Feynman integrals with tensorial structure in the negative dimensional integration scheme

The negative-dimensional integration method (NDIM) is revealing itself as a very useful technique for computing massless and/or massive Feynman integrals, covariant and noncovanant alike. Up until now however, the illustrative calculations done using such method have been mostly covariant scalar integrals/without numerator factors. We show here how those integrals with tensorial structures also can be handled straightforwardly and easily. However, contrary to the absence of significant features in the usual approach, here the NDIM also allows us to come across surprising unsuspected bonuses. Toward this end, we present two alternative ways of working out the integrals and illustrate them by taking the easiest Feynman integrals in this category that emerge in the computation of a standard one-loop self-energy diagram. One of the novel and heretofore unsuspected bonuses is that there are degeneracies in the way one can express the final result for the referred Feynman integral.

Synthesis, structure, and thermal stability of poly(methyl methacrylate)-co- poly(3-tri(methoxysilyil)propyl methacrylate)/ montmorillonite nanocomposites

The structure and the thermodegradation behavior of both poly(methyl methacrylate)-co-poly(3-tri(methoxysilyil)propyl methacrylate) polymer modified with silyl groups and of intercalated poly(methyl methacrylate)-co-poly(3- tri(methoxysilyil)propyl methacrylate)/Cloisite 15A™ nanocomposite have been in situ probed. The structural feature were comparatively studied by Fourier transform infrared spectroscopy (FTIR), 13C and 29Si nuclear magnetic resonance (NMR), and small angle X-ray scattering (SAXS) measurements. The intercalation of polymer in the interlayer galleries was evidenced by the increment of the basal distance from 31 to 45 Å. The variation of this interlayer distance as function of temperature was followed by in situ SAXS. Pristine polymer decomposition pathway depends on the atmosphere, presenting two steps under air and three under N2. The nanocomposites are more stable than polymer, and this thermal improvement is proportional to the clay loading. The experimental results indicate that clay nanoparticles play several different roles in polymer stabilization, among them, diffusion barrier, charring, and suppression of degradation steps by chemical reactions between polymer and clay. Charring is atmosphere dependent, occurring more pronounced under air. © 2012 Society of Plastics Engineers.

Modelling the surface circulation and thermal structure of a tropical reservoir using three-dimensional hydrodynamic lake model and remote-sensing data

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A new approach to the electronic structure of two dimensional disordered alloys

We propose a novel method to calculate the electronic Density of States (DOS) of a two dimensional disordered binary alloy. The method is highly reliable and numerically efficient, and Short Range Order (SRO) correlations can be included with no extra computational cost. The approach devised rests on one dimensional calculations and is applied to very long stripes of finite width, the bulk regime being achieved with a relatively small number of chains in the disordered case. Our approach is exact for the pure case and predicts the correct DOS structure in important limits, such as the segregated, random, and ordered alloy regimes. We also suggest important extensions of the present work. © 1995.

Stoichiometry, structure, and transport in the quasi-one-dimensional metal Li0.9Mo6O17

A correlation between lattice parameters, oxygen composition, and the thermoelectric and Hall coefficients is presented for single-crystal Li0.9Mo6O17, a quasi-one-dimensional (Q1D) metallic compound. The possibility that this compound is a compensated metal is discussed in light of a substantial variability observed in the literature for these transport coefficients.

Novel sst2-selective somatostatin agonists. Three-dimensional consensus structure by NMR

The 3D NMR structures of six octapeptide agonist analogues of somatostatin (SRIF) in the free form are described. These analogues, with the basic sequence H-DPhe/Phe2-c[Cys3-Xxx7-DTrp8-Lys9-Thr10-Cys14]-Thr-NH2 (the numbering refers to the position in native SRIF), with Xxx7 being Ala/Aph, exhibit potent and highly selective binding to human SRIF type 2 (sst2) receptors. The backbone of these sst2-selective analogues have the usual type-II' beta-turn reported in the literature for sst2/3/5-subtype-selective analogues. Correlating the biological results and NMR studies led to the identification of the side chains of DPhe2, DTrp8, and Lys9 as the necessary components of the sst2 pharmacophore. This is the first study to show that the aromatic ring at position 7 (Phe7) is not critical for sst2 binding and that it plays an important role in sst3 and sst5 binding. This pharmacophore is, therefore, different from that proposed by others for sst2/3/5 analogues.

