  We propose a simple nonlocal energy functional that is suitable for the
continuum field characterization of nonperiodic and localized textures. The
phenomenological functional is based on the pairwise direction-dependent
interaction of field gradients that are separated by a fixed distance. In an
appendix, we describe the numerical minimization of our functional. On that
basis, we investigate the kinetic evolution of thread-like stripe patterns that
are created by the functional when we start from an initially disordered state.
At later stages, we find a coarse-graining that shows the same scaling behavior
as was obtained for the Cahn-Hilliard equation. In fact, the Cahn-Hilliard
model is contained in our characterization as a limiting case. A slight
modification of our model omits this coarse-graining and leads to nonperiodic
stripe phases. For the latter case, we investigate the temporal evolution of
the defects (end points) of the thread-like stripes. In view of possible
applications of this functional, we discuss a possible characterization of
polymeric systems and vesicles. The statistics of the growth of the thread-like
structures is compared to the case of step-growth polymerization reactions.
Furthermore, we demonstrate that the functional may be applied for the study of
vesicles in a continuum field description. Basic features, such as the tendency
of tank-treading in simple shear flows and parachute folding in pipe flows, are
reproduced.
