Gauge invariance,charge conservation,and variational principles

We present new results on the correspondence between symmetries, conservation laws and variational principles for field equations in general non-abelian gauge theories. Our main result states that second order field equations possessing translational and gauge symmetries and the corresponding conservation laws are always derivable from a variational principle. We also show by the way of examples that the above result fails in general for third order field equations.     

The zonal architecture of human articular cartilage described by T2 relaxation time in the presence of Gd-DTPA2-

The depth-wise variation of T(2) relaxation time is known to reflect the collagen network architecture in cartilage, while the delayed Gadolinium Enhanced MRI of Cartilage (dGEMRIC) technique is sensitive to tissue proteoglycan (PG) concentration. As the cartilage PG content varies along the tissue depth, the depth-dependent accumulation of the contrast agent may affect the inherent T(2) of cartilage in a nonconstant manner. Therefore, T(2) and dGEMRIC are typically measured in separate MRI sessions. In the present in vitro MRI study at 9.4 T, depth-wise T(2) profiles and collagenous zone thicknesses as determined from T(2) maps in the absence and presence of Gd-DTPA(2-) (T(2) and T(2Gd), respectively) were compared in samples of intact human articular cartilage (n=65). These T(2) measures were further correlated with birefringence (BF) of polarized light microscopy (PLM) to quantify the ability of MRI to predict the properties of the collagen fibril network. The reproducibility of the T(2) measurement in the current setup was also studied. Typical tri-laminar collagen network architecture was observed both with and without Gd-DTPA(2-). The inverse of BF (1/BF) correlated significantly with both T(2) and T(2Gd) (r=0.91, slope=0.56 and r=0.90, slope=0.63), respectively. The statistically significant linear correlations between zone thicknesses as determined from T(2) and T(2Gd) were r=0.55 (slope=0.49), r=0.74 (slope=0.71) and r=0.95 (slope=0.94) for superficial, middle and deep tissue zones, respectively. Reproducibility of the T(2) measurement was worst for superficial cartilage. Consistent with PLM, T(2) and T(2Gd) measurements reveal highly similar depth-dependent information on collagen network in intact human cartilage. Thus, dGEMRIC and T(2) measurements in one MRI session are feasible for intact articular cartilage in vitro.     

Estimates for Divergence Velocities of Axially Moving Orthotropic Thin Plates

Some models for axially moving orthotropic thin plates are investigated analytically via methods of complex analysis to derive estimates for critical plate velocities. The linearized Kirchhoff plate theory is used, and the energy forms of steady-state models are considered with homogeneous and inhomogeneous tension profiles in the cross direction of the plate. With the help of the energy forms, some limits for the divergence velocity of the plate are found analytically. In numerical examples, the derived lower limits for the divergence velocity are analyzed for plates with small flexural rigidity.     

Principles and calibration of collinear photofragmentation and atomic absorption spectroscopy

The kinetics of signal formation in collinear photofragmentation and atomic absorption spectroscopy (CPFAAS) are discussed, and theoretical equations describing the relation between the concentration of the target molecule and the detected atomic absorption in case of pure and impure samples are derived. The validity of the equation for pure samples is studied experimentally by comparing measured target molecule concentrations to concentrations determined using two other independent techniques. Our study shows that CPFAAS is capable of measuring target molecule concentrations from parts per billion (ppb) to hundreds of parts per million (ppm) in microsecond timescale. Moreover, the possibility to extend the dynamic range to cover eight orders of magnitude with a proper selection of fragmentation light source is discussed. The maximum deviation between the CPFAAS technique and a reference measurement technique is found to be less than 5 %. In this study, potassium chloride vapor and atomic potassium are used as a target molecule and a probed atom, respectively.     

Quasiregular maps on Carnot groups

In this paper we initiate the study of quasiregular maps in a sub-Riemannian geometry of general Carnot groups. We suggest an analytic definition for quasiregularity and then show that nonconstant quasiregular maps are open and discrete maps on Carnot groups which are two-step nilpotent and of Heisenberg type; we further establish, under the same assumption, that the branch set of a nonconstant quasiregular map has Haar measure zero and, consequently, that quasiregular maps are almost everywhere differentiable in the sense of Pansu. Our method is that of nonlinear potential theory. We have aimed at an exposition accessible to readers of varied background. Dedicated to Seppo Rickman on his sixtieth birthday J.H. was partially supported by NSF, the Academy of Finland, and the A. P. Sloan Foundation. I.H. was partially supported by the EU HCM contract no. CHRX-CT92-0071.     

