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An empirical principle for the construction of a linear relationship between the total angular momentum and squared-mass of baryons is proposed. In order to examine linearity of the trajectories, a rigorous least-squares regression analysis…
In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan et al, Nucl.Phys.B862:553-575,2012]. Here we develop a general formalism of rectangle boundary states using…
A scheme suggested in the literature to determine the symmetry-imposed shape of linear response tensors is revised and extended to allow for the treatment of more complex situations. The extended scheme is applied to discuss the shape of…
Poincar\'e recognized that phase portraits are mainly structured around fixed points. Nevertheless, the knowledge of fixed points and their properties is not sufficient to determine the whole structure of chaotic attractors. In order to…
A ridge function is a function of several variables that is constant along certain directions in its domain. Using classical dimensional analysis, we show that many physical laws are ridge functions; this fact yields insight into the…
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…
Let $R$ be a rational function. The iterations $(R^n)_n$ of $R$ gives a complex dynamical system on the Riemann sphere. We associate a $C^*$-algebra and study a relation between the $C^*$-algebra and the original complex dynamical system.…
We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…
A central hyperplane arrangement in C^2 with multiplicity is called a `locus configuration' if it satisfies a series of `locus equations' on each hyperplane. Following Chalykh, Feigin and Veselov [CFV99], we demonstrate that the first locus…
Many physically important mechanical systems may be described with a Lie group $G$ as configuration space. According to the well-known Noether's theorem, underlying symmetries of the Lie group may be used to considerably reduce the…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
The volume of a cyclic polytope can be obtained by forming an iterated integral along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial…
Relativistic invariant projectors of states in a complex bispinor space on a complex spinor space are constructed. An expression for sections of bundle with connection on group SU(4) in an explicit form has been obtained. Within the…
In a series of papers, we propose a theory to explain the formation and properties of rings and spirals in barred galaxies. The building blocks of these structures are orbits guided by the manifolds emanating from the unstable Lagrangian…
Using contact dynamics simulations, we compare the effect of rolling resistance at the contacts in granular systems composed of disks with the effect of angularity in granular systems composed of regular polygonal particles. In simple shear…
We introduce the edge Schur functions $E^{\lambda}$ that are defined as a generating series over edge labeled tableaux. We formulate $E^{\lambda}$ as the partition function for a solvable lattice model, which we use to show they are…
Functional methods and a derivative expansion are employed for laying out a procedure to compute the effective action to any loop order, for scalar fields parametrising an arbitrary Riemannian manifold, while maintaining explicit…
We compute small rational models for configuration spaces of points on oriented surfaces, as right modules over the framed little disks operad. We do this by splitting these surfaces in unions of several handles. We first describe rational…
In this paper, we give an explicit construction of dynamical systems (defined within a solid torus) containing any knot (or link) and arbitrarily knotted chaos. The first is achieved by expressing the knots in terms of braids, defining a…