Navier–Stokes equations and forward–backward SDEs on the group of diffeomorphisms of a torus

We establish a connection between the strong solution to the spatially periodic Navier–Stokes equations and a solution to a system of forward–backward stochastic differential equations (FBSDEs) on the group of volume-preserving diffeomorphisms of a flat torus. We construct representations of the strong solution to the Navier–Stokes equations in terms of diffusion processes.     

Folded and unfolded conformations of the omega-3 polyunsaturated fatty acid family: ch(3)ch(2)[ch=chch(2)](b)[ch(2)](m)cooh: first principles study

Polyunsaturated fatty acids (PUFA) like stearidonic acid (SDA;18:4 n-3) eicosapentaenoic acid (EPA; 20:5 n-3), and docosahexaenoic acid (DHA; 22:6 n-3) and its chain fragment models were studied at B3LYP/6-31G(d) levels of theory. Significant conformations for the cis and trans isomers were selected to obtained the thermodynamic functions (DeltaH, DeltaS, DeltaG) for the cis-trans isomerization and for folding using the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d) level of theory. The structural analysis shows that there are significant differences in thermodynamic function of the trans- and cis-PUFAs. The trans-cis isomerization energy values reinforce the consistency and the relative accuracy of theoretical model calculations. The observed flexibility of naturally cis PUFAs could be explained by a very special "smooth basin" PES of the motif of sp(2)-sp(3)-sp(2) hybrid states as reported previously (J. Phys. Chem. A 2005, 109, 520-533). We assumed that intrinsic thermodynamic functions may describe this flexible folding process. The folding enthalpy as well as the folding entropy suggests that there is a new role of the cis-PUFAs in membranes: these cis isomers may have a strong influence on membrane stability and permeability. The average length of the cis helix and beta PUFA was approximated. The difference between the lengths of these two structures is approximately 10 A.     

First-principle computational study on the full conformational space of L-threonine diamide, the energetic stability of cis and trans isomers

First-principle computations were carried out on the conformational space of trans and cis peptide bond isomers of HCO-Thr-NH2. Using the concept of multidimensional conformational analysis (MDCA), geometry optimizations were performed at the B3LYP/6-31G(d) level of theory, and single-point energies as well as thermodynamic functions were calculated at the G3MP2B3 level of theory for the corresponding optimized structures. Two backbone Ramachandran-type potential energy surfaces (PESs) were computed, one each for the cis and trans isomers, keeping the side chain at the fully extended orientation (chi1=chi2=anti). Similarly, two side chain PESs for the cis and trans isomers were generated for the (phi=psi=anti) orientation corresponding to approximately the betaL backbone conformation. Besides correlating the relative Gibbs free energy of the various stable conformations with the number of stabilizing hydrogen bonds, the process of trans-->cis isomerization is discussed in terms of intrinsic stabilities as measured by the computed thermodynamic functions.     

Role of aromacity, ring strain, and stereochemistry of selected disulfides and their congeners in the oxidative linkage of DNA strands at the major groove. A computational study

Three aromatic disulfides and their two selected congeners were studied in order to see if they could be initiators or catalysts in a process that aims to tie together the two strands of a DNA double helix. Thermodynamic functions were calculated from first principle molecular computations on deoxyribose models and the disulfide congener. The gas reaction of one of the disulfides turned out to be the closest to the thermoneutral process. Solvation study caused a relatively minor energetic modification. The disulfides were subjected to docking studies, and the stabilities of the complexes obtained were further analyzed by molecular dynamics simulations. Only one of the two atropic disulfide enantiomers was the matching partner of the chiral DNA double helix, and therefore this remained in the major groove of the DNA. The other enantiomer dissociated from the major groove as it was incapable of forming a stable complex with the chiral double helix. A mechanistic scheme for the reaction has been investigated.     

What tunes the structural anisotropy of magnetic fluids under a magnetic field?

