial computations which we explain.

A novel method for tailoring the pore-opening size of MCM-41 materials

A novel pore tailoring method is proposed by which the pore-opening sizes of MCM-41 materials can be finely tuned without significant loss in pore volume and surface area.

Quantum and classical chaos for a single trapped ion

In this paper we investigate the quantum and classical dynamics of a single trapped ion subject to nonlinear kicks derived from a periodic sequence of Gaussian laser pulses. We show that the classical system exhibits: diffusive growth in the energy, or heating,'' while quantum mechanics suppresses this heating. This system may be realized in current single trapped-ion experiments with the addition of near-field optics to introduce tightly focused laser pulses into the trap.

Cyclotron effective masses in layered metals

Many layered metals such as quasi-two-dimensional organic molecular crystals show properties consistent with a Fermi-liquid description at low temperatures. The effective masses extracted from the temperature dependence of the magnetic oscillations observed in these materials are in the range, m(c)*/m(e) similar to 1 - 7, suggesting that these systems are strongly correlated. However, the ratio m(c)*/m(e) contains both the renormalization due to the electron-electron interaction and the periodic potential of the lattice. We show that for any quasi-two-dimensional band structure, the cyclotron mass is proportional to the density-of-states at the Fermi energy. Due to Luttinger's theorem, this result is also valid in the presence of interactions. We then evaluate m(c) for several model band structures for the beta, kappa, and theta families of (BEDT-TTF)(2)X, where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene) and X is an anion. We find that for kappa-(BEDT-TTF)(2)X, the cyclotron mass of the beta orbit, m(c)*(beta) is close to 2 m(c)*(alpha), where m(c)*(alpha) is the effective mass of the alpha orbit. This result is fairly insensitive to the band-structure details. For a wide range of materials we compare values of the cyclotron mass deduced from band-structure calculations to values deduced from measurements of magnetic oscillations and the specific-heat coefficient gamma.

Characterization of the structural and surface properties of chemically modified MCM-41 material

Mesoporous Mobil catalytic materials of number 41 (MCM-41) silica was chemically modified using both inorganic and organic precursors and characterized using the techniques, XRD, XPS, MAS NMR, FTIR, W-Vis, and physical adsorption of nitrogen, hydrocarbons (hexane, benzene, acetone, and methanol) and water vapor. Modification using organic reagents was found to result in a significant loss in porosity and a shape change of surface properties (increased hydrophobicity and decreased acidity). With inorganic modifying reagents, the decrease in porosity was also observed while the surface properties were not significantly altered as reflected by the adsorption isotherms of organics and water vapors. Chemical modifications can greatly improve the hydrothermal stability of MCM-41 material because of the enhanced surface hydrophobicity (with organic modifiers) or increased pore wall thickness (with inorganic modifiers). (C) 2000 Elsevier Science B.V. All rights reserved.

Quantum chaos in atom optics

I shall discuss the quantum and classical dynamics of a class of nonlinear Hamiltonian systems. The discussion will be restricted to systems with one degree of freedom. Such systems cannot exhibit chaos, unless the Hamiltonians are time dependent. Thus we shall consider systems with a potential function that has a higher than quadratic dependence on the position and, furthermore, we shall allow the potential function to be a periodic function of time. This is the simplest class of Hamiltonian system that can exhibit chaotic dynamics. I shall show how such systems can be realized in atom optics, where very cord atoms interact with optical dipole potentials of a far-off resonance laser. Such systems are ideal for quantum chaos studies as (i) the energy of the atom is small and action scales are of the order of Planck's constant, (ii) the systems are almost perfectly isolated from the decohering effects of the environment and (iii) optical methods enable exquisite time dependent control of the mechanical potentials seen by the atoms.

