Variational methods for a singular SPDE yielding the universality of the magnetization ripple

The magnetization ripple is a microstructure formed in thin ferromagnetic films. It can be described by minimizers of a nonconvex energy functional leading to a nonlocal and nonlinear elliptic SPDE in two dimensions driven by white noise, which is singular. We address the universal character of the magnetization ripple using variational methods based on Γ-convergence. Due to the infinite energy of the system, the (random) energy functional has to be renormalized. Using the topology of Γ-convergence, we give a sense to the law of the renormalized functional that is independent of the way white noise is approximated. More precisely, this universality holds in the class of (not necessarily Gaussian) approximations to white noise satisfying the spectral gap inequality, which allows us to obtain sharp stochastic estimates. As a corollary, we obtain the existence of minimizers with optimal regularity.     

The stabilized set of p's in Krivine's theorem can be disconnected

For any closed subset F   of [1,∞]$[1,\infty ]$ which is either finite or consists of the elements of an increasing sequence and its limit, a reflexive Banach space X with a 1-unconditional basis is constructed so that in each block subspace Y of X  , _?p${?}_p$ is finitely block represented in Y   if and only if p∈F$p\in F$. In particular, this solves the question as to whether the stabilized Krivine set for a Banach space had to be connected. We also prove that for every infinite dimensional subspace Y of X there is a dense subset G of F such that the spreading models admitted by Y   are exactly the _?p${?}_p$ for p∈G$p\in G$.     

Integrable Non-QRT Mappings of the Plane

We construct 9-parameter and 13-parameter dynamical systems of the plane which map bi-quadratic curves to other bi-quadratic curves and return to the original curve after two iterations. These generalize the QRT maps which map each such curve to itself. The new families of maps include those that were found as reductions of integrable lattices by Joshi et al. (Lett. Math. Phys. 78:27–37, 2006).     

Controlled photochemical release of nitric oxide from O2-benzyl-substituted diazeniumdiolates

An investigation of potential photosensitive protecting groups for diazeniumdiolates (R2N-N(O)=NO-) has been initiated, and here the effect of meta electron-donating groups on the photochemistry of O2-benzyl-substituted diazeniumdiolates (R2N-N(O)=NOCH2Ar) is reported. Photolysis of the parent benzyl derivative (Ar = Ph) results almost exclusively in undesired photochemistry-the formation of nitrosamine and an oxynitrene intermediate with very little, if any, photorelease of the diazeniumdiolate. We have been able to use meta substitution to tune the photochemistry of these benzylic systems. The desired diazeniumdiolate photorelease has been shown to become more substantial with stronger pi-donating meta substituents. This effect has been verified by direct observation of the photoreleased diazeniumdiolate with 1H NMR spectroscopy and by NO quantification measurements conducted in high- and low-pH solutions. In addition, the observed rates of NO release are consistent with that expected for normal thermal decomposition of the diazeniumdiolate in aqueous solutions and also show the same pH dependence.     

An explicit version of a theorem of Stickelberger

We give an explicit version of a classical theorem of Stickelberger on the representation of certain integers by binary quadratic forms. This is achieved by generalizing Stickelberger's original congruences via an extension of a recent result of Young.     

Solid state polymerization of poly(lactic acid): Some fundamental parameters

Poly(lactic acid) (PLA) was submitted to solid state polymerization (SSP) in a fixed bed reactor under nitrogen flow, so as to examine technique efficiency for increasing the molecular weight and hence permitting the reduction of the melt polymerization residence times. In order to use a suitable starting material, SSP prepolymers of low and medium molecular weight were first prepared through solid state hydrolysis of commercial PLA grade under acidic and alkaline conditions. During these degradation runs, hydrolysis involved the random scission of ester groups in the polymer backbone, while the relevant kinetics and the resulting thermal properties were also examined. In a subsequent step, the prepolymers obtained were subjected to SSP at three temperatures, approximately 2.5–25.0 °C below their melting point. The process achieved an increase of up to 1.7 times the initial molecular weight, however, with different trends depending on the prepolymer characteristics, reaction temperature and time, as well as the pH of the hydrolysis medium. In addition to molecular weight build up, the effect of the SSP process on end product thermal properties was also investigated.     

Experimental determination of three-dimensional finite-time Lyapunov exponents in multi-component flows

We present an experimental approach for estimating finite-time Lyapunov exponent fields (FTLEs) in three-dimensional multi-component or multi-phase flows. From time-resolved sequences of particle images, we directly compute the flow map and coherent structures, while avoiding and outperforming the computationally costly numerical integration. Performing this operation independently on each flow component enables the determination of three-dimensional Lagrangian coherent structures (LCSs) without any bias from the other components. The locations of concurrent LCSs for different flow elements (e.g., passive tracers, inertial particles, bubbles, or active particles) can provide new insight into the interpenetrating FTLE structure in complex flows.     

Symmetries and conservation laws of lattice Boussinesq equations

Sequences of canonical conservation laws and generalized symmetries for the lattice Boussinesq and the lattice modified Boussinesq systems are successively derived. The interpretation of these symmetries as differential-difference equations leads to corresponding hierarchies of such equations for which conservation laws and Lax pairs are constructed. Finally, using the continuous symmetry reduction approach, an integrable, multidimensionally consistent system of partial differential equations is derived in relation with the lattice modified Boussinesq system.     

Vortex rings in radially confined domains

The dynamics of vortex rings generated within confined domains are relevant to important hydrodynamic processes such as flow past heart valves or severe arterial constrictions. However, despite their importance, these flows have not received much attention to date. This study examines the development and evolution of radially confined vortex rings. Time-resolved digital particle image velocimetry was used to investigate two levels of radial confinement and a range of vortex ring strengths. We found that for severely confined vortex rings, the formation time and peak circulation values were unaffected for L/D ₀?<?4 cases and slightly affected for larger L/D ₀ cases. After pinch-off, circulation decay was observed with an approximately constant normalized circulation decay rate. We found that with increasing circulation strength, the nondimensional time delay between the pinch-off and the onset of circulation decay reduced due to an increased vortex ring diameter within the confinement domain and a reduction in the necessary time for the surface induced and core vorticity regions to interact. This study uncovers the dynamics of radially confined vortex rings and show that the nondimensional rate of circulation decay is dependent on the vortex ring confinement ratio (ratio of the vortex ring orifice diameter to the diameter of the outer cylinder), and the time delay between the vortex pinch-off and the onset of circulation is dependent on the vortex ring circulation strength.