In the present study, the structure of monophasic ionic magnetic fluids under a static magnetic field is explored. In these aqueous electrostatically stabilized ferrofluids, we vary both the isotropic interparticle interactions and the anisotropic dipolar magnetic interaction by tuning the ionic strength and the size of the nanoparticles. Small angle neutron scattering measurements carried out on nanoparticles dispersed in light water exhibit miscellaneous 2D nuclear patterns under a magnetic field with various q-dependent anisotropies. In this nondeuterated solvent where the magnetic scattering is negligible, this anisotropy originates from an anisotropy of the structure of the dispersions. Both the low q region and the peak of the structure factor can be anisotropic. On the scale of the interparticle distance, the structure is better defined in the direction perpendicular to the field. In the thermodynamic limit (q-->0), the model previously described in ref 10 matches the data without any fitting parameters: the interparticle interaction is more repulsive in the direction parallel to the magnetic field. At low q, the amplitude of the anisotropy of the pattern is governed by the ratio of two interaction parameters: the reduced parameter of the anisotropic magnetic dipolar interaction, gamma/Phi, over the isotropic interaction parameter, , in zero field, which is proportional to the second virial coefficient.     

Economical Covers with Geometric Applications

A cover of a hypergraph is a collection of edges whose unioncontains all vertices. Let H = (V, E) be a k-uniform, D-regularhypergraph on n vertices, in which no two vertices are containedin more than o(D/e^2k log D) edges as D tends to infinity. Ourresults include the fact that if k = o(log D), then there isa cover of (1 + o(1))n/k edges, extending the known result thatthis holds for fixed k. On the other hand, if k 4 log D thenthere are k-uniform, D-regular hypergraphs on n vertices inwhich no two vertices are contained in more than one edge, andyet the smallest cover has at least (nk) log (k log D)) edges.Several extensions and variants are also obtained, as well asthe following geometric application. The minimum number of linesrequired to separate n random points in the unit square is,almost surely, (n^2/3 / (log n)^1/3). 2000 Mathematical SubjectClassification: 05C65, 05D15, 60D05.     

THE KINETICS OF THE EARLY STAGES OF THE PHYTOCHROME PHOTOTRANSFORMATION Pr→ Pfr. A COMPARATIVE STUDY OF SMALL (60 kDalton) and NATIVE (124 kDalton) PHYTOCHROMES FROM OAT

A comparative study of the decay kinetics of photogenerated transients from small (60 kDalton) and native (124 kDalton) oat phytochrome in the red-absorbing form (P_r) in phosphate buffer containing 5 mM ethylenediamine tetraacetic acid, pH 7.8, (PB) and in PB containing 20% ethylene glycol, has been carried out in the temperature range 275–298 K. The analysis confirmed that at least two primary photoproducts, intermediates Iⁱ₇₀₀s and Iⁱ_7oo are formed from P_r. The kinetic parameters, as observed in PB at 695 nm and 275 K, are similar for the I₇₀₀ intermediates of both small and native phytochrome. Namely, the lifetimes are about 21 μs (component percentages 38%) for the I Iⁱ₇₀₀s and about 200 μ.s (62%) for the Iⁱ₇₀₀S- Arrhenius preexponential factors (A) of about 10¹⁶ and 10¹⁵ s-¹and activation energies of about 61 and 56 kJ/mol were measured for the absorbance decays of the I₇₀₀S of small and native phytochrome, respectively. The kinetic data favour parallel paths for the formation of the Iⁱ₇₀₀s from P_r, and the activation parameters indicate that the primary photoreactions of the transformation from P_r to the far-red-absorbing form are restricted to the chromophore within the protein. Moreover, the relatively modest temperature dependence of the lifetimes of the Iⁱ₇₀₀^S from small and native P_r supports the working hypothesis that the ground state reactions to the Iⁱ_bl, intermediates–although somewhat influenced by the polypeptide fragment that is removed upon degradation of native to small P_r–are localized to the chromophore, as is most probably the case also for the primary photoreactions. The effect of the addition of 20% ethylene glycol on the pre-exponential factors of the time-dependent decay functions is discussed in similar terms of the early stages of the phototransformation.     

Unicité de solutions d'équations différentielles sur l'espace de Wiener

Unicity of the flow associated to a good vector field on the Wiener space.     

Non-existence of infinitesimally invariant measures on loop groups

Let G be a compact Lie group, L(G) the associated loop group, ω the canonical symplectic form on L(G). Set H the Hamiltonian function for which the associated ω-Hamiltonian vector field is the infinitesimal rotation. Then H generates a canonical semi-definite Riemannian structure on L(G), which induces a Riemannian structure on the free loop groupL(G)/G=L₀(G). This metric corresponds to the Sobolev norm H¹. Using orthonormal frame methodology the positivity and finiteness of the Ricci curvature of L₀(G) is proved. By studying the dissipation towards high modes of a unitary group valued SDE it is proved that the loop group does not have any infinitesimally invariant measure.