Physics based basis function for vibration analysis of high speed rotating beams

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

Tidally compressed gas in centers of early-type and ultraluminous galaxies

In this paper we propose that the compressive tidal held in the centers of flat-core early-type galaxies and ultraluminous galaxies compresses molecular clouds producing dense gas observed in the centers of these galaxies. The effect of galactic tidal fields is usually considered disruptive in the literature. However, for some galaxies, the mass profile flattens toward the center and the resulting galactic tidal field is not disruptive, but instead it is compressive within the flat-core region. We have used the virial theorem to determine the minimum density of a molecular cloud to be stable and gravitationally bound within the tidally compressive region of a galaxy. We have applied the mechanism to determine the mean molecular cloud densities in the centers of a sample of flat-core, early-type galaxies and ultraluminous galaxies. For early-type galaxies with a core-type luminosity profile, the tidal held of the galaxy is compressive within half the core radius. We have calculated the mean gas densities for molecular gas in a sample of early-type galaxies which have already been detected in CO emission, and we obtain mean densities of [n] similar to 10(3)-10(6) cm(-3) within the central 100 pc radius. We also use our model to calculate the molecular cloud densities in the inner few hundred parsecs of a sample of ultraluminous galaxies. From the observed rotation curves of these galaxies we show that they have a compressive core within their nuclear region. Our model predicts minimum molecular gas densities in the range 10(2)-10(4) cm(-3) in the nuclear gas disks; the smaller values are applicable typically for galaxies with larger core radii. The resulting density values agree well with the observed range. Also, for large core radii, even fairly low-density gas (similar to 10(2) cm(-3)) can remain bound and stable close to the galactic center.

Precoding with X-codes to increase capacity with discrete input alphabets

We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non-diagonal precoder based on X-Codes in to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using Singular Value Decomposition (SVD) and X-codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and the 2 × 2 real rotation matrices for each pair (parameterized with a single angle). This precoding structure enables to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is equivalent to i) optimizing the rotation angle and the power allocation within each pair and ii) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal precoder by Cruz et al., and significantly better than mercury/waterfilling strategy by Lozano et al.. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.

X-Codes: A Low Complexity Full-Rate High-Diversity Achieving Precoder for TDD MIMO Systems

We consider a time division duplex multiple-input multiple-output (nt × nr MIMO). Using channel state information (CSI) at the transmitter, singular value decomposition (SVD) of the channel matrix is performed. This transforms the MIMO channel into parallel subchannels, but has a low overall diversity order. Hence, we propose X-Codes which achieve a higher diversity order by pairing the subchannels, prior to SVD preceding. In particular, each pair of information symbols is encoded by a fixed 2 × 2 real rotation matrix. X-Codes can be decoded using nr very low complexity two-dimensional real sphere decoders. Error probability analysis for X-Codes enables us to choose the optimal pairing and the optimal rotation angle for each pair. Finally, we show that our new scheme outperforms other low complexity precoding schemes.

Performance analysis of single-symbol maximum likelihood decodable linear STBCs

Performance of space-time block codes can be improved using the coordinate interleaving of the input symbols from rotated M-ary phase shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) constellations. This paper is on the performance analysis of coordinate-interleaved space-time codes, which are a subset of single-symbol maximum likelihood decodable linear space-time block codes, for wireless multiple antenna terminals. The analytical and simulation results show that full diversity is achievable. Using the equivalent single-input single-output model, simple expressions for the average bit error rates are derived over flat uncorrelated Rayleigh fading channels. Optimum rotation angles are found by finding the minimum of the average bit error rate curves.

Precoding by Pairing Subchannels to Increase MIMO Capacity With Discrete Input Alphabets

We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non-diagonal precoder based on the X-Codes in 1] to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using singular value decomposition (SVD) and X-Codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and a 2 x 2 real rotation matrix for each pair (parameterized with a single angle). This precoding structure enables us to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is solved by: i) optimizing the rotation angle and the power allocation within each pair and ii) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal precoder by Cruz et al., and is significantly better than Mercury/waterfilling strategy by Lozano et al. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.

