Non-periodic tilings in 2-dimensions with 4, 6, 8, 10 and 12-fold symmetries

The two dimensional plane can be filled with rhombuses, so as to generate non-periodic tilings with 4, 6, 8, 10 and 12-fold symmetries. Some representative tilings constructed using the rule of inflation are shown. The numerically computed diffraction patterns for the corresponding tilings are also shown to facilitate a comparison with possible X-ray or electron diffraction pictures.

Non-periodic tilings in 2-dimensions: 4- and 7-fold symmetries

By inflating basic rhombuses, with a self-similarity principle, non-periodic tiling of 2-d planes is possible with 4, 5, 6, 7, 8, … -fold symmetries. As examples, non-periodic tilings with crystallographically allowed 4-fold symmetry and crystallographically forbidden 7-fold symmetry are presented in detail. The computed diffraction patterns of these tilings are also discussed.

New La2CuO4 derivatives La(2-2x)Sr(2x)Cu(1-x)M(x)O(4) (M=Ti, Mn, Fe, or Ru): A study of linear Cu-O-M electronic interaction in two dimensions

Oxides of the general formula La2-2xSr2xCu1-xII,M(x)(IV)O(4) (M = Ti, Mn, Fe, or Ru), crystallizing in the tetragonal K,NIF, structure, have been synthesized. For M=Ti, only the x=0,5 member could be prepared, while for M=Mn and Fe, the composition range is 0 Cu(III)-O-Fe(III) valence degeneracy. Increasing the strontium content at the expense of lanthanum in La2-2xSr2xCu1-xFexO4 for x less than or equal to 0.20 renders the samples metallic but not superconducting. (C) 1997 Academic Press.

Axial binding of 2-methylimidazole to the tetraarylcarboxylatodiruthenium (II, III) core: X-ray crystal structure of [Ru-2(O2CC6H4-p-OMe)(4)(2-mimH)(2)](ClO4). 1.75CH(2)Cl(2).H2O

Diruthenium (II. III) complexes of the type [Ru-2(O2CAr)(4) (2-mimH)(2)](ClO4) (Ar = C6H4-p-X : X=OMe,1, X=Me, 2, 2-mimH=2-methylimidazole) have been isolated from the reaction of Ru2Cl(O2CAr)(4) with 2-mimH in CH2Cl2 followed by the addition of NaClO4. The crystal structure of 1.1.75CH(2)Cl(2).H2O has been determined. The crystal belongs to the monoclinic space group p2(1)/c with the following unit cell dimensions for the C40H40N4O16ClRu2.1.75CH(2)Cl(2).H2O (M = 1237.0) : a = 12.347(3)Angstrom, b = 17.615(5)Angstrom, c = 26.148(2)Angstrom,beta = 92.88(1)degrees. v = 5679(2)Angstrom(3). Z=4, D-c = 1.45 g cm(-3). lambda(Mo-K-alpha) = 0.7107 Angstrom, mu(Mo-K-alpha) = 8.1 cm(-1), T = 293 K, R = 0.0815 (wR(2) = 0.2118) for 5834 reflections with 1 > 2 sigma(I). The complex has a tetracarboxylatodiruthenium (II, III) core and two axially bound 2-methylimidazole ligands. The Ru-Ru bond length is 2.290(1)Angstrom. The Ru-Ru bond order is 2.5 and the complex is three-electron paramagnetic. The complex shows an irreversible Ru-2(II,III)-->Ru-2(Il,II) reduction near -0.2 V vs SCE in CH2Cl2-0. 1 MTBAP. The complexes exemplify the first adduct of the tetracarboxylatodiruthenium (II,III) core having N-donor ligands

A note on fractal dimensions of biomedical waveforms

In this paper, we study performance of Katz method of computing fractal dimension of waveforms, and its estimation accuracy is compared with Higuchi's method. The study is performed on four synthetic parametric fractal waveforms for which true fractal dimensions can be calculated, and real sleep electroencephalogram. The dependence of Katz's fractal dimension on amplitude, frequency and sampling frequency of waveforms is noted. Even though the Higuchi's method has given more accurate estimation of fractal dimensions, the study suggests that the results of Katz's based fractal dimension analysis of biomedical waveforms have to be carefully interpreted.

