Geometry of the de-Sitter universe

By making use of the fact that the de-Sitter metric corresponds to a hyperquadric in a five-dimensional flat space, it is shown that the three Robertson-Walker metrics for empty spacetime and positive cosmological constant, corresponding to 3-space of positive, negative and zero curvative, are geometrically equivalent. The 3-spaces correspond to intersections of the hyperquadric by hyperplanes, and the time-like geodesics perpendicular to them correspond to intersections by planes, in all three cases.

In-plane normal vibrations of 1,2,5-oxa-, thia- and selena-diazoles, 1,3,4-oxa- and thia-diazoles and 1,2,3,4-thiatriazoles

In-plane vibration modes of 1,2,5- and 1,3,4-oxa- and thia-diazoles, and 1,2,5-selenadiazole have been assigned on the basis of detailed normal coordinate analysis employing data on several deuterated species. In-plane vibration frequencies of two 1,2,3,4-thiatriazole derivatives have been calculated and compared with observed values.

Structural studies of analgesics and their interactions. Part 4. Crystal structures of phenylbutazone and a 2 : 1 complex between phenylbutazone and piperazine

The X-ray crystal structures of 4-butyl-1,2-diphenylpyrazolidine-3,5-dione (phenylbutazone)(I). and its 2 : 1 complex (II) with piperazine have been determined by direct methods and the structures refined to R 0.096 (2 300 observed reflections measured by diffractometer) and 0.074 (2 494 observed reflections visuallyestimated). Crystals are monoclinic, space group P21/c; for (I)a= 21.695(4), b= 5.823(2), c= 27.881(4)Å, = 108.06 (10)°, Z= 8, and for (II)a= 8.048(4), b= 15.081(4), c= 15.583(7)Å, = 95.9(3)°, Z= 2. The two crystallographically independant molecules in the structure of (I) are similar except for the conformation of the butyl group, which is disordered in one of the molecules. In the pyrazolidinedione group, the two C–C bonds are single and the two C–O bonds double. The two nitrogen atoms in the five-membered ring are pyramidal with the attached phenyl groups lying on the opposite sides of the mean plane of the ring. The phenylbutazone molecule in (II) exists as a negative ion owing to deprotonation of C-4. C-4 is therefore trigonal and the orientation of the Bu group with respect to the pyrazolidinedione group is considerably different from that in (I); there is also considerable electron delocalization along the C–O and C–C bonds. These changes in geometry and electronic structure may relate to biological activity. The doubly charged cationic piperazine molecule exists in the chair form with the nitrogen atoms at the apices. The crystal structure of (II) is stabilized by ionic interactions and N–H O hydrogen bonds.

On plane-wave propagation in a uniform pipe in the presence of a mean flow and a temperature gradient

A theoretical study on the propagation of plane waves in the presence of a hot mean flow in a uniform pipe is presented. The temperature variation in the pipe is taken to be a linear temperature gradient along the axis. The theoretical studies include the formulation of a wave equation based on continuity, momentum, and state equation, and derivation of a general four-pole matrix, which is shown to yield the well-known transfer matrices for several other simpler cases.

Stereospecific photodimerization of coumarins in crystalline inclusion complexes. Molecular and crystal structure of 1:2 complex of (S,S)-(-)-1,6-bis(o-chlorophenyl)-1,6-diphenyl-hexa-2,4-diyne-1,6-diol and coumarin

Proximity of molecules is a crucial factor in many solid- state photochemical processes.'S2 The biomolecular photodimerization reactions in the solid state depend on the relative geometry of reactant molecules in the crystal lattice with center-to-center distance of nearest neighbor double bonds of the order of ca. 4 A. This fact emanates from the incisive studies of Schmidt and Cohen.2 One of the two approaches to achieve this distance requirement is the so-called "Crystal-Engineering" of structures, which essentially involves the introduction of certain functional groups that display in-plane interstacking interactions (Cl...Cl, C-He-0, etc.) in the crystal The chloro group is by far the most successful in promoting the /3- packing m ~ d e ,th~o,u~gh recent studies have shown its limitations? Another approach involves the use of constrained media in which the reactants could hopefully be aligned.

Design and characterization of in-plane MEMS yaw rate sensor

In this paper, we present the design and characterization of a vibratory yaw rate MEMS sensor that uses in-plane motion for both actuation and sensing. The design criterion for the rate sensor is based on a high sensitivity and low bandwidth. The required sensitivity of the yawrate sensor is attained by using the inplane motion in which the dominant damping mechanism is the fluid loss due to slide film damping i.e. two-three orders of magnitude less than the squeeze-film damping in other rate sensors with out-of-plane motion. The low bandwidth is achieved by matching the drive and the sense mode frequencies. Based on these factors, the yaw rate sensor is designed and finally realized using surface micromachining. The inplane motion of the sensor is experimentally characterized to determine the sense and the drive mode frequencies, and corresponding damping ratios. It is found that the experimental results match well with the numerical and the analytical models with less than 5% error in frequencies measurements. The measured quality factor of the sensor is approximately 467, which is two orders of magnitude higher than that for a similar rate sensor with out-of-plane sense direction.