Half-sandwich (eta(6)-arene)ruthenium(II) chiral Schiff base complexes: Analysis of the diastereomeric mixtures in solution by 2D-NMR spectroscopy

2D NMR spectroscopy has been used to determine the metal configuration in solution of three complexes, viz. [(eta(6)-p-cymene)Ru(L*)Cl] (1) and [(eta(6)-p-cymene)Ru(L*)(L')] (ClO4) (L' = H2O, 2; PPh3, 3), where L* is the anion of (S)-(1-phenylethyl)salicylaldimine. The complexes exist in two diastereomeric forms in solution. Both the (R-Ru,S-C)- and (S-Ru,S-C)-diastereomers display the presence of attractive, CH/pi interaction involving the phenyl group attached to the chiral carbon and the cymene ring hydrogens. This interaction restricts the rotation of the C*-N single bond and, as a result, two structural types with either the hydrogen atom attached to the chiral carbon (C*) or the methyl group attached to C* in close proximity of the cymene ring protons get stabilized. Using 2D NMR spectroscopy as a tool, the spatial interaction involving these protons are studied in order to obtain the metal configuration(s) of the diastereomeric complexes in solution. This technique has enabled us to determine the metal configuration as (R-Ru,S-C) for the major isomers of 1-3 in solution.

On the importance of backbone loop and peptide flip in the Walker sequence in F-1-ATPase action

The Walker sequence, GXXXXGKT, present in all the six subunits of F-1-ATPase exists in a folded form, known as phosphate-binding loop (P-loop). Analysis of the Ramachandran angles showed only small RMS deviation between the nucleotide-bound and nucleotide-free forms. This indicated a good overlap of the backbone loops. The catalytic beta-subunits (chains D, E and F) showed significant changes in the Ramachandran angles and the side chain torsion angles, but not the structural alpha-subunits (chains A, B and C). Most striking among these are the changes associated with Val160 and Gly161 corresponding to a flip in the peptide unit between them when a nucleotide is bound (chains D or F compared to nucleotide-free chain E). The conformational analysis further revealed a hitherto unnoticed hydrogen bond between amide-N of the flipped Gly161 and terminal phosphate-O of the nucleotide. This assigns a role for this conserved amino acid, otherwise ignored, of making an unusual direct interaction between the peptide backbone of the enzyme protein and the incoming nucleotide substrate. Significance of this interaction is enhanced, as it is limited only to the catalytic subunits, and also likely to involve a mechanical rotation of bonds of the peptide unit. Hopefully this is part of the overall events that link the chemical hydrolysis of ATP with the mechanical rotation of this molecule, now famous as tiny molecular motor.

Unimolecular HCl elimination from 1,2-dichloroethane: A single pulse shock tube and ab initio study

Thermal decomposition of 1,2-dichloroethane (1,2-DCE) has been studied in the temperature range of 10501175 K behind reflected shock waves in a single pulse shock tube. The unimolecular elimination of HCl is found to be the major channel through which 1,2-DCE decomposes under these conditions. The rate constant for the unimolecular elimination of HCl from 1,2-dichloroethane is found to be 10(13.98+/-0.80) exp(-57.8+/-2.0/RT) s(-1), where the activation energy is given in kcal mol(-1) and is very close to that value for CH3CH2Cl (EC). Ab initio (HF and MP2) and DFT calculations have been carried out to find the activation barrier and the structure of the transition state for this reaction channel from both EC and 1,2-DCE. The preexponential factors calculated at various levels of theory (BF/6-311++G**, MP2/6-311++G**, and B3LYP/6-311++G**) are (approximate to10(15) s(-1)) significantly larger than the experimental results. If the torsional mode in the ground state is treated as free internal rotation the preexponential factors reduce significantly, giving excellent agreement with experimental values. The DFT results are in excellent (fortuitous?) agreement with the experimental value for activation energy for 1,2-DCE while the MP2 and HF results seem to overestimate the barrier. However, DFT results for EC is 4.5 kcal mol(-1) less than the previously reported experimental values. At all levels, theory predicts an increase in HCI elimination barrier on beta-Cl substitution on EC.

Mutagenicity associated with O6-methylguanine-DNA damage and mechanism of nucleotide flipping by AGT during repair

Methylated guanine damage at O6 position (i.e. O6MG) is dangerous due to its mutagenic and carcinogenic character that often gives rise to G:C-A:T mutation. However, the reason for this mutagenicity is not known precisely and has been a matter of controversy. Further, although it is known that O6-alkylguanine-DNA alkyltransferase (AGT) repairs O6MG paired with cytosine in DNA, the complete mechanism of target recognition and repair is not known completely. All these aspects of DNA damage and repair have been addressed here by employing high level density functional theory in gas phase and aqueous medium. It is found that the actual cause of O6MG mediated mutation may arise due to the fact that DNA polymerases incorporate thymine opposite to O6MG, misreading the resulting O6MG:T complex as an A:T base pair due to their analogous binding energies and structural alignments. It is further revealed that AGT mediated nucleotide flipping occurs in two successive steps. The intercalation of the finger residue Arg 128 into the DNA double helix and its interaction with the O6MG: C base pair followed by rotation of the O6MG nucleotide are found to be crucial for the damage recognition and nucleotide flipping.