Three-dimensional consensus structure of sst2-selective somatostatin (SRIF) antagonists by NMR

The three-dimensional NMR structures of seven octapeptide analogs of somatostatin (SRIF), based on octreotide, with the basic sequence H-Cpa/Phe2-c[DCys3-Xxx7-DTrp/DAph(Cbm)8-Lys9-Thr10-Cys14]-Yyy-NH2 (the numbering refers to the position in native SRIF), with Xxx7 being Aph(Cbm)/Tyr/Agl(NMe,benzoyl) and Yyy being Nal/DTyr/Thr, are presented here. Most of these analogs exhibit potent and highly selective binding to sst2 receptors, and all of the analogs are antagonists inhibiting receptor signaling. Based on their consensus 3D structure, the pharmacophore of the sst2-selective antagonist has been defined. The pharmacophore involves the side chains of Cpa2, DTrp/DAph(Cbm)8, and Lys9, with the backbone for most of the sst2-selective antagonists comprised a Type-II' beta-turn. Hence, the sst2-selective antagonist pharmacophore is very similar to the sst2-selective agonist pharmacophore previously described.

Two dimensional Lattice Boltzmann simulation of fluid flow through an idealized micro-structure of disordered media

This technical report discusses the application of Lattice Boltzmann Method (LBM) in the fluid flow simulation through porous filter-wall of disordered media. The diesel particulate filter (DPF) is an example of disordered media. DPF is developed as a cutting edge technology to reduce harmful particulate matter in the engine exhaust. Porous filter-wall of DPF traps these soot particles in the after-treatment of the exhaust gas. To examine the phenomena inside the DPF, researchers are looking forward to use the Lattice Boltzmann Method as a promising alternative simulation tool. The lattice Boltzmann method is comparatively a newer numerical scheme and can be used to simulate fluid flow for single-component single-phase, single-component multi-phase. It is also an excellent method for modelling flow through disordered media. The current work focuses on a single-phase fluid flow simulation inside the porous micro-structure using LBM. Firstly, the theory concerning the development of LBM is discussed. LBM evolution is always related to Lattice gas Cellular Automata (LGCA), but it is also shown that this method is a special discretized form of the continuous Boltzmann equation. Since all the simulations are conducted in two-dimensions, the equations developed are in reference with D2Q9 (two-dimensional 9-velocity) model. The artificially created porous micro-structure is used in this study. The flow simulations are conducted by considering air and CO2 gas as fluids. The numerical model used in this study is explained with a flowchart and the coding steps. The numerical code is constructed in MATLAB. Different types of boundary conditions and their importance is discussed separately. Also the equations specific to boundary conditions are derived. The pressure and velocity contours over the porous domain are studied and recorded. The results are compared with the published work. The permeability values obtained in this study can be fitted to the relation proposed by Nabovati [8], and the results are in excellent agreement within porosity range of 0.4 to 0.8.

Magnetic structure of two- and three-dimensional supramolecular compounds

Supramolecular chiral networks of oxalato-bridged transition metals show either two- or three-dimensional structural features. The magnetic structures of such compounds have been investigated by means of elastic neutron powder diffraction.

Morphological Functions to Quantify Three-Dimensional Tomograms of Macropore Structure in a Vineyard Soil with Two Different Management Regimes

Soil tomography and morphological functions built over Minkowski functionals were used to describe the impact on pore structure of two soil management practices in a Mediterranean vineyard. Soil structure controls important physical and biological processes in soil–plant–microbial systems. Those processes are dominated by the geometry of soil pore structure, and a correct model of this geometry is critical for understanding them. Soil tomography has been shown to provide rich three-dimensional digital information on soil pore geometry. Recently, mathematical morphological techniques have been proposed as powerful tools to analyze and quantify the geometrical features of porous media. Minkowski functionals and morphological functions built over Minkowski functionals provide computationally efficient means to measure four fundamental geometrical features of three-dimensional geometrical objects, that is, volume, boundary surface, mean boundary surface curvature, and connectivity. We used the threshold and the dilation and erosion of three-dimensional images to generate morphological functions and explore the evolution of Minkowski functionals as the threshold and as the degree of dilation and erosion changes. We analyzed the three-dimensional geometry of soil pore space with X-ray computed tomography (CT) of intact soil columns from a Spanish Mediterranean vineyard by using two different management practices (conventional tillage versus permanent cover crop of resident vegetation). Our results suggested that morphological functions built over Minkowski functionals provide promising tools to characterize soil macropore structure and that the evolution of morphological features with dilation and erosion is more informative as an indicator of structure than moving threshold for both soil managements studied.

Definition of a metal-dependent/Li(+)-inhibited phosphomonoesterase protein family based upon a conserved three-dimensional core structure.