Qed On The Groenewold-Moyal Plane

We investigate a version of noncommutative QED where the interaction term, although natural, breaks the spin-statistics connection. We calculate e(-) + e(-) -> e(-) + e(-) and gamma + e(-) -> gamma + e(-) cross-sections in the tree approximation and explicitly display their dependence on theta(mu nu). Remarkably the zero of the elastic e(-) + e(-) -> e(-) + e(-) cross-section at 90 degrees in the center-of-mass system, which is due to Pauli principle, is shifted away as a function of theta(mu nu) and energy.

A Compact Defected Ground Microstrip Device with Photonic Bandgap Effects

Filters and other devices using photonic bandgap (PBG) theory are typically implemented in microstrip lines by etching periodic holes on the ground plane of the microstrip. The period of such several holes corresponds to nearly half the guided wavelength of the transmission line. In this paper we study the effects of miniaturization of the PBG device by meandering the microstrip line about one single hole in the ground plane. A comparison of the S-parameters and dispersion behavior of the modified geometry and a conventional PBG device with a straight microstrip line shows that these devices have similar behaviors.

Inter-helical Interactions in Membrane Proteins: Analysis Based on the Local Backbone Geometry and the Side Chain Interactions

The availability of a significant number of the Structures of helical membrane proteins has prompted us to investigate the mode of helix-helix packing. In the present study, we have considered a dataset of alpha-helical membrane proteins representing Structures solved from all the known superfamilies. We have described the geometry of all the helical residues in terms of local coordinate axis at the backbone level. Significant inter-helical interactions have been considered as contacts by weighing the number of atom-atom contacts, including all the side-chain atoms. Such a definition of local axis and the contact criterion has allowed us to investigate the inter-helical interaction in a systematic and quantitative manner. We show that a single parameter (designated as alpha), which is derived from the parameters representing the Mutual orientation of local axes, is able to accurately Capture the details of helix-helix interaction. The analysis has been carried Out by dividing the dataset into parallel, anti-parallel, and perpendicular orientation of helices. The study indicates that a specific range of alpha value is preferred for interactions among the anti-parallel helices. Such a preference is also seen among interacting residues of parallel helices, however to a lesser extent. No such preference is seen in the case of perpendicular helices, the contacts that arise mainly due to the interaction Of Surface helices with the end of the trans-membrane helices. The Study Supports the prevailing view that the anti-parallel helices are well packed. However, the interactions between helices of parallel orientation are non-trivial. The packing in alpha-helical membrane proteins, which is systematically and rigorously investigated in this study, may prove to be useful in modeling of helical membrane proteins.

Crack Tip Fields in a Single Edge Notched Aluminum Single Crystal Specimen

We report a combined experimental and computational study of a low constraint aluminum single crystal fracture geometry and investigate the near-tip stress and strain fields. To this end, a single edge notched tensile (SENT) specimen is considered. A notch, with a radius of 50 µm, is taken to lie in the (010) plane and its front is aligned along the [101] direction. Experiments are conducted by subjecting the specimen to tensile loading using a special fixture inside a scanning electron microscope chamber. Both SEM micrographs and electron back-scattered diffraction (EBSD) maps are obtained from the near-tip region. The experiments are complemented by performing 3D and 2D plane strain finite element simulations within a continuum crystal plasticity framework assuming an isotropic hardening response characterized by the Pierce–Asaro–Needleman model. The simulations show a distinct slip band forming at about 55 deg with respect to the notch line corresponding to slip on (11-bar 1)[011] system, which corroborates well with experimental data. Furthermore, two kink bands occur at about 45 deg and 90 deg with respect to the notch line within which large rotations in the crystal orientation take place. These predictions are in good agreement with the EBSD observations. Finally, the near-tip angular variations of the 3D stress and plastic strain fields in the low constraint SENT fracture geometry are examined in detail.

