A numerical method to compute exactly the partition function with application toZ(n) theories in two dimensions

I present a new method to exactly compute the partition function of a class of discrete models in arbitrary dimensions. The time for the computation for ann-state model on anL ^d lattice scales like . I show examples of the use of this method by computing the partition function of the 2D Ising and 3-state Potts models for maximum lattice sizes 10×10 and 8×8, respectively. The critical exponentsv and and the critical temperature one obtains from these are very near the exactly known values. The distribution of zeros of the partition function of the Potts model leads to the conjecture that the ratio of the amplitudes of the specific heat below and above the critical temperature is unity.     

Laser desorption VUV postionization MS imaging of a cocultured biofilm

Laser desorption postionization mass spectrometry (LDPI-MS) imaging is demonstrated with a 10.5 eV photon energy source for analysis and imaging of small endogenous molecules within intact biofilms. Biofilm consortia comprised of a synthetic Escherichia coli K12 coculture engineered for syntrophic metabolite exchange are grown on membranes and then used to test LDPI-MS analysis and imaging. Both E. coli strains displayed many similar peaks in LDPI-MS up to m/z 650, although some observed differences in peak intensities were consistent with the appearance of byproducts preferentially expressed by one strain. The relatively low mass resolution and accuracy of this specific LDPI-MS instrument prevented definitive assignment of species to peaks, but strategies are discussed to overcome this shortcoming. The results are also discussed in terms of desorption and ionization issues related to the use of 10.5 eV single-photon ionization, with control experiments providing additional mechanistic information. Finally, 10.5 eV LDPI-MS was able to collect ion images from intact, electrically insulating biofilms at ～100 μm spatial resolution. Spatial resolution of ～20 μm was possible, although a relatively long acquisition time resulted from the 10 Hz repetition rate of the single-photon ionization source.

Does the quenched reduced U(∞) chiral model break spontaneously in weak coupling?

The U(N) chiral model, when quenched using Parisi's rule, has a [U(1) × U(1)]^N/U(1) global invariance. To determine whether this symmetry breaks spontaneously in weak coupling for N=∞, a one-loop calculation of the distribution of eigenvalues of the single U(N) matrix of the model is performed. This distribution is shown to be uniform on the unit circle and hence, no symmetry breaking occurs. Further, the order parameter | tr U|²/N², which should be zero at N=∞ in the absence of spontaneous symmetry breaking, is evaluated in the weak coupling phase for one, two and three dimensions for N varying from 2 to 50 by Monte Carlo simulation of the quenched model. The data indicate that this parameter indeed goes to zero as N→∞ implying that the symmetry does not break.     

Rotary disc bioreactor-based approach for bacterial nanocellulose production using Gluconacetobacter xylinus NCIM 2526 strain

Bacterial nanocellulose (BNC) is an indomitable biomaterial of utmost usage in different technological areas. Previously, the BNC production has been reported in the simplified bioreactors. Thus, pioneering bioreactor-assisted strategies are desirable for the commendable BNC production. Advanced bioreactors must be corroborated along with different bacterial strains to obtain creditable BNC yield. This study deals with BNC production in rotary disc bioreactor (RDBR) using Gluconacetobacter xylinus NCIM 2526 strain. RDBR-based production of BNC provided 189?±?14 gL^?1 of wet BNC, i.e., equivalent to 6.6?±?0.3 gL^?1 dry BNC yield in 10 days. However, in static cultivation mode, 56?±?12 gL^?1 wet weight of BNC, corresponding to 2.4?±?0.4 gL^?1 dry weight, was produced. Thus, BNC production was approximately 2.75 folds higher in RDBR than statically produced BNC from the same volume of the media. The sugar to BNC conversion yield (12.2?±?0.8%) was doubled in RDBR-based production as compared to static BNC production (6.2?±?1.4%) with efficient sugar consumption (90.0?±?3.3%). The maximum amount of BNC was produced at 7 RPM and pH 6. RDBR-based BNC showed a more hydrophilic nature than statically produced BNC. The RDBR might be appropriate for large-scale BNC production, especially for wet-end applications, as an ample amount of BNC can be produced from a single fermentation process. These BNC pellicles might have the potential for biomedical applications like wound dressings, biofacial masks, hydrogels, and tissue engineering scaffolds.

     

Partition function zeros and the three-dimensional Ising spin glass

We have computed the exact partition function of the 3D Ising spin glass on lattices of effective size 3×3×L_z, 4×4×L_z, and 5×5×L_z forL _z up to 9, and several random bond configurations. Studying the distribution of zeros of the associated partition functions, we find further evidence that these systems have a singularity in the thermodynamic limit.     

The quenched Eguchi-Kawai model

It is argued that spontaneous symmetry breaking occurs in the recently proposed Eguchi-Kawai model. The argument is based on an analytic investigation and on Monte Carlo simulations. A quenched version of the model is proposed which gives good behavior at weak couplings.     

Dynamic viscosity versus probe-reported microviscosity of aqueous mixtures of poly(ethylene glycol)

Correlation between the dynamic viscosity (η) and the microviscosity of a hybrid green medium constituted of water and poly(ethylene glycol) (PEG) of average molar mass (200, 400, and 600) g · mol^?1, respectively, is explored over the temperatures range (10 to 90) °C across the complete composition regime. The microviscosity is obtained using a fluorescence probe 1,3-bis-(1-pyrenyl)propane (BPP), which is manifested through the ratio of the monomer-to-intramolecular excimer intensities (I_M/I_E). Aqueous PEG mixtures are observed to behave similar to Newtonian fluids as the temperature dependence of dynamic viscosity follows Arrhenius-type behavior. Surprisingly, a simple and convenient linear dependence of ln η with wt% PEG of the mixture is established. The BPP I_M/I_E is observed, in general, to increase with the bulk dynamic viscosity of the mixture having >10 wt% PEG suggesting a good correlation between the bulk dynamic viscosity and BPP-reported microviscosity when the viscosity of the aqueous PEG mixture is relatively high.     

Bosonic lattice gauge theory with noise

We apply the recently suggested linear updating algorithm of Kennedy and Kuti to four-dimensional SU(3) bosonic gauge theory with the Wilson action. The change in the action for each link update is estimated stochastically, and we find that the algorithm gives the mean plaquette correctly for reasonable parameter values. Our results indicate that this method should be efficient for Monte Carlo computations with complicated “improved” actions, and they also show the feasibility of using such “noisy” methods to include the dynamical effects of fermions.     

A fast algorithm for the Cyber 205 to simulate the 3D Ising model

We describe a computer program that performs the Metropolis algorithm for the 3D Ising model at a peak speed of 98 million spin updates per second on a 2-pipe CDC Cyber 205. This speed is achieved using the special vector capabilities of the Cyber 205 and multispin coding techniques.