Accelerating seismic energy release and evolution of event time and size statistics: Results from two heterogeneous cellular automaton models

The evolution of event time and size statistics in two heterogeneous cellular automaton models of earthquake behavior are studied and compared to the evolution of these quantities during observed periods of accelerating seismic energy release Drier to large earthquakes. The two automata have different nearest neighbor laws, one of which produces self-organized critical (SOC) behavior (PSD model) and the other which produces quasi-periodic large events (crack model). In the PSD model periods of accelerating energy release before large events are rare. In the crack model, many large events are preceded by periods of accelerating energy release. When compared to randomized event catalogs, accelerating energy release before large events occurs more often than random in the crack model but less often than random in the PSD model; it is easier to tell the crack and PSD model results apart from each other than to tell either model apart from a random catalog. The evolution of event sizes during the accelerating energy release sequences in all models is compared to that of observed sequences. The accelerating energy release sequences in the crack model consist of an increase in the rate of events of all sizes, consistent with observations from a small number of natural cases, however inconsistent with a larger number of cases in which there is an increase in the rate of only moderate-sized events. On average, no increase in the rate of events of any size is seen before large events in the PSD model.

Comprehensive structural characterization of MCM-41: From mesopores to particles

In the present work the meso- and macro-structural characteristics of the mesoporous adsorbent MCM-41 have been estimated with the help of various techniques. The structure is found to comprise four different length scales: that of the mesopores, the crystallites, the grains and of the particles. It was found that the surface area estimated by the use of small angle scattering techniques is higher, while that estimated by mercury porosimetry is much lower, than that obtained from gas adsorption methods. Based on the macropore characterization by mercury porosimetry, and the considerable macropore area determined, it is seen that the actual mesopore area of MCM-41 may be significantly lower than the BET area. TEM studies indicated that MCM-41 does not have an ideal mesopore structure; however, it may still be treated as a model mesoporous material for gas adsorption studies because of the large radius of curvature of the channels.

Identifying rate-limiting nodes in large-scale cortical networks for visuospatial processing: an illustration using fMRI

With the advent of functional neuroimaging techniques, in particular functional magnetic resonance imaging (fMRI), we have gained greater insight into the neural correlates of visuospatial function. However, it may not always be easy to identify the cerebral regions most specifically associated with performance on a given task. One approach is to examine the quantitative relationships between regional activation and behavioral performance measures. In the present study, we investigated the functional neuroanatomy of two different visuospatial processing tasks, judgement of line orientation and mental rotation. Twenty-four normal participants were scanned with fMRI using blocked periodic designs for experimental task presentation. Accuracy and reaction time (RT) to each trial of both activation and baseline conditions in each experiment was recorded. Both experiments activated dorsal and ventral visual cortical areas as well as dorsolateral prefrontal cortex. More regionally specific associations with task performance were identified by estimating the association between (sinusoidal) power of functional response and mean RT to the activation condition; a permutation test based on spatial statistics was used for inference. There was significant behavioral-physiological association in right ventral extrastriate cortex for the line orientation task and in bilateral (predominantly right) superior parietal lobule for the mental rotation task. Comparable associations were not found between power of response and RT to the baseline conditions of the tasks. These data suggest that one region in a neurocognitive network may be most strongly associated with behavioral performance and this may be regarded as the computationally least efficient or rate-limiting node of the network.

Copper/MCM-41 as catalyst for the wet oxidation of phenol

A heterogeneous copper catalyst supported on mesoporous MCM-41 was developed. The parent MCM-41 has a large pore area of over 1400 m(2)/g. Copper was chosen as the active element of catalyst and loaded into MCM-41 by adsorption at ambient temperature. The prepared catalysts were evaluated in the catalytic wet oxidation of phenol solution with an initial concentration of 1,300 ppm at 150 and 200 degreesC. The catalyst was found to be of high catalytic activity. It is also shown that the catalyst with a higher copper loading exhibits higher ability of accelerating the catalytic reaction to certain extent but reaches its constant level afterwards. (C) 2001 Elsevier Science B.V. All rights reserved.

