Interaction between a disclination and a uniaxial-isotropic phase interface in a nematic liquid crystal

We consider the interaction between a disclination line of strength +/-1/2 and an interface between the uniaxial and isotropic phases of a nematic liquid crystal. We apply a recently developed set of interface conditions including a configurational force balance which generalizes the Gibbs-Thomson equation to account for the curvature elasticity of the uniaxial phase and the orientation dependence of the interfacial free-energy density. We consider a rectangular vessel containing both phases and a disclination. We formulate a relevant free-boundary problem and use numerical methods to determine equilibrium shapes of the interface. When the interfacial free-energy is constant, the shape of the interface is insensitive to whether the strength of the defect is +1/2 or -1/2 and to rotations of the director field consistent with the boundary conditions. Accounting for the dependence of the interfacial free-energy density on the angle between the interfacial unit normal field and the director field eliminates these degeneracies. In particular, when such dependence is taken into account, different solution branches are found, indicating the presence of a bifurcation. We find also that, depending on the magnitude of the anisotropic contribution to the interfacial free-energy density, the interaction between the disclination and the interface may be repulsive or attractive. When the interaction is repulsive, the disclination line positions itself at an energetically optimal distance adjacent to the interface. Otherwise, the uniaxial phase expels the disclination to the interface where a cusp forms.     

Spin hamiltonian for which the chiral spin liquid is the exact ground state

We construct a Hamiltonian that singles out the chiral spin liquid on a square lattice with periodic boundary conditions as the exact and, apart from the twofold topological degeneracy, unique ground state.     

Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization

A new slender-body theory for viscous flow, based on the concepts of dimensional reduction and hyperviscous regularization, is presented. The geometry of flat, elongated, or point-like rigid bodies immersed in a viscous fluid is approximated by lower-dimensional objects, and a hyperviscous term is added to the flow equation. The hyperviscosity is given by the product of the ordinary viscosity with the square of a length that is shown to play the role of effective thickness of any lower-dimensional object. Explicit solutions of simple problems illustrate how the proposed method is able to represent with good approximation both the velocity field and the drag forces generated by rigid motions of the immersed bodies, in analogy with classical slender-body theories. This approach has the potential to open up the way to more effective computational techniques, since geometrical complexities can be significantly reduced. This, however, is achieved at the expense of involving higher-order derivatives of the velocity field. Importantly, both the dimensional reduction and the hyperviscous regularization, combined with suitable numerical schemes, can be used also in situations where inertia is not negligible.     

Sharp-crack limit of a phase-field model for brittle fracture

A matched asymptotic analysis is used to establish the correspondence between an appropriately scaled version of the governing equations of a phase-field model for fracture and the equations of the two-dimensional sharp-crack theory of Gurtin and Podio-Guidugli (1996) that arise on assuming that the bulk constitutive behavior is nonlinearly elastic, requiring that surface energy provides the only factor limiting crack propagation, and assuming that the fracture kinetics are isotropic. Consistent with the prominence of the configurational momentum balance at the crack tip in the latter theory, the approach capitalizes on the configurational momentum balance that arises naturally in the context of the phase-field model. The model developed and utilized here incorporates irreversibility of the phase-field evolution. This is achieved by introducing a suitable constraint and by carefully heeding the influence of that constraint on the kinetics underlying microstructural changes associated with fracture. The analysis is predicated on the assumption that the phase-field variable takes values in the closed interval between zero and unity.     

Correspondence between a phase-field theory and a sharp-interface theory for crystal growth

A matched asymptotic analysis is used to show that, under certain constitutive hypotheses and a particular scaling, a recently developed phase-field theory corresponds to a sharp-interface theory for crystal growth that accounts for orientation dependence in the crystalline surface energy density as well as orientation and surface normal velocity dependence in the crystalline surface mobility. Received: May 6, 1996     

Chemistry of condensed thiophenes. V. Sulfonation and sulfonyl bridging of m-terphenyl. Conversion to sulfonamides

Reaction of m-terphenyl with 20% oleum at 100° gives both disulfonation and double sulfonyl bridging to yield benzo[1]thieno[2,3-b]dibenzothiophene-3,9-disulfonic acid 5,5,7,7-tetraoxide, isolated as the disodium salt (24%) and convertible (via the disulfonyl chloride) to the bis-sulfonanilide (44%) and the bis-N-butylsulfonamide (40%). Analogously, reaction of m-terphenyl with chlorosulfonic acid at 100° gives disulfonation plus only single sulfonyl bridging to produce 2-(4-chlorosulfonyl)-7-chlorosulfonyldibenzothiophene 5,5-dioxide (80%), convertible to the corresponding bis-sulfonanilide (63%) and the bis-N-butylsulfonamide (45%).