Baryon squishing in synthetic dimensions by effective SU(M) gauge fields

The ``synthetic dimension'' proposal A. Celi et al., Phys. Rev. Lett. 112, 043001 (2014)] uses atoms with M internal states (''flavors'') in a one-dimensional (1D) optical lattice, to realize a hopping Hamiltonian equivalent to the Hofstadter model (tight-binding model with a given magnetic flux per plaquette) on an M-sites-wide square lattice strip. We investigate the physics of SU(M) symmetric interactions in the synthetic dimension system. We show that this system is equivalent to particles with SU(M) symmetric interactions] experiencing an SU(M) Zeeman field at each lattice site and a non-Abelian SU(M) gauge potential that affects their hopping. This equivalence brings out the possibility of generating nonlocal interactions between particles at different sites of the optical lattice. In addition, the gauge field induces a flavor-orbital coupling, which mitigates the ``baryon breaking'' effect of the Zeeman field. For M particles, concomitantly, the SU(M) singlet baryon which is site localized in the usual 1D optical lattice, is deformed to a nonlocal object (''squished baryon''). We conclusively demonstrate this effect by analytical arguments and exact (numerical) diagonalization studies. Our study promises a rich many-body phase diagram for this system. It also uncovers the possibility of using the synthetic dimension system to laboratory realize condensed-matter models such as the SU(M) random flux model, inconceivable in conventional experimental systems.

Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

Solution conformations of penta and heptapeptides containing repetitive α-aminoisobutyryl-Image -alanyl and α -aminoisobutyryl-Image -valyl sequences

The presence of folded solution conformations in the peptides Boc-Ala-(Aib-Ala)2-OMe, Boc-Val-(Aib-Val) 2-OMe, Boc-Ala-(Aib-Ala)3-OMe and Boc-Val-(Aib-Val)3-OMe has been established by 270MHz 1H NMR. Intramolecularly H-bonded NH groups have been identified using temperature and solvent dependence of NH chemical shifts and paramagnetic radical induced broadening of NH resonances. Both pentapeptides adopt 310 helical conformations possessing 3 intramolecular H-bonds in CDCl3 and (CD3)2SO. The heptapeptides favour helical structures with 5 H-bonds in CDCl3. In (CD3)2SO only 4 H-bonds are readily detected.

Characterization of alinite cements through X-ray diffraction and mas 29Si NMR studies

Alinite cements have been synthesized using mining and steel plant wastes and pulverized fuel ash (fly ash) as raw materials and a clinkering temperature of 1150°C. The cements possess hydration characteristics comparable to those of portland cements. X-ray diffraction studies on these samples confirm the presence of alinite as the predominant phase. MAS 29Si NMR spectra have been used to distinguish alinite and alite cements. While both show resonances characteristic of Q° type silicate species, the portland cements exhibit three distinct peaks corresponding to three inequivalent SiO4 units present, while alinite shows a single sharp peak corresponding to the unique Si position.

Solid state and solution conformation of Boc-L-Met-Aib-L-Phe-OMe. Beta-turn conformation of a sequence related to an active chemotactic peptide analog

The conformation of the peptide Boc-L-Met-Aib-L-Phe-OMe has been studied in the solid state and solution by X-ray diffraction and 1H n.m.r., respectively. The peptide differs only in the N-terminal protecting group from the biologically active chemotactic peptide analog formyl-L-Met-Aib-L-Phe-OMe. The molecules adopt a type-II beta-turn in the solid state with Met and Aib as the corner residues (phi Met = -51.8 degrees, psi Met = 139.5 degrees, phi Aib = 58.1 degrees, psi Aib = 37.0 degrees). A single, weak 4----1 intramolecular hydrogen bond is observed between the Boc CO and Phe NH groups (N---O 3.25 A, N-H---O 128.4 degrees). 1H n.m.r. studies, using solvent and temperature dependencies of NH chemical shifts and paramagnetic radical induced line broadening of NH resonances, suggest that the Phe NH is solvent shielded in CDCl3 and (CD3)2SO. Nuclear Overhauser effects observed between Met C alpha H and Aib NH protons provide evidence of the occurrence of Met-Aib type-II beta-turns in these solvents.

