In this paper we deal with defects inside defects in systems of two scalar fields in 3 + 1 dimensions. The systems we consider are defined by potentials containing two real scalar fields, and so we are going to investigate domain ribbons inside domain walls. After introducing some general comments on the possibility of finding domain ribbons inside domain walls in two specific systems, we intro...

Your education heretofore has been focused on the horizon which opens for the first time to-day, to fit you to receive training as entered apprentices of the mystery and art of clinical medicine and surgery. From now on you will come into contact with the raw material of our craft, the sick and suffering who seek relief within the walls of this hospital. It will be your duty and inestimable pri...

After introducing the subject or shielding high energy accelerators, point source, line-of-sight models, and in particular the Moyer Model, are discussed. Their use in the shielding of proton and electron accelerators is demonstrated and their limitations noted, especially in relation to shielding in the forward direction provided by large, flat walls. The limitations of reducing problems to th...

We investigate Poincaré series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms and harmonic Maass forms are almost holomorphic, in which case the corresponding Poincaré series are almost holomorphic as well. In general, this is not the c...

A thin elastic sheet lying on a soft substrate develops wrinkled patterns when subject to an external forcing or as a result of geometric incompatibility. Thin sheet elasticity and substrate response equip such wrinkles with a global preferred wrinkle spacing length and with resistance to wrinkle curvature. These features are responsible for the liquid crystalline smectic-like behaviour of such...

We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate stru...

The spontaneous formation of domains of commensurate vortex patterns near rational fractional matching fields of a periodic pinning array has been investigated with high resolution scanning Hall probe microscopy. We show that domain formation is promoted due to the efficient incorporation of mismatched excess vortices and vacancies at the corners of domain walls, which outweighs the energetic c...

We consider linear arrays of cells of volume V(c) populated by monodisperse rods of size σV(c),σ=1,2,..., subject to hardcore exclusion interaction. Each rod experiences a position-dependent external potential. In one application we also examine effects of contact forces between rods. We employ two distinct methods of exact analysis with complementary strengths and different limits of spatial r...