From modular invariants to graphs: the modular splitting method

We start with a given modular invariant M of a two dimensional su(n)_k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; 2) the quantum symmetries of the higher ADE graph G associated to the initial modular invariant M. Notice that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyze several su(3)_k exceptional cases at levels 5 and 9.Comment: 28 pages, 7 figures. Version 2: updated references. Typos corrected. su(2) example has been removed to shorten the paper. Dual annular matrices for the rejected exceptional su(3) diagram are determine

A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

Mesoscale properties of clay aggregates from potential of mean force representation of interactions between nanoplatelets

Face-to-face and edge-to-edge free energy interactions of Wyoming Na-montmorillonite platelets were studied by calculating potential of mean force along their center to center reaction coordinate using explicit solvent (i.e., water) molecular dynamics and free energy perturbation methods. Using a series of configurations, the Gay-Berne potential was parametrized and used to examine the meso-scale aggregation and properties of platelets that are initially random oriented under isothermal-isobaric conditions. Aggregates of clay were defined by geometrical analysis of face-to-face proximity of platelets with size distribution described by a log-normal function. The isotropy of the microstructure was assessed by computing a scalar order parameter. The number of platelets per aggregate and anisotropy of the microstructure both increases with platelet plan area. The system becomes more ordered and aggregate size increases with increasing pressure until maximum ordered state at confining pressure of 50 atm. Further increase of pressure slides platelets relative to each other leading to smaller aggregate size. The results show aggregate size of (3–8) platelets for sodium-smectite in agreement with experiments (3–10). The geometrical arrangement of aggregates affects mechanical properties of the system. The elastic properties of the meso-scale aggregate assembly are reported and compared with nanoindentation experiments. It is found that the elastic properties at this scale are close to the cubic systems. The elastic stiffness and anisotropy of the assembly increases with the size of the platelets and the level of external pressure.National Science Foundation (U.S.) (Extreme Science and Engineering Discovery Environment (XSEDE) and Texas Advanced Computing Center Grant TG-DMR100028)X-Shale Hub at MITSingapore-MIT Alliance for Research and Technolog

Accurate method for the Brownian dynamics simulation of spherical particles with hard-body interactions

In Brownian Dynamics simulations, the diffusive motion of the particles is simulated by adding random displacements, proportional to the square root of the chosen time step. When computing average quantities, these Brownian contributions usually average out, and the overall simulation error becomes proportional to the time step. A special situation arises if the particles undergo hard-body interactions that instantaneously change their properties, as in absorption or association processes, chemical reactions, etc. The common "naive simulation method" accounts for these interactions by checking for hard-body overlaps after every time step. Due to the simplification of the diffusive motion, a substantial part of the actual hard-body interactions is not detected by this method, resulting in an overall simulation error proportional to the square root of the time step. In this paper we take the hard-body interactions during the time step interval into account, using the relative positions of the particles at the beginning and at the end of the time step, as provided by the naive method, and the analytical solution for the diffusion of a point particle around an absorbing sphere. Ottinger used a similar approach for the one-dimensional case [Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996), p. 270]. We applied the "corrected simulation method" to the case of a simple, second-order chemical reaction. The results agree with recent theoretical predictions [K. Hyojoon and Joe S. Kook, Phys. Rev. E 61, 3426 (2000)]. The obtained simulation error is proportional to the time step, instead of its square root. The new method needs substantially less simulation time to obtain the same accuracy. Finally, we briefly discuss a straightforward way to extend the method for simulations of systems with additional (deterministic) forces. (C) 2002 American Institute of Physics

Rouse Chains with Excluded Volume Interactions: Linear Viscoelasticity

Linear viscoelastic properties for a dilute polymer solution are predicted by modeling the solution as a suspension of non-interacting bead-spring chains. The present model, unlike the Rouse model, can describe the solution's rheological behavior even when the solvent quality is good, since excluded volume effects are explicitly taken into account through a narrow Gaussian repulsive potential between pairs of beads in a bead-spring chain. The use of the narrow Gaussian potential, which tends to the more commonly used delta-function repulsive potential in the limit of a width parameter "d" going to zero, enables the performance of Brownian dynamics simulations. The simulations results, which describe the exact behavior of the model, indicate that for chains of arbitrary but finite length, a delta-function potential leads to equilibrium and zero shear rate properties which are identical to the predictions of the Rouse model. On the other hand, a non-zero value of "d" gives rise to a prediction of swelling at equilibrium, and an increase in zero shear rate properties relative to their Rouse model values. The use of a delta-function potential appears to be justified in the limit of infinite chain length. The exact simulation results are compared with those obtained with an approximate solution which is based on the assumption that the non-equilibrium configurational distribution function is Gaussian. The Gaussian approximation is shown to be exact to first order in the strength of excluded volume interaction, and is found to be accurate above a threshold value of "d", for given values of chain length and strength of excluded volume interaction.Comment: Revised version. Long chain limit analysis has been deleted. An improved and corrected examination of the long chain limit will appear as a separate posting. 32 pages, 9 postscript figures, LaTe