1H and 13C NMR spectral studies of C-2 substituted isomeric exo- and endo-5-methyl-bicyclo[3.2.1]octane-6,8-diones

A detailed analysis of the 1H and 13C NMR spectra of C-2 aryl and alkyl/desalkyl substituted isomeric exo- and endo-5-methylbicyclo[3.2.1]octane-6,8-diones is presented. The chemical shift of the C-5 angular methyl, the C-2 alkyl/olefinic (C-10)/C-2 methine protons, the aromatic proton shieldings and the characteristic AMX and ABX spectral pattern of the ketomethylene and bridgehead protons were found to be sensitive to the phenyl ring orientation (anisotropy). These distinctive features could be used for configurational distinction for this class of compounds. With increasing ortho-methoxy substitution on the phenyl ring, considerable deshilelding of the bridgehead proton was observed (ca. 0.6 ppm). Absence of the C-2 alkyl group in the desalkyl isomers resulted in substantial changes in the chemical shifts of different protons. A study of the NMR spectra of the corresponding bicyclic compounds with C-2 methoxy/hydroxy substitution instead of the aryl group revealed that the anisotropy of the phenyl ring and the electronegative oxygen substituents have opposite effects. The 13C NMR spectral assignment of each carbon resonance of C-2 aryl and alkyl/desalkyl substituted isomeric exo- and endo-5-methylbicyclo[3.2.1]octane-6,8-diones and the corresponding C-2 methoxy/hydroxy/chloro and methyl bicyclic compounds are reported. Additional ortho-methoxy substitution on the phenyl ring was found to produce considerable high field shifts of the C-10 and C-1 carbon resonances. A high-field shift was observed for the C-6 and C-8 carbonyl carbons, presumably due to 1,3-dicarbonyl interactions. The chemical shifts of C-1 aromatic, C-10 alkyl and C-2 carbons, which are sensitive to exo/endo isomerism, could be utilized in differentiating a pair of isomers.

Pressure dependence of 35Cl nuclear quadrupole resonance in 2,5-, 2,6- and 3,5-dichlorophenols

Pressure dependence of the 35Cl Nuclear Quadrupole Resonances (N.Q.R.) in 2,5-, 2,6- and 3,5-dichlorophenols (DCP) has been studied up to a pressure of about 6·5 kbar at room temperature. While the pressure dependence of the two resonance lines in 2,6-DCP is essentially similar, the lower frequency line in 2,5-DCP is almost pressure independent and the higher frequency line shows a linear variation with pressure upto about 3·5 kbar but shows a negative pressure coefficient beyond this pressure. The two lines in 3,5-DCP have a non-linear pressure dependence with the curvature changing smoothly with pressure. The pressure coefficient for both lines becomes negative beyond a pressure of 5 kbar. The pressure dependence of the N.Q.R. frequencies is discussed in relation to intra- and inter-molecular contacts. Also, a thermodynamic analysis of the data is carried out to determine the constant volume temperature derivative of the N.Q.R. frequency.

Fluorescent probe and NMR studies of the aggregation of bile salts in aqueous solution

The binding of the fluorescent probes 1-anilino-8-naphthalene sulfonate and dansyl cadaverine to the sodium salts of cholic, deoxycholic and dehydrocholic acids has been investigated. Enhanced probe solubilisation accompanies aggregation. Monitoring of fluorescence intensities as a function of bile salt concentration permits the detection of primary micelle formation, as well as secondary association. The transition concentrations obtained by fluorescence are in good agreement with values determined for the critical micelle concentrations, by other methods. Differences in the behaviour of cholate and deoxycholate have been noted. Fluorescence polarisation studies of 1,6-diphenyl-1,3,5-hexatriene solubilised in bile salt micelles suggest a higher microviscosity for the interior of the deoxycholate micelle as compared to cholate. 1H NMR studies of deoxycholate over the range 1–100 mg/ml suggest that micelle formation leads to a greater immobilisation of the C18 and C19 methyl groups as compared to the C21 methyl group. Well resolved 13C resonances are observed for all three steroids even at high concentration. Both fluorescence and NMR studies confirm that dehydrocholate does not aggregate.

