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Classical results on aperiodic tilings are rather complicated and not widely understood. Below, an alternative approach is discussed in hope to provide additional intuition not apparent in classical works.
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
In an equiangular spiral, "the whorls continually increase in breadth and do so in a steady and unchanging ratio... It follows that the sectors cut off by successive radii, at equal vectorial angles, are similar to one another in every…
This is an application of the theory of tilting objects to the geometric setting of perverse sheaves. We show that this theory is a natural framework for Beilinson's gluing of perverse sheaves construction. In the special case of Schubert…
We study here slopes of periodicity of tilings. A tiling is of slope if it is periodic along direction but has no other direction of periodicity. We characterize in this paper the set of slopes we can achieve with tilings, and prove they…
We define (higher rank) spinorially twisted spin structures and deduce various curvature identites as well as estimates for the eigenvalues of the corresponding twisted Dirac operators.
The chirality induced spin selectivity effect remains a challenge to capture with theoretical modeling. While at least a decade was spent on independent electron models, which completely fail to reproduce the experimental results, the…
The spiral is one of Nature's more ubiquitous shape: it can be seen in various media, from galactic geometry to cardiac tissue. In the literature, very specific models are used to explain some of the observed incarnations of these dynamic…
A new way of computing scattering amplitudes in a certain very important QFT (N=4 SYM) has recently been developed, in which an algebraic structure called the positive Grassmannian plays a very important role. The mathematics of the…
The origin of galactic spiral arms is one of fundamental problems in astrophysics. Based on the local analysis Toomre (1981) proposed the swing amplification mechanism in which the self-gravity forms spiral arms as leading waves of stars…
Spin textures, i.e., the distribution of spin polarization vectors in reciprocal space, exhibit diverse patterns determined by symmetry constraints, resulting in a variety of spintronic phenomena. Here, we propose a universal theory to…
We present a unified theory of linear spiral structure in stellar disks. We begin by identifying the characteristic scales involved in the spiral structure problem and listing some quantitative requirements of a successful theory. We then…
The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open…
Self-healing of light refers to the ability of a light field to recover its structure after being damaged by a partial obstruction placed in its propagation path. Here, we will give a comprehensive review of the history and development of…
A sketch of the chapter appearing under the same heading in the book ``New Optimization Algorithms in Physics'' (A.K. Hartmann and H. Rieger, Eds.) is given. After a general introduction to spin glasses, important aspects of heuristic…
We describe a new formula capable of quantitatively characterizing the Hubble sequence of spiral galaxies including grand design and barred spirals. Special shapes such as ring galaxies with inward and outward arms are also described by the…
The incorporation of structured light techniques into vision science has enabled more selective probes of polarization related entoptic phenomena. Diverse sets of stimuli have become accessible in which the spatially dependant optical…
The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may…
A semiclassical constrained Hamiltonian system which was established to study dynamical systems of matrix valued non-Abelian gauge fields is employed to formulate spin Hall effect in noncommuting coordinates at the first order in the…
Two new series of substitution tilings are introduced in which the tiles appear in infinitely many orientations. It is shown that several properties of the well-known pinwheel tiling do also hold for these new examples, and, in fact, for…