A solution framework for scheduling a BPM with non-identical job dimensions

A Batch Processing Machine (BPM) is one which processes a number of jobs simultaneously as a batch with common beginning and ending times. Also, a BPM, once started cannot be interrupted in between (Pre-emption not allowed). This research is motivated by a BPM in steel casting industry. There are three main stages in any steel casting industry viz., pre-casting stage, casting stage and post-casting stage. A quick overview of the entire process, is shown in Figure 1. There are two BPMs : (1) Melting furnace in the pre-casting stage and (2) Heat Treatment Furnace (HTF) in the post casting stage of steel casting manufacturing process. This study focuses on scheduling the latter, namely HTF. Heat-treatment operation is one of the most important stages of steel casting industries. It determines the final properties that enable components to perform under demanding service conditions such as large mechanical load, high temperature and anti-corrosive processing. In general, different types of castings have to undergo more than one type of heat-treatment operations, where the total heat-treatment processing times change. To have a better control, castings are primarily classified into a number of job-families based on the alloy type such as low-alloy castings and high alloy castings. For technical reasons such as type of alloy, temperature level and the expected combination of heat-treatment operations, the castings from different families can not be processed together in the same batch.

Melting of an Anchored Bilayer: Phase Transitions in the Organic-Inorganic Hybrid Pervoskite (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 (n=11, 13, 15, 17)

The conformation, organization, and phase transitions of alkyl chains in organic-inorganic hybrids based on the double pervoskite-slab lead iodides, (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 (n = 11, 13, 15, 17) have been investigated by X-ray diffraction, calorimetry, and infrared vibrational spectroscopy. In these hybrid solids, double pervoskite (CH3NH3)Pb2I7 slabs are interleaved with alkyl ammonium chains with the anchored alkyl chains arranged as tilted bilayers and adopting a planar all-trans conformation at room temperature. The (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 compounds exhibit a single reversible phase transition above room temperature with the associated enthalpy change varying linearly with alkyl chain length. This transition corresponds to the melting in two-dimensions of the alkyl chains of the anchored bilayer and is characterized by increased conformational disorder of the methylene units of the chain and loss of tilt angle coherence leading to an increase in the interslab spacing. By monitoring features in the infrared spectra that are characteristic of the global conformation of the alkyl chains, a quantitative relation between conformational disorder and melting of the anchored bilayer is established. It is found that, irrespective of the alkyl chain length, melting occurs when at least 60% of the chains in the anchored bilayer of (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 have one or more gauche defects. This concentration is determined by the underlying lattice to which the alkyl chains are anchored.

Experimental studies on a two stage pulse tube cryocooler reaching 2.5K

A two stage Pulse Tube Cryocooler (PTC) is designed and fabricated which reaches a no-load temperature of 2.5K in the second stage and similar to 60 K in the first stage respectively. The system provides a cooling power of similar to 250 mW at 5K in the second stage. Stainless steel meshes (size 200) and lead (Pb) granules are used as the first stage regenerator materials and combination of Pb with Er3Ni / HoCu2 are used as the second stage regenerator materials. The system operates at 1.6 Hz using a 6 kW water cooled helium compressor. Studies conducted by varying the dimensions of Pulse Tubes and regenerators show that the dimensions of the Pulse Tubes are more critical to the performance of the Cryocooler than those of the regenerators. Experimental studies show that the optimum volume ratios of Er3Ni to Pb and HoCu2 to Pb in the second stage regenerator should be 3:2 and 2:3 respectively for the best performance. Further, systems with HoCu2 performed better than those with Er3Ni. The theoretical analysis of the system has been carried out using a simple isothermal model. The experimentally measured cooling powers are in good agreement with the theoretical predictions.

Crystal And Molecular-Structure Of 8-Acetoxy-6-(2,4-Dimethoxy-5-Bromophenyl)-3-Methyl-Tricyclo[5,2,1,03,8 ]Decan-2-One

The crystal and molecular structure has been determined by the heavy-atom method and refined by the least-squares procedure to R= 8"3 % for 2033 photographically observed reflexions. The compound crystallizes in the space group P]" with two molecules in a unit cell of dimensions a = 11"68 + 0-02, b = 12"91 +0"02, c= 10"43+0"02/~, e= 114"7+ 1, fl=90-2+ 1 and 7,= 118.3+ 1 °. The unit cell also contains one molecule of the solvent, benzene. The 'cage' part of the molecule exhibits a large number of elongated bonds and strained internal valency angles. The bridgehead angle in the bicyclic heptane ring system is 89 °. The acetate group at C(16) and the methyl group at C(15) are cis to each other.

