Current density in a perfect mirror

Electromagnetic radiation incident upon a perfect mirror induces a current density on the surface of the conducting material of the mirror. It is shown that this surface current density can be expressed directly in terms of the source current density, which generates the incident field, without evaluating the electric and magnetic fields first.     

Subwavelength displacement of the far-field image of a radiating dipole

The field lines of the Poynting vector for light emitted by a dipole with a rotating dipole moment show a vortex pattern near the location of the dipole. In the far field, each field line approaches a straight line, but this line does not appear to come exactly from the location of the dipole. As a result, the image of the dipole in its plane of rotation seems displaced. Secondly, the image in the far field is displaced as compared with the image of a source for which the field lines run radially outward. It turns out that both image displacements are the same. The displacements are of subwavelength scale, and they depend on the angles of observation. The maximum displacement occurs for observation in the plane of rotation and equals lambda/pi, where lambda is the wavelength of the light.     

Hopf saddle-node bifurcation for fixed points of 3D-diffeomorphisms: Analysis of a resonance ‘bubble’

The dynamics near a Hopf saddle-node bifurcation of fixed points of diffeomorphisms is analysed by means of a case study: a two-parameter model map G is constructed, such that at the central bifurcation the derivative has two complex conjugate eigenvalues of modulus one and one real eigenvalue equal to 1. To investigate the effect of resonances, the complex eigenvalues are selected to have a 1:5 resonance. It is shown that, near the origin of the parameter space, the family G has two secondary Hopf saddle-node bifurcations of period five points. A cone-like structure exists in the neighbourhood, formed by two surfaces of saddle-node and a surface of Hopf bifurcations. Quasi-periodic bifurcations of an invariant circle, forming a frayed boundary, are numerically shown to occur in model G. Along such Cantor-like boundary, an intricate bifurcation structure is detected near a 1:5 resonance gap. Subordinate quasi-periodic bifurcations are found nearby, suggesting the occurrence of a cascade of quasi-periodic bifurcations.     

Depletion-driven four-phase coexistences in discotic systems

ABSTRACT

Free volume theory (FVT) is a versatile and tractable framework to predict the phase behaviour of mixtures of platelets and non-adsorbing polymer chains in a common solvent. Within FVT, three principal reference phases for the hard platelets are considered: isotropic (I), nematic (N) and columnar (C). We derive analytical expressions that enable us to systematically trace the different types of phase coexistences revealed upon adding depletants and confirm the predictive power of FVT by testing the calculated diagrams against phase stability scenarios from computer simulation. A wide range of multi-phase equilibria is revealed, involving two-phase isostructural transitions of all phase symmetries (INC) considered as well as the possible three-phase coexistences. Moreover, we identify the system parameters, relative disk shapes and colloid–polymer size ratios, at which four-phase equilibria are expected. These involve a remarkable coexistence of all three-phase states commonly encountered in discotics including isostructural coexistences I₁–I₂–N–C, I–N₁–N₂–C and I–N–C₁–C₂.     

The effect of composition drift and copolymer microstructure on mechanical bulk properties of styrene-methyl acrylate emulsion copolymers

In order to determine the influence of composition drift and copolymer microstructure on the mechanical bulk properties of styrene -methyl acrylate copolymers, several copolymers were produced by emulsion copolymerization. Three different average compositions were used. By performing the copolymerizations under batch and semicontinuous conditions with two different monomer addition strategies (starved conditions and optimal addition) it was possible to control composition drift and to produce copolymers with different microstructures (chemical composition distributions). All these copolymers were processed in a way that ensured that the original particle structure was lost before the polymers were tested. It was found that composition drift had an influence on the mechanical properties (Young's modulus, maximum stress, elongation at break). This influence could be understood very well on the basis of present knowledge about structure-mechanical properties relationships. In the case of homogeneous copolymers maximum stress and elongation at break are dependent on the molecular weight, and only weakly dependent on the chemical composition, and Young's modulus is independent of chemical composition and molecular weight in the range of compositions investigated, as expected. In the case of heterogeneous copolymers, the influence of copolymer microstructure on Young's modulus, maximum stress and elongation at break is very large. Depending on the extent of control of composition drift during the polymerizations, phase separation was observed in the processed polymers, and the presence of a rubber phase affected the properties profoundly.     

Compositional heterogeneity in pectic polysaccharides: NMR studies and statistical analysis

Pectins are a class of heterogeneous polysaccharides used in the food industry as a result of their ability to form gels. They are primarily composed of a (1ŕ4)-α-D-galactopyranosyluronic acid backbone where the carboxylic acid group is methyl esterified at a level which depends on the source of the pectin and processing conditions used to isolate the material. Of considerable interest is the distribution of the free acid and methyl ester groups along this polymer chain. NMR spectroscopy, coupled with statistical analysis, is a powerful technique for the study of sequence distribution of monomers. Experimental conditions (temperature, pD) are reported which are appropriate for the analysis of pectic polysaccharides. Results are presented from a study of sequence distribution in native, modified, and fractionated pectins using ¹H and ¹³C solution NMR methods. The triad sequence information was examined using Bernoullian and Markovian probability models in conjunction with continuous Gaussian distribution and discrete models. Intermolecular heterogeneity in pectins results in triad frequencies which reflect the distribution of acid and ester monomers for native and base saponified pectins. Fractionation of pectin through physicochemical methods and subsequent spectroscopic analysis provide insight into this heterogeneity. Segregation into discrete polymer populations shows a structural diversity best approximated by a 3-component statistical model.     

Conformational transmission in pentacoordinated phosphorus systems,modelling the activated state of cyclic AMP

The proposed activated state of cyclic adenosine 3′,5′-monophosphate (cAMP) is modelled by two nucleoside cyclic 3 ′,5 ′ P^v-TBP compounds 3 and 4 . The reason for the design of compound 3 , in which a probe fragment (O CH₂ CH₂ OCH₃ group) is linked to phosphorus, was reflected in a conformational transmission effect, which occurs when the probe is located in the axis of a P^v-TBP. This means that the six-membered 3′5′-dioxaphosphorinane ring predominantly remains in a diequatorial (e,e) orientation. In the absence of conformational transmission, as in compound 4 , the 3′,5′-dioxaphosphorinane ring favors an equatorial-axial (e,a) orientation. From this we conclude that the occurrence of conformational transmission can stabilize the (e,e) orientation of the 3′,5′-ring. This can be of relevance to the activation of protein kinase by cAMP. In order to obtain more structural information from 3 and 4 , we performed MNDO calculations on the models 8–10 . These calculations revealed that the (e,e) orientation of the 3′,5′-ring is destabilized by 3–4 kcal/mol compared to the (e,a) orientation. For the (e,a) geometry, the 3′,5′-ring adopts a twist conformation, whereas the (e,e) orientated 3′,5′-ring shows a half-chair geometry.