Measuring the criticality of a Hopf bifurcation

Nonlinear Dynamics - This work is based on the observation that the first Poincaré–Lyapunov constant is a quadratic function of the coefficients of the two-dimensional vector field at a...     

Isotope Effect on Diffusion in Nafion Studied by NMR Diffusometry

Applied Magnetic Resonance - The isotope effect H → D on diffusion in proton-exchange membrane Nafion 212 is investigated using 1H and 2H nuclear magnetic resonance (NMR)...     

Collapse of polyelectrolyte networks induced by their interaction with an oppositely charged surfactant. Theory

A very simple theory of swelling and collapse of weakly charged polyelectrolyte networks in the solution of an oppositely charged surfactant has been developed. The following contributions to the free energy were taken into account: free energy of volume interaction and of elastic deformation of the network chains, free energy connected with micelle formation and free energy of translational motion of all mobile ions in the system (translational entropy). Both the cases of a solution of charged surfactant and that of a mixed solution of charged and neutral surfactant components have been taken into account. It has been shown that the behaviour of the network depends on the total surfactant concentration in the system and corresponds to one of the three following regimes: At low concentration, micelles inside the network are not formed and the behaviour of the polymer network is similar to that of a network swelling in the solution of a lowmolecular-weight salt (regime 1). In the second regime, surfactant concentration inside the network exceeds the critical micelle concentration and micelles are formed; in this regime the network collapses because surfactant molecules, aggregated in micelles, cease to create “exerting” osmotic pressure in the network sample. In the third regime, at very high surfactant concentration, formation of additional micelles inside the network ceases, and the network dimensions coincide with those of the corresponding neutral network.     

Comparison of photodynamic efficacy of tetraarylporphyrin pegylated or encapsulated in liposomes: In vitro studies

Two photosensitizing systems: (1) tetrakis(4-hydroxyphenyl)porphyrin (p-THPP) encapsulated in sterically stabilized liposomes (SSL) and (2) p-THPP functionalized by covalent attachment of poly(ethylene glycol) (p-THPP–PEG₂₀₀₀) were studied in vitro. The dark and photo cytotoxicity of these systems were evaluated on two cell lines: HCT 116, a human colorectal carcinoma cell line, and DU 145, a prostate cancer cell line and compared with these determined for free p-THPP. It was demonstrated that both encapsulation in liposomes as well as attachment of PEG chain result in pronounced reduction of the dark cytotoxicity of the parent porphyrin. The liposomal formulation showed higher than p-THPP–PEG₂₀₀₀ photocytotoxicity towards both cell lines used in the studies.     

Molecular dynamics simulations of EXAFS in germanium

Classical molecular dynamics simulations have been performed for crystalline germanium with the aim to estimate the thermal effects within the first three coordination shells and their influence on the single-scattering and multiple-scattering contributions to the Ge K-edge extended x-ray absorption fine structure (EXAFS).     

Erratum to: The Ginibre Ensemble of Real Random Matrices and its Scaling Limits

We correct an error in Theorem 12 of the original article concerning the edge scaling limit of the law of real eigenvalues for the real Ginibre ensemble.     

One-sided invertibility of binomial functional operators with a shift on rearrangement-invariant spaces

Let be an oriented Jordan smooth curve and a diffeomorphism of onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertibility of the binomial functional operator

Spectral function of a quarter-filled one-dimensional charge density wave insulator

We consider a one-dimensional charge density wave insulator formed by umklapp processes in a quarter-filled band. The spectrum of the model consists of gapless, uncharged excitations carrying spin +/- 1/2 (spinons) and gapped, spinless excitations carrying charge -/+ signe/2 (solitons and antisolitons). We calculate the low-energy behavior of the single-electron Green's function at zero temperature. The spectral function exhibits a featureless scattering continuum of two solitons and many spinons. The theory predicts that the gap observed by angle resolved photoemission is twice the activation gap in the dc conductivity. We comment on possible applications to PrBa(2)Cu(3)O(7) and to the Bechgaard salts.