Investigations of a two-stage pulse tube cryocooler operating down to 2.5K

A two-stage pulse tube cryocooler (PTC) which produces a no-load temperature of similar to 2.5 K in its second stage at an operating frequency of 1.6 Hz has been designed and fabricated. The second stage of the system provides a refrigeration power of similar to 250 mW at 5.0 K. The system uses stainless steel meshes (mesh size 200) along with lead (Pb) granules and combinations of Pb, Er3Ni, and HoCu2 as the first and second stage regenerator materials, respectively. Experimental studies have been carried out on different pulse tube configurations by varying the dimensions of the pulse tubes and regenerators to arrive at the best one, which leads to the lowest no-load second stage cold head temperature. Using this configuration, detailed experimental studies have been conducted by varying the volume percentage ratios of the second stage regenerator materials such as HoCu2, Er3Ni, and Pb (with an average grain size of similar to 250 mu m). This article presents the results of our experimental studies on cryocoolers with the regenerator material arranged in layered structures. Comparative studies have also been presented for specific cases where the regenerator materials are arranged as a homogeneous mixture in the second stage. The experimental results clearly indicate that the design of PTCs should use only layered structures of regenerator materials and not homogenous mixtures.

Non-Abelian chiral gauge theories in two dimensions

An anomalous multiflavor chiral theory, with the gauge group SU(N), is studied using non-Abelian bosonization. The theory can be made gauge invariant by introducing Wess-Zumino fields and it is particularly simple if the Jackiw-Rajaraman parameter equals 2. In the strong-coupling limit, the low-energy effective theory only contains light unconfined fermions which interact weakly.

Studies in biogas technology. Part II. Optimisation of plant dimensions

In this paper, the design basis of the conventional Khadi and Village Industries Commission biogas plants has been elucidated. It has been shown that minimisation of the cost of the gas holder alone leads to the narrow and deep digesters of conventional plants. If instead, the total capital cost of the gas holder plus digester is minimised, the optimisation leads to wide and shallow digesters, which are less expensive. To test this alternative, two prototype plants have been designed, constructed and operated. These plants are not only 25–40% cheaper, but their performance is actually slightly better than the conventional plants.

Infrared divergences and confinement in massive (2+1)-dimensional QED

In (2+1)-dimensional quantum electrodynamics with massless photons and massive matter fields, it is shown that the mass renormalization of the latter is infrared divergent at one loop. This result remains unchanged at two loops. A simple argument based on a similar divergence of the Coulomb potential leads us to conjecture that charged states are not observable in this model. This argument holds in 1+1 dimensions also.

Euclideanization, topological theories, higher dimensions and all that

It is shown that the euclideanized Yukawa theory, with the Dirac fermion belonging to an irreducible representation of the Lorentz group, is not bounded from below. A one parameter family of supersymmetric actions is presented which continuously interpolates between the N = 2 SSYM and the N = 2 supersymmetric topological theory. In order to obtain a theory which is bounded from below and satisfies Osterwalder-Schrader positivity, the Dirac fermion should belong to a reducible representation of the Lorentz group and the scalar fields have to be reinterpreted as the extra components of a higher dimensional vector field.

Double helix conformation, groove dimensions and ligand binding potential of a G/C stretch in B-DNA

The self-complementary DNA fragment CCGGCGCCGG crystallizes in the rhombohedral space group R3 with unit cell parameters a = 54.07 angstrom and c = 44.59 angstrom. The structure has been determined by X-ray diffraction methods at 2.2 angstrom resolution and refined to an R value of 16.7%. In the crystal, the decamer forms B-DNA double helices with characteristic groove dimensions: compared with B-DNA of random sequence, the minor groove is wide and deep and the major groove is rather shallow. Local base pair geometries and stacking patterns are within the range commonly observed in B-DNA crystal structures. The duplex bears no resemblance to A-form DNA as might have been expected for a sequence with only GC base pairs. The shallow major groove permits an unusual crystal packing pattern with several direct intermolecular hydrogen bonds between phosphate oxygens and cytosine amino groups. In addition, decameric duplexes form quasi-infinite double helices in the crystal by end-to-end stacking. The groove geometries and accessibilities of this molecule as observed in the crystal may be important for the mode of binding of both proteins and drug molecules to G/C stretches in DNA.