DNA cleavage in red light promoted by copper(II) complexes of -amino acids and photoactive phenanthroline bases

Ternary copper(II) complexes [Cu(L-trp)(B)(H2O)](NO3) ( 1–3) and [Cu(L-phe)(B)(H2O)](NO3) ( 4–6) of L-tryptophan (L-trp) and L-phenylalanine (L-phe) having phenanthroline bases (B), viz. 1,10-phenanthroline (phen, 1 and 4), dipyrido[3,2-d:2,3-f]quinoxaline (dpq, 2 and 5) and dipyrido[3,2-a:2,3-c]phenazine (dppz, 3 and 6), were prepared and characterized by physico-chemical techniques. Complexes 3 and 6 were structurally characterized by X-ray crystallography and show the presence of a square pyramidal (4 + 1) CuN3O2 coordination geometry in which the N,O-donor amino acid (L-trp or L-phe) and N,N-donor phenanthroline base bind at the equatorial plane with an aqua ligand coordinated at the elongated axial site. Complex 3 shows significant distortion from the square pyramidal geometry and a strong intramolecular – stacking interaction between the pendant indole ring of L-trp and the planar dppz aromatic moiety. All the complexes display good binding propensity to the calf thymus DNA giving an order: 3, 6 (dppz) > 2, 5 (dpq) > 1, 4 (phen). The binding constant (Kb) values are in the range of 2.1 × 104–1.1 × 106 mol-1 with the binding site size (s) values of 0.17–0.63. The phen and dpq complexes are minor groove binders while the dppz analogues bind at the DNA major groove. Theoretical DNA docking studies on 2 and 3 show the close proximity of two photosensitizers, viz. the indole moiety of L-trp and the quinoxaline/phenazine of the dpq/dppz bases, to the complementary DNA strands. Complexes 2 and 3 show oxidative DNA double strand breaks (dsb) of supercoiled (SC) DNA forming a significant quantity of linear DNA along with the nicked circular (NC) form on photoexposure to UV-A light of 365 nm and red light of 647.1 nm (Ar–Kr laser). Complexes 1, 5 and 6 show only single strand breaks (ssb) forming NC DNA. The red light induced DNA cleavage involves metal-assisted photosensitization of L-trp and dpq/dppz base resulting in the formation of a reactive singlet oxygen (1O2) species.

Synthesis and structural characterization of a new ruthenium hydride ethylene complex

A ruthenium(II) ethylene complex, trans-[Ru(H)(C2H4)- (dppm)(2)][BF4], hearing two 1,1-bis(diphenylphosphino) methane (dppm) ligands has been synthesized and structurally characterized using X-ray crystallography. In the molecular structure, the Ru-II center shows a distorted octahedral coordination geometry formed by four P atoms of the two chelating dppm ligands, a hydride, and an ethylene ligands. The four dppm P atoms are almost co-planar with the hydride and the ethylene ligands perpendicular to this plane. The C-C bond distance of the bound ethylene is 1.375(6) angstrom, which is elongated by 0.042 angstrom as compared to free ethylene (1.333(2) angstrom). The packing diagram of the complex shows two voids or channels, which are occupied by BF4- counterion and water molecules.

Design of plane sand-bed channels affected by seepage

The importance of seepage in the design of channels is discussed. Experimental investigations reveal that seepage, either in the downward direction (suction) or in the upward direction (injection), can significantly change the resistance as well as the mobility of the sand-bed particles. A resistance equation relating 'particle Reynolds number' and 'shear Reynolds number' under seepage conditions is developed for plane sediment beds. Finally, a detailed design procedure of the plane sediment beds affected by seepage is presented.

Simultaneous material selection and geometry design of statically determinate trusses using continuous optimization

In this work, we explore simultaneous geometry design and material selection for statically determinate trusses by posing it as a continuous optimization problem. The underlying principles of our approach are structural optimization and Ashby’s procedure for material selection from a database. For simplicity and ease of initial implementation, only static loads are considered in this work with the intent of maximum stiffness, minimum weight/cost, and safety against failure. Safety of tensile and compression members in the truss is treated differently to prevent yield and buckling failures, respectively. Geometry variables such as lengths and orientations of members are taken to be the design variables in an assumed layout. Areas of cross-section of the members are determined to satisfy the failure constraints in each member. Along the lines of Ashby’s material indices, a new design index is derived for trusses. The design index helps in choosing the most suitable material for any geometry of the truss. Using the design index, both the design space and the material database are searched simultaneously using gradient-based optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous, although the material selection from a database is an inherently discrete problem. A few illustrative examples are included. It is observed that the method is capable of determining the optimal topology in addition to optimal geometry when the assumed layout contains more links than are necessary for optimality.

Strong motion compatible source geometry

Strong motion array records are analyzed in this paper to identify and map the source zone of four past earthquakes. The source is represented as a sequence of double couples evolving as ramp functions, triggering at different instants, distributed in a region yet to be mapped. The known surface level ground motion time histories are treated as responses to the unknown double couples on the fault surface. The location, orientation, magnitude, and risetime of the double couples are found by minimizing the mean square error between analytical solution and instrumental data. Numerical results are presented for Chi-Chi, Imperial Valley, San Fernando, and Uttarakashi earthquakes. Results obtained are in good agreement with field investigations and those obtained from conventional finite fault source inversions.