Finite deformations of an electroelastic circular cylindrical tube

In this paper the theory of nonlinear electroelasticity is used to examine deformations of a pressurized thick-walled circular cylindrical tube of soft dielectric material with closed ends and compliant electrodes on its curved boundaries. Expressions for the dependence of the pressure and reduced axial load on the deformation and a potential difference between, or uniform surface charge distributions on, the electrodes are obtained in respect of a general isotropic electroelastic energy function. To illustrate the behaviour of the tube, specific forms of energy functions accounting for different mechanical properties coupled with a deformation independent quadratic dependence on the electric field are used for numerical purposes, for a given potential difference and separately for a given charge distribution. Numerical dependences of the non-dimensional pressure and reduced axial load on the deformation are obtained for the considered energy functions. Results are then given for the thin-walled approximation as a limiting case of a thick-walled cylindrical tube without restriction on the energy function. The theory described herein provides a general basis for the detailed analysis of the electroelastic response of tubular dielectric elastomer actuators, which is illustrated for a fixed axial load in the absence of internal pressure and fixed internal pressure in the absence of an applied axial load

Bifurcation of finitely deformed thick-walled electroelastic cylindrical tubes subject to a radial electric field

This paper is concerned with the bifurcation analysis of a pressurized electroelastic circular cylindrical tube with closed ends and compliant electrodes on its curved boundaries. The theory of small incremental electroelastic deformations superimposed on a finitely deformed electroelastic tube is used to determine those underlying configurations for which the superimposed deformations do not maintain the perfect cylindrical shape of the tube. First, prismatic bifurcations are examined and solutions are obtained which show that for a neo-Hookean electroelastic material prismatic modes of bifurcation become possible under inflation. This result contrasts with that for the purely elastic case for which prismatic bifurcation modes were found only for an externally pressurized tube. Second, axisymmetric bifurcations are analyzed, and results for both neo-Hookean and Mooney–Rivlin electroelastic energy functions are obtained. The solutions show that in the presence of a moderate electric field the electroelastic tube becomes more susceptible to bifurcation, i.e., for fixed values of the axial stretch axisymmetric bifurcations become possible at lower values of the circumferential stretches than in the corresponding problems in the absence of an electric field. As the magnitude of the electric field increases, however, the possibility of bifurcation under internal pressure becomes restricted to a limited range of values of the axial stretch and is phased out completely for sufficiently large electric fields. Then, axisymmetric bifurcation is only possible under external pressure

General variational approach to nuclear-quadrupole coupling in rovibrational spectra of polyatomic molecules

A general algorithm for computing the quadrupole-hyperfine effects in the rovibrational spectra of polyatomic molecules is presented for the case of ammonia (NH$_3$). The method extends the general variational approach TROVE by adding the extra term in the Hamiltonian that describes the nuclear quadrupole coupling, with no inherent limitation on the number of quadrupolar nuclei in a molecule. We applied the new approach to compute the nitrogen-nuclear-quadrupole hyperfine structure in the rovibrational spectrum of NH$_3$. These results agree very well with recent experimental spectroscopic data for the pure rotational transitions in the ground vibrational and $\nu_2$ states, and the rovibrational transitions in the $\nu_1$, $\nu_3$, $2\nu_4$, and $\nu_1+\nu_3$ bands. The computed hyperfine-resolved rovibrational spectrum of ammonia will be beneficial for the assignment of experimental rovibrational spectra, further detection of ammonia in interstellar space, and studies of the proton-to-electron mass variation

Structure of Polymer Brushes in Cylindrical Tubes: A Molecular Dynamics Simulation

Molecular Dynamics simulations of a coarse-grained bead-spring model of flexible macromolecules tethered with one end to the surface of a cylindrical pore are presented. Chain length $N$ and grafting density $\sigma$ are varied over a wide range and the crossover from ``mushroom'' to ``brush'' behavior is studied for three pore diameters. The monomer density profile and the distribution of the free chain ends are computed and compared to the corresponding model of polymer brushes at flat substrates. It is found that there exists a regime of $N$ and $\sigma$ for large enough pore diameter where the brush height in the pore exceeds the brush height on the flat substrate, while for large enough $N$ and $\sigma$ (and small enough pore diameters) the opposite behavior occurs, i.e. the brush is compressed by confinement. These findings are used to discuss the corresponding theories on polymer brushes at concave substrates.Comment: 11 figure

Theory of non-Fermi liquid and pairing in electron-doped cuprates

We apply the spin-fermion model to study the normal state and pairing instability in electron-doped cuprates near the antiferromagnetic QCP. Peculiar frequency dependencies of the normal state properties are shown to emerge from the self-consistent equations on the fermionic and bosonic self-energies, and are in agreement with experimentally observed ones. We argue that the pairing instability is in the $d_{x^{2}-y^{2}}$ channel, as in hole-doped cuprates, but theoretical $T_{c}$ is much lower than in the hole-doped case. For the same hopping integrals and the interaction strength as in hole-doped materials, we obtain $T_{c}\sim10$K at the end point of the antiferromagnetic phase. We argue that a strong reduction of $T_{c}$ in electron-doped cuprates compared to hole-doped ones is due to critical role of the Fermi surface curvature for electron-doped materials. The $d_{x^{2}-y^{2}}$-pairing gap $\Delta(\mathbf{k},\omega)$ is strongly non-monotonic along the Fermi surface. The position of the gap maxima, however, does not coincide with the hot spots, as the non-monotonic $d_{x^{2}-y^{2}}$ gap persists even at doping when the hot spots merge on the Brillouin zone diagonals.Comment: 16 page