Natural Abundant Solid State NMR Studies in Designed Tripeptides for Differentiation of Multiple Conformers

Solid state NMR (SSNMR) experiments on heteronuclei in natural abundance are described for three synthetically designed tripeptides Piv-(L)Pro_(L)Pro-(L)Phe-OMe (1), Piv-(D)Pro_(L)Pro_(L)Phe-OMe (2), and Piv-(D)Pro_(L)Pro_(L)Phe-NHMe (3). These peptides exist in different conformation as shown by solution state NMR and single crystal X-ray analysis (Chatterjee et al., Chem Eur J 2008, 14, 6192). In this study, SSNMR has been used to probe the conformations of these peptides in their powder form. The C-13 spectrum of peptide (1) showed doubling of resonances corresponding to cis/cis form, unlike in solution where the similar doubling is attributed to cis/trans form. This has been confirmed by the chemical shift differences of C-beta and C-gamma carbon of Proline in peptide (1) both in solution and SSNMR. Peptide (2) and (3) provided single set of resonances which represented all transform across the di-Proline segment. The results are In agreement with the X-ray analysis. Solid state N-15 resonances, especially from Proline residues provided additional information, which is normally not observable in solution state NMR. H-1 chemical shifts are also obtained from a two-dimensional heteronuclear correlation experiment between H-1-C-13. The results confirm the utility of NMR as a useful tool for identifying different conformers in peptides in the solid state. (C) 2009 Wiley Periodicals, Inc. Biopolymers 91: 851-860, 2009.

Temperature dependence of 35Cl NQR in 3,4-Dichlorophenol

NQR frequencies in 3,4-dichlorophenol are investigated in the temperature range 77 K to room temperature. Two resonances have been observed throughout the temperature range, corresponding to the two chemically inequivalent chlorine sites. Using Bayer's theory and Brown's method torsional frequencies and their temperature dependence in this range are estimated.

Low-frequency degenerate surface modes of an electron-hole plasma

The computations of Flahive and Quinn1 of the dispersion curves of low frequency degenerate surface (DS) modes propagating along the magnetic field in an electron-hole plasma are extended to higher values of the wavenumber. We find that beyond a certain value of the wavenumber the DS mode re-enters the allowed region of surface wave propagation and tends to an asymptotic frequency ωR (<ωLH). These low frequency resonances of an electron-hole plasma are discussed with reference to the experimental observations.

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.

Development of Very High Frequency Damped Sine Wave Generator

In order to protect the critical electronic equipment/system against damped sine transient currents induced into its cables due to transient electromagnetic fields, switching phenomena, platform resonances, etc. it is necessary to provide proper hardening. The hardness assurance provided can be evaluated as per the test CS 116 of MIL STD 461E/F in laboratory by generating & inducing the necessary damped sine currents into the cables of the Equipment Under Test (EUT). The need and the stringent requirements for building a damped sine wave current generator for generation of damped sine current transients of very high frequencies (30 MHz & 100 MHz) have been presented. A method using LC discharge for the generation has been considered in the development. This involves building of extremely low & nearly loss less inductors (about 5 nH & 14 nH) as well as a capacitor & a switch with much lower inductances. A technique for achieving this has been described. Two units (I No for 30 MHz. & 100 MHz each) have been built. Experiments to verify the output are being conducted.

13C nuclear magnetic resonance studies of the binding of alkali and alkaline earth metal salts to amides

3C resonances of carbonyl and methyl groups in amides are shifted down-field on interaction with alkali and alkaline earth metal salts. The magnitude of the shift depends on the ionic potential of the cation. Ions like Li+ bind to the amide carbonyl group both in neat amide solutions as well as in concentrated salt solutions in water.

Rotational isomerism about the Ca-CO bond in proline derivatives. 1H and 13C NMR studies of benzyloxycarbonyl-Pro-N-methylamide and pivaloyl-Pro-N-methylamide

The 270 MHz 1H n.m.r. spectrum of benzyloxycarbonyl-Pro-N-methylamide in CDCl3 is exchange broadened at 293° K. Spectral lines due to two species are frozen out at 253° K and a dynamically averaged spectrum is obtained at 323° K. A selective broadening of the Cβ and Cγ resonances in the 13C n.m.r. spectrum is observed at 253° K, with a splitting of the Cβ and Cγ resonances into a pair of lines of unequal intensity. A similar broadening of Cβ and Cγ peaks is also detected in pivaloyl-Pro-N-methylamide where cis-trans interconversion about the imide bond is precluded by the bulky t-butyl group. The rate process is thus attributed to rotation about the Cα-CO bond (ψ) and a barrier (ΔG#) of 14kcal mol-1 is estimated. 13C n.m.r. data for pivaloyl-Pro-N-methylamide in a number of solvents is presented and the differences in the Cβ and Cγ chemical shifts are interpreted in terms of rotational isomerism about the Cα-CO bond.