The microbial ferrous wheel in a neutral pH groundwater seep

Evidence for microbial Fe redox cycling was documented in a circumneutral pH ground-water seep near Bloomington, Indiana. Geochemical and microbiological analyses were conducted at two sites, a semi-consolidated microbial mat and a floating puffball structure. In situ voltammetric microelectrode measurements revealed steep opposing gradients of o2 and Fe(I I) at both sites, similar to other groundwater seep and sedimentary environments known to support microbial Fe redox cycling. The puffball structure showed an abrupt increase in dissolved Fed I) just at its surface (~5cm depth), suggesting an internal Fe(I I) source coupled to active Fed 1I) reduction. Most probable number enumerations detected microaerophilic Fe(II)-oxidizing bacteria (FeoB) and dissimilatory Fe(III)-reducing bacteria (FeRB) at densities of 102 to 105 cells ml_~1 in samples from both sites. In vitro Fed 1I) reduction experiments revealed the potential for immediate reduction (no lag period) of native Fe(III) oxides. Conventional full-length 16S rRNA gene clone libraries were compared with high throughput barcode sequencing of theV1, V4, orV6 variable regions of 16S rRNA genes in order to evaluate the extent to which new sequencing approaches could provide enhanced insight into the composition of Fe redox cycling microbial community structure. The composition of the clone libraries suggested a lithotroph-dominated microbial community centered around taxa related to known FeoB (e.g., Gallionella, Sideroxydans, Aquabacterium). Sequences related to recognized FeRB (e.g., Rhodoferax, Aeromonas, Geobacter, Desulfovibrio) were also well-represented. overall, sequences related to known FeoB and FeRB accounted for 88 and 59% of total clone sequences in the mat and puffball libraries, respectively. Taxa identified in the barcode libraries showed partial overlap with the clone libraries, but were not always consistent across different variable regions and sequencing platforms. However, the barcode libraries provided confirmation of key clone library results (e.g., the predominance of Betaproteobacteria) and an expanded view of lithotrophic microbial community composition

Polymer transport in random flow

The dynamics of polymers in a random smooth flow is investigated in the framework of the Hookean dumbbell model. The analytical expression of the time-dependent probability density function of polymer elongation is derived explicitly for a Gaussian, rapidly changing flow. When polymers are in the coiled state the pdf reaches a stationary state characterized by power-law tails both for small and large arguments compared to the equilibrium length. The characteristic relaxation time is computed as a function of the Weissenberg number. In the stretched state the pdf is unstationary and exhibits multiscaling. Numerical simulations for the two-dimensional Navier-Stokes flow confirm the relevance of theoretical results obtained for the delta-correlated model.Comment: 28 pages, 6 figure

Diagenetic Crystal Growth in the Murray Formation, Gale Crater, Mars

The Pahrump region (Gale Crater, Mars) marks a critical transition between sedimentary environments dominated by alluvial-to-fluvial materials associated with the Gale crater rim, and depositional environments fundamentally linked to the crater's central mound, Mount Sharp. At Pahrump, the Murray formation consists of an approximately 14-meter thick succession dominated by massive to finely laminated mudstone with occasional interbeds of cross-bedded sandstone, and is best interpreted as a dominantly lacustrine environment containing tongues of prograding fluvial material. Murray formation mudstones contain abundant evidence for early diagenetic mineral precipitation and its subsequent removal by later diagenetic processes. Lenticular mineral growth is particularly common within lacustrine mudstone deposits at the Pahrump locality. High-resolution MAHLI images taken by the Curiosity rover permit detailed morphological and spatial analysis of these features. Millimeter-scale lenticular features occur in massive to well-laminated mudstone lithologies and are interpreted as pseudomorphs after calcium sulfate. The distribution and orientation of lenticular features suggests deposition at or near the sediment-water (or sediment-air) interface. Retention of chemical signals similar to host rock suggests that original precipitation was likely poikilotopic, incorporating substantial amounts of the primary matrix. Although poikilotopic crystal growth is common in burial environments, it also occurs during early diagenetic crystal growth within unlithified sediment where high rates of crystal growth are common. Loss of original calcium sulfate mineralogy suggests dissolution by mildly acidic, later-diagenetic fluids. As with lenticular voids observed at Meridiani by the Opportunity Rover, these features indicate that calcium sulfate deposition may have been widespread on early Mars; dissolution of depositional and early diagenetic minerals is a likely source for both calcium and sulfate ion-enrichment in burial fluids that precipitated in ubiquitous late-stage hydrofracture vein

Determination of the Michel Parameters rho, xi, and delta in tau-Lepton Decays with tau --> rho nu Tags

Using the ARGUS detector at the $e^+ e^-$ storage ring DORIS II, we have measured the Michel parameters $\rho$, $\xi$, and $\xi\delta$ for $\tau^{\pm}\to l^{\pm} \nu\bar\nu$ decays in $\tau$-pair events produced at center of mass energies in the region of the $\Upsilon$ resonances. Using $\tau^\mp \to \rho^\mp \nu$ as spin analyzing tags, we find $\rho_{e}=0.68\pm 0.04 \pm 0.08$, $\xi_{e}= 1.12 \pm 0.20 \pm 0.09$, $\xi\delta_{e}= 0.57 \pm 0.14 \pm 0.07$, $\rho_{\mu}= 0.69 \pm 0.06 \pm 0.08$, $\xi_{\mu}= 1.25 \pm 0.27 \pm 0.14$ and $\xi\delta_{\mu}= 0.72 \pm 0.18 \pm 0.10$. In addition, we report the combined ARGUS results on $\rho$, $\xi$, and $\xi\delta$ using this work und previous measurements.Comment: 10 pages, well formatted postscript can be found at http://pktw06.phy.tu-dresden.de/iktp/pub/desy97-194.p