Integration of ε-Fenchel Subdifferentials and Maximal Cyclic Monotonicity

This paper concerns the integration of ε-Fenchel subdifferentials of proper lower semicontinuous convex functions defined on arbitrary topological vector spaces. We make use of integration tools to provide a representation formula of the approximate subdifferential of convex functions, and also to identify the class of maximal cyclically monotone families of operators.     

Back and forth transfer and coherent coupling in a cold Rydberg dipole gas

Coupling by the resonant dipole-dipole energy transfer between cold cesium Rydberg atoms is investigated using time-resolved narrow-band deexcitation spectroscopy. This technique combines the advantage of efficient Rydberg excitation with high-resolution spectroscopy at variable interaction times. Dipole-dipole interaction is observed spectroscopically as avoided level crossing. The coherent character of the process is linked to back and forth transfer in the np + np <--> ns + (n + 1)s reaction. Decoherence in the ensemble has two different origins: the atom motion induced by dipole-dipole interaction and the migration of the s-Rydberg excitation in the environment of p-Rydberg atoms.     

Local differentiability of distance functions

Recently Clarke, Stern and Wolenski characterized, in a Hilbert space, the closed subsets for which the distance function is continuously differentiable everywhere on an open ``tube' of uniform thickness around . Here a corresponding local theory is developed for the property of being continuously differentiable outside of on some neighborhood of a point . This is shown to be equivalent to the prox-regularity of at , which is a condition on normal vectors that is commonly fulfilled in variational analysis and has the advantage of being verifiable by calculation. Additional characterizations are provided in terms of being locally of class or such that is convex around for some 0$">. Prox-regularity of at corresponds further to the normal cone mapping having a hypomonotone truncation around , and leads to a formula for by way of . The local theory also yields new insights on the global level of the Clarke-Stern-Wolenski results, and on a property of sets introduced by Shapiro, as well as on the concept of sets with positive reach considered by Federer in the finite dimensional setting.

     

Relaxation of an optimal control problem involving a perturbed sweeping process

We establish first, in the setting of infinite dimensional Hilbert space, a result concerning the existence of solutions for perturbed sweeping processes whose perturbations are Lipschitz single-valued maps. Then we use this result to extend to the infinite dimensional setting a relaxation result concerning optimal control problems involving such processes. Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday     

A noncontacting system for measuring effective stress-strain curves of ultra-thin X-ray-mask materials

A noncontacting test system has been developed for making measurements of the deformation characteristics of the ultra-thin (≈10μm) membrane structures of X-ray masks using a pneumatic bulge test. These measurements, which include the bulge height and radius-of-curvature at the pole, are then analyzed to provide composite estimates of the effective stress and effective strain of the mask membrane materials.     

Decay of 48K, 49K and 50K

The ⁴⁸K, ⁴⁹K and ⁵⁰K nuclides have been produced in high energy fragmentation and analyzed by mass spectroscopy techniques. Their half-lives have been measured as 6 ± 1 s, 1.1 ± 0.3 s and and 0.7 ± 0.3 s, respectively. The γ-rays from their radioactive decay have been observed and the corresponding γ-intensities measured. The nuclide ⁵⁰K is shown to be a delayed neutron emitter. The antianalog states in the daughter Ca nuclei with a $\text{(1d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?}}$ neutron configuration, preferentially populated in the β-decay, have been located. The corresponding $\text{1d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ neutron single-particle energy is found to remain approximately constant for these neutron-rich Ca isotopes.     

Experimental and theoretical study of line mixing in NH3 spectra. II. Effect of the perturber in infrared parallel bands

In a previous paper [J. Chem. Phys. 116, 7544 (2002) (Paper I)] a model, based on the energy corrected sudden approximation, was proposed for the construction of the line-mixing relaxation matrix. It was successfully tested by comparisons with measured infrared spectra of ammonia-helium mixtures. The present paper extends this preliminary study by considering mixtures of NH3 with H2 and Ar. Measurements have been made at room temperature in the regions of the nu2 and nu1 bands for pressures up to several hundred atmospheres. As in Paper I, the relaxation operator is constructed, within the impact approximation, using the ECS approximation. The data required are dynamical factors (which can be predicted from the NH3-X potential energy surface) and a scaling length (adjusted using line broadening data). Comparisons between measured and calculated absorptions demonstrate the quality of the model which satisfactory corrects for the large deviations with respect to the purely Lorentzian behavior. Line-mixing effects for NH3-Ar and NH3-H2 are qualitatively similar to those observed for NH3-He but quantitative differences exist, particularly when intra- and interbranch couplings are considered. Finally, the proposed model leads to very satisfactory results in the wings of both the purely rotational and nu2 bands of NH3 diluted in H2, opening promising perspectives for the remote sensing study of planetary atmospheres.     

Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order

The gravitational radiation from point particle binaries is computed at the third post-Newtonian (3PN) approximation of general relativity. Three previously introduced ambiguity parameters, coming from the Hadamard self-field regularization of the 3PN source-type mass quadrupole moment, are consistently determined by means of dimensional regularization, and proved to have the values xi=-9871/9240, kappa=0, and zeta=-7/33. These results complete the derivation of the general relativistic prediction for compact binary inspiral up to 3.5PN order, and should be of use for searching and deciphering the signals in the current network of gravitational wave detectors.     

Specific interactions of complementary mono- and multivalent guests with recognition-induced polymersomes

We have explored the interactions of mono- and multivalent guests with Recognition-Induced Polymersomes (RIPs) formed from complementary random copolymers featuring diamidopyridine and thymine functionality. Addition of monovalent guests featuring imide functionality to these RIPs induced a temporary swelling of the vesicles, followed by dissociation of the vesicles due to competitive binding of the guest. Conversely, multivalent thymine-functionalized nanoparticle guests were rapidly incorporated into the RIPs, inducing a contraction of RIP diameter over time. These mono- and multivalent interactions were extremely specific: highly analogous control systems showed no interaction with the RIP structures. Taken together, these studies demonstrate highly selective molecular "lock and key" control over higher-order assembly and recognition processes.