Inositol polyphosphate 1-phosphatase, inositol monophosphate phosphatase, and fructose 1,6-bisphosphatase share a sequence motif, Asp-Pro-(Ile or Leu)-Asp-(Gly or Ser)-(Thr or Ser), that has been shown by crystallographic and mutagenesis studies to bind metal ions and participate in catalysis. We compared the six alpha-carbon coordinates of this motif from the crystal structures of these three phosphatases and found that they are superimposable with rms deviations ranging from 0.27 to 0.60 A. Remarkably, when these proteins were aligned by this motif a common core structure emerged, defined by five alpha-helices and 11 beta-strands comprising 155 residues having rms deviations ranging from 1.48 to 2.66 A. We used the superimposed structures to align the sequences within the common core, and a distant relationship was observed suggesting a common ancestor. The common core was used to align the sequences of several other proteins that share significant similarity to inositol monophosphate phosphatase, including proteins encoded by fungal qa-X and qutG, bacterial suhB and cysQ (identical to amtA), and yeast met22 (identical to hal2). Evolutionary comparison of the core sequences indicate that five distinct branches exist within this family. These proteins share metal-dependent/Li(+)-sensitive phosphomonoesterase activity, and each predicted tree branch exhibits unique substrate specificity. Thus, these proteins define an ancient structurally conserved family involved in diverse metabolic pathways including inositol signaling, gluconeogenesis, sulfate assimilation, and possibly quinone metabolism. Furthermore, we suggest that this protein family identifies candidate enzymes to account for both the therapeutic and toxic actions of Li+ as it is used in patients treated for manic depressive disease.

The structure and dynamics of 2-dimensional fluids in swelling clays

The interlayer pores of swelling 2:1 clays provide an ideal 2-dimensional environment in which to study confined fluids. In this paper we discuss our understanding of the structure and dynamics of interlayer fluid species in expanded clays, based primarily on the outcome of recent molecular modelling and neutron scattering studies. Counterion solvation is compared with that measured in bulk solutions, and at a local level the cation-oxygen coordination is found to be remarkably similar in these two environments. However, for the monovalent ions the contribution to the first coordination shell from the clay surfaces increases with counterion radius. This gives rise to inner-sphere (surface) complexes in the case of potassium and caesium. In this context, the location of the negative clay surface charge (i.e. arising from octahedral or tetrahedral substitution) is also found to be of major importance. Divalent cations, such as calcium, eagerly solvate to form outer-sphere complexes. These complexes are able to pin adjacent clay layers together, and thereby prevent colloidal swelling. Confined water molecules form hydrogen bonds to each other and to the clays' surfaces. In this way their local environment relaxes to close to the bulk water structure within two molecular layers of the clay surface. Finally, we discuss the way in which the simple organic molecules methane, methanol and ethylene glycol behave in the interlayer region of hydrated clays. Quasi-elastic neutron scattering of isotopically labelled interlayer CH 3OD and (CH2OD)2 in deuterated clay allows us to measure the diffusion of the CH3- and CH2-groups in both clay and liquid environments. We find that in both the one-layer methanol solvates and the two-layer glycol solvates the diffusion of the most mobile organic molecules is close to that in the bulk solution.

Structure and physical properties of [µ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘')iron(II)] Bis(hexafluorophosphate), a new Fe(II) spin-crossover compound with a three-dimensional threefold interlocked crystal lattice

[μ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘)iron(II)] bis(hexafluorophosphate), [Fe(btzb)3](PF6)2, crystallizes in a three-dimensional 3-fold interlocked structure featuring a sharp two-step spin-crossover behavior. The spin conversion takes place between 164 and 182 K showing a discontinuity at about T1/2 = 174 K and a hysteresis of about 4 K between T1/2 and the low-spin state. The spin transition has been independently followed by magnetic susceptibility measurements, 57Fe-Mössbauer spectroscopy, and variable temperature far and midrange FTIR spectroscopy. The title compound crystallizes in the trigonal space group P30¯(No. 147) with a unit cell content of one formula unit plus a small amount of disordered solvent. The lattice parameters were determined by X-ray diffraction at several temperatures between 100 and 300 K. Complete crystal structures were resolved for 9 of these temperatures between 100 (only low spin, LS) and 300 K (only high spin, HS), Z = 1 [Fe(btzb)3](PF  6)2:  300 K (HS), a = 11.258(6) Å, c = 8.948(6) Å, V = 982.2(10) Å3; 100 K (LS), a = 10.989(3) Å, c = 8.702(2) Å, V = 910.1(4) Å3. The molecular structure consists of octahedral coordinated iron(II) centers bridged by six N4,N4‘ coordinating bis(tetrazole) ligands to form three 3-dimensional networks. Each of these three networks is symmetry related and interpenetrates each other within a unit cell to form the interlocked structure. The Fe−N bond lengths change between 1.993(1) Å at 100 K in the LS state and 2.193(2) Å at 300 K in the HS state. The nearest Fe separation is along the c-axis and identical with the lattice parameter c.