Copper/MCM-41 as catalyst for photochemically enhanced oxidation of phenol by hydrogen peroxide

Heterogeneous copper catalyst was developed using the mesoporous molecular sieve MCM-41 as the catalyst support. Copper was impregnated onto the support. Catalysts with different copper loadings were obtained. The performance of the developed catalysts was evaluated in photochemically enhanced oxidation of phenol using hydrogen peroxide as the oxidant. The catalyst was found to significantly increase the oxidation rate and enhance the removal level of phenol with UV light present. The effects of copper loading on the catalyst, photo (UV), H2O2 concentration, and catalyst dosage on the photo-oxidation of phenol were studied. (C) 2001 Elsevier Science B.V. All rights reserved.

Structural development of silicated films self-assembled at the air-water interface

The development of structure perpendicular to and in the plane of the interface has been studied for mesoporous silicate films self-assembled at the air/water interface. The use of constrained X-ray and neutron specular reflectometry has enabled a detailed study of the structural development perpendicular to the interface during the pre-growth phase. Off-specular neutron reflectometry and grazing incidence X-ray diffraction has enabled the in-plane structure to be probed with excellent time resolution. The growth mechanism under the surfactant to silicate source ratios used in this work is clearly due to the self-assembly of micellar and molecular species at the air/liquid interface, resulting in the formation of a planar mesoporous film that is tens of microns thick. (C) 2003 Elsevier Science B.V. All rights reserved.

Controlling chaos in a Lorenz-like system using feedback

We demonstrate that the dynamics of an autonomous chaotic laser can be controlled to a periodic or steady state under self-synchronization. In general, past the chaos threshold the dependence of the laser output on feedback applied to the pump is submerged in the Lorenz-like chaotic pulsation. However there exist specific feedback delays that stabilize the chaos to periodic behavior or even steady state. The range of control depends critically on the feedback delay time and amplitude. Our experimental results are compared with the complex Lorenz equations which show good agreement.

Solid-State Experimental and Theoretical Investigation of the Ammonium Salt of Croconate Violet, a Pseudo-Oxocarbon Ion

The present work describes the crystal structure, vibrational spectra, and theoretical calculations of ammonium salts of 3,5-bis-(dicyanomethylene)cyclopentane-1,2,4-trionate, (NH(4))(2)(C(11)N(4)O(3)) [(NH(4))(2)CV], also known as ammonium croconate violet. This compound crystallizes in triclinic P (1) over bar and contains two water molecules per unit formula. The crystal packing is stabilized by hydrogen bonds involving water molecules and ammonium cations, giving rise to a 3D polymeric arrangement. In this structure, a pi-stacking interaction is not observed, as the smaller centroid-centroid distance is 4.35 angstrom. Ab initio electronic structure calculations under periodic boundary conditions were performed to predict vibrational and electronic properties. The vibrational analysis was used to assist the assignments of the Raman and infrared bands. The solid structure was optimized and characterized as a minimum in the potential-energy surface. The stabilizing intermolecular hydrogen bonds in the crystal Structure were characterized by difference charge-density analysis. The analysis of the density of states of (NH(4))(2)CV gives an energy gap of 1.4 eV with a significant contribution of carbon and nitrogen 2p states for valence and conduction bands.

Effect of mesoporosity of vanadium oxide prepared by sol-gel process as cathodic material evaluated by cyclability during Li(+) insertion/deinsertion

The effect of pore structure on the behavior of lithium intercalation into an electrode containing porous V(2)O(5) film has been investigated and compared with the electrode containing a non-porous V(2)O(5) film. X-ray diffraction patterns indicate a lamellar structure for both materials. Nitrogen adsorption isotherms, t-plot method, and Scanning Electronic Microscopy show that the route employed for the preparation of mesoporous V(2)O(5) was successful. The electrochemical performance of these matrices as lithium intercalation cathode materials was evaluated. The porous material reaches stability after several cycles more easily compared with the V(2)O(5) xerogel. Lithium intercalation into the porous V(2)O(5) film electrode is crucially influenced by pore surface and film surface irregularity, in contrast with the non-porous surface of the V(2)O(5) xerogel.