Toward calculations of the 129Xe chemical shift in Xe@C60 at experimental conditions: relativity, correlation, and dynamics

We calculate the 129Xe chemical shift in endohedral Xe@C60 with systematic inclusion of the contributing physical effects to model the real experimental conditions. These are relativistic effects, electron correlation, the temperature-dependent dynamics, and solvent effects. The ultimate task is to obtain the right result for the right reason and to develop a physically justified methodological model for calculations and simulations of endohedral Xe fullerenes and other confined Xe systems. We use the smaller Xe...C6H6 model to calibrate density functional theory approaches against accurate correlated wave function methods. Relativistic effects as well as the coupling of relativity and electron correlation are evaluated using the leading-order Breit-Pauli perturbation theory. The dynamic effects are treated in two ways. In the first approximation, quantum dynamics of the Xe atom in a rigid cage takes advantage of the centrosymmetric potential for Xe within the thermally accessible distance range from the center of the cage. This reduces the problem of obtaining the solution of a diatomic rovibrational problem. In the second approach, first-principles classical molecular dynamics on the density functional potential energy hypersurface is used to produce the dynamical trajectory for the whole system, including the dynamic cage. Snapshots from the trajectory are used for calculations of the dynamic contribution to the absorption 129Xe chemical shift. The calculated nonrelativistic Xe shift is found to be highly sensitive to the optimized molecular structure and to the choice of the exchange-correlation functional. Relativistic and dynamic effects are significant and represent each about 10% of the nonrelativistic static shift at the minimum structure. While the role of the Xe dynamics inside of the rigid cage is negligible, the cage dynamics turns out to be responsible for most of the dynamical correction to the 129Xe shift. Solvent effects evaluated with a polarized continuum model are found to be very small.     

Synthesis, characterization, and saccharide binding studies of bile acid-porphyrin conjugates

Synthesis and characterization of bile acid-porphyrin conjugates (BAPs) are reported. Binding of saccharides with BAPs in aqueous methanol was studied by monitoring changes in the visible absorption spectral of the porphyrin-moieties. Although these studies clearly showed absorbance changes, suggesting quite high if non-selective binding, the mass spectral studies do not unambiguously support these results.     

Nuclear magnetic resonance chemical shifts and quadrupole couplings for different hydrogen-bonding cases occurring in liquid water: a computational study

Nuclear magnetic resonance (NMR) parameters are determined theoretically for the oxygen and hydrogen/deuterium nuclei of differently hydrogen-bonded water molecules in liquid water at 300 K. The parameters are the chemical shift, the shielding anisotropy, the asymmetry parameter of shielding, the nuclear quadrupole coupling constant, and the asymmetry parameter of the nuclear quadrupole coupling. We sample instantaneous configurations from a Car-Parrinello molecular dynamics simulation and feed nuclear coordinates into a quantum chemical program for the calculation of NMR parameters using density-functional theory with the three-parameter hybrid exchange-correlation (B3LYP) functional. In the subsequent analysis, molecules are divided into groups according to the number of hydrogen bonds they possess, and the full average NMR tensors are calculated separately for each group. The classification of the hydrogen-bonding cases is performed using a simple distance-based criterion. The analysis reveals in detail how the NMR tensors evolve as the environment changes gradually from gas to liquid upon increasing the number of hydrogen bonds to the molecule of interest. Liquid-state distributions of the instantaneous values of the NMR properties show a wide range of values for each hydrogen-bonding species with significant overlap between the different cases. Our study shows how local changes in the environment, along with classical thermal averaging, affect the NMR parameters in liquid water. For example, a broken or alternatively extra hydrogen bond induces major changes in the NMR tensors, and the effect is more pronounced for hydrogen or deuterium than for oxygen. The data sheds light on the usefulness of NMR experiments in investigating the local coordination of liquid water.