Analysis of shear bands in slow granular flows using a frictional Cosserat model

The slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

Full Sphere Axisymmetric Simulations of the Solar Dynamo

We explore a full sphere (2D axisymmetric) kinematic solar dynamo model based on the Babcock-Leighton idea that the poloidal field is generated in the surface layers from the decay of tilted bipolar solar active regions. This model incorporates the helioseismically deduced solar rotation profile and an algorithm for buoyancy motivated from simulations of flux tube dynamics. A prescribed deep meridional circulation plays an important role in the advection of magnetic flux. We specifically address the parity issue and show that – contrary to some recent claims – the Babcock-Leighton dynamo can reproduce solar-like dipolar parity if certain reasonable conditions are satisfied in the solar interior, the most important requirement being that the poloidal field of the two hemispheres be efficiently coupled across the equator.

Cloning, expression, purification and preliminary X-ray diffraction studies of a putative Mycobacterium smegmatis thiolase

Thiolases are important in fatty-acid degradation and biosynthetic pathways. Analysis of the genomic sequence of Mycobacterium smegmatis suggests the presence of several putative thiolase genes. One of these genes appears to code for an SCP-x protein. Human SCP-x consists of an N-terminal domain (referred to as SCP2 thiolase) and a C-terminal domain (referred as sterol carrier protein 2). Here, the cloning, expression, purification and crystallization of this putative SCP-x protein from M. smegmatis are reported. The crystals diffracted X-rays to 2.5 angstrom resolution and belonged to the triclinic space group P1. Calculation of rotation functions using X-ray diffraction data suggests that the protein is likely to possess a hexameric oligomerization with 32 symmetry which has not been observed in the other six known classes of this enzyme.

Dynamics of bound dyes in a nonpolymeric aqueous gel derived from a tripodal bile salt

Rotational dynamics of polarity sensitive fluorescent dyes (ANS and DPH) in a nonpolymertic aqueous gel derived from tripodal cholamide I was studied using ultrafast time-resolved fluorescence technique. Results were compared with that of naturally occurring di- and trihydroxy bile salts. ANS in the gel showed two rotational correlation time (phi) components, 13.2 ns (bound to the hydrophobic region of the gel) and 1.0 ns (free aqueous ANS), whereas DPH showed only one component (4.8 ns). In the sol state, faster rotational motion was observed, both for ANS and DPH. Our data revealed that dyes get encapsulated more tightly in the gel network when compared to the micellar aggregates. ANS has more restrained rotation compared to DPH. This was attributed to the interaction of the sulfonate group of ANS with water molecules and hydrophilic parts of the gelator molecule. No restricted rotation was observed for DPH in the gel state unlike when it is in the gel phase of lipid bilayer.

Theoretical determination of HI vertical scale heights in the dwarf galaxies DDO 154, Ho II, IC 2574 and NGC 2366

In this paper, we model dwarf galaxies as a two-component system of gravitationally coupled stars and atomic hydrogen gas in the external force field of a pseudo-isothermal dark matter halo, and numerically obtain the radial distribution of HI vertical scale heights. This is done for a group of four dwarf galaxies (DDO 154, Ho II, IC 2574 and NGC 2366) for which most necessary input parameters are available from observations. The formulation of the equations takes into account the rising rotation curves generally observed in dwarf galaxies. The inclusion of self-gravity of the gas into the model at par with that of the stars results in scale heights that are smaller than what was obtained by previous authors. This is important as the gas scale height is often used for deriving other physical quantities. The inclusion of gas self-gravity is particularly relevant in the case of dwarf galaxies where the gas cannot be considered a minor perturbation to the mass distribution of the stars. We find that three out of four galaxies studied show a flaring of their HI discs with increasing radius, by a factor of a few within several disc scale lengths. The fourth galaxy has a thick HI disc throughout. This flaring arises as a result of the gas velocity dispersion remaining constant or decreasing only slightly while the disc mass distribution declines exponentially as a function of radius.