Analytical estimates of the contact zone area for a pressurized flat-oval cylindrical shell placed between two parallel rigid plates

The paper presents an analytical estimate for an area of contact for a thin-walled noncircular cylindrical shell placed between two parallel rigid plates with an initial gap and then pressurized hydrostatically up to the contact appearance. The Euler–Bernoulli beam is used to model the shell deformation under the plane strain assumption. Such a simplification allows one to obtain the simplest closed-form estimate for the contact zone area. The first approximation is obtained neglecting the deformation of the curvilinear segments of the flat oval shell cross-section while the solution for the curved beam loaded by the homogeneous pressure is considered as a second approximation. The accuracy of the proposed analytical solutions as well as their usability in the preliminary design of thin-walled elements of various cooling systems is validated by the results of both numerical simulations and experimental tests.     

Three-dimensional topological field theory and symplectic algebraic geometry I

We study boundary conditions and defects in a three-dimensional topological sigma-model with a complex symplectic target space X (the Rozansky–Witten model). We show that boundary conditions correspond to complex Lagrangian submanifolds in X   equipped with complex fibrations. The set of boundary conditions has the structure of a 2-category; morphisms in this 2-category are interpreted physically as one-dimensional defect lines separating parts of the boundary with different boundary conditions. This 2-category is a categorification of the Z₂${\mathbb{Z}}_2$-graded derived category of X; it is also related to categories of matrix factorizations and a categorification of deformation quantization (quantization of symmetric monoidal categories). In Appendix B we describe a deformation of the B-model and the associated category of branes by forms of arbitrary even degree.     

Localized States of an Excess Electron in an Ionic Cluster

A theory of an electron affinity for an ionic cluster is proposed both in a quasiclassical approach and with quantization of a polarization electric field in a nanoparticle. A critical size of the cluster regarding in formation of an electron's autolocalized state, dependencies of energy and radius of a polaron on a cluster's size are obtained by a variational method. It has been found that binding energy of the electron in the cluster depends on a cluster's radius but a radius of electron's auto-localization does not depend on the cluster's radius and it equals to the polaron radius in a corresponding infinity crystal. A bound state of the electron in a cluster is possible only if the cluster's radius is more than the polaron radius.     

Synthesis and conformational analysis of a small meta‐cyclophane,bis(5‐carbomethoxy‐1,3‐phenylene)‐14‐crown‐4

A small cyclophane, bis(5‐carbometh‐oxy‐1,3‐phenylene)‐14‐crown‐4 (BCMP14C4, 3 ) and its diacid, bis(5‐carboxy‐1,3‐phenylene)‐14‐crown‐4 ( 4 ), were synthesized and characterized. The solid‐state molecular structures of 3 and 4 were determined by X‐ray crystallography as ladder or stepped conformations in which the two aromatic rings are antiparallel to each other without overlap and the ethylene tethers both take trans‐conformations. Diester 3 is formed in the lowest cyclization yield (under the same reaction conditions) and exhibits the highest melting point compared to its larger ring (20‐, 26‐ and 32‐membered) analogs. In CD₂Cl₂ solution, diester 3 exists predominantly as a nonplanar gauche–gauche structure as deduced by H NMR studies. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:48–54, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20393     

Particle transport and acceleration in a time-varying electromagnetic field with a multi-scale structure

We present the results of a numerical study of particle transport and acceleration by an ensemble of electromagnetic waves with a multi-scale spatio-temporal structure. We explore the dependence of acceleration and transport on the properties of turbulence. We found that an initially Maxwellian distribution of particle velocities evolves into a heavy-tailed distribution, which resembles the ubiquitous kappa-distribution, often used in non-thermal plasma phenomenology. The results of this study may be used to explain plasma heating and energization in turbulent current sheets such as the current sheets often observed in the Earth's magnetotail and discussed in relation to solar corona.     

Microscopic origin of low-frequency flux noise in josephson circuits

We analyze the data and discuss their implications for the microscopic origin of the low-frequency flux noise in superconducting circuits. We argue that this noise is produced by spins at superconductor insulator boundary whose dynamics is due to RKKY interaction. We show that this mechanism explains size independence of the noise, different frequency dependences of the spectra reported in large and small SQUIDs, and gives the correct intensity for realistic parameters.     

Exploiting the Hydrogen Bond Donor/Acceptor Properties of PN‐Heterocycles: Selective Anion Receptors for Hydrogen Sulfate

We describe two novel hybrid receptors combining a phosphorus‐/nitrogen‐containing (PN) phosphonamidate heterocycle with urea recognition units in an arylethynyl backbone. Structural, spectroscopic and computational studies reveal that the origin of superior binding for hydrogen sulfate (HSO₄^?) anion is correlated with the formation of strong hetero‐complementary hydrogen bonds with the phosphonamidate motif. We further demonstrate that the hybrid host system is capable of capturing/transporting the HSO₄^? anion from an aqueous, biphasic system.     

Amide-ligand hydrogen bonding in reverse micelles

One approach to modeling the second coordination shell of metalloproteins is to pair amide-containing counterions with metal complexes to form hydrogen bonds in the solid state. In a more general approach, we have designed a surfactant counterion that can sustain hydrogen bonding interactions with metal complexes in solution. The surfactant is cationic and incorporates an amide as part of its headgroup to form hydrogen. The surfactant forms hydrogen bonding reverse micelles that accommodate anionic metal complexes in their polar core. In reverse micelles containing an iron(III) hexacyanide complex, spectroscopic evidence suggests that the anion is confined to the polar core region in solution. Single-crystal X-ray diffraction data on the surfactant ferricyanide system reveals a layered structure with interdigitated alkyl chains and an extensive network of hydrogen bonds that link amide groups to the cyanide ligands and to neighboring headgroups.     

Direct, noninvasive detection of photon density in turbid media

Ultrasound tagging of light provides a unique way to probe photon density inside turbid media. We show that this technique allows one to probe the well-known banana-shaped photon density noninvasively, giving rise to a new tool for modeling diffusive photon propagation. Moreover, we show that this technique is quantitative and allows one to get a precise determination of the absorbing constituents inside the turbid medium.