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Vortices are localized planar structures that attain topological stability and can be used to describe collective behavior in a diversity of situations of current interest in nonlinear science. In high energy physics, vortices engender…
Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear…
We study the pair correlations of a spin-imbalanced two-leg ladder with attractive interactions, using the density matrix renormalization group method (DMRG). We identify regions in the phase diagram spanned by the chemical potential and…
A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered…
There has been considerable controversy regarding the structure of TiBe$_{12}$, which is variously reported as hexagonal and tetragonal. Lattice dynamics simulations based on density functional theory show the tetragonal phase space group…
Random bond Ising systems on a general hierarchical lattice are considered. Interesting inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These lead to upper bounds on the…
It is well known by analysts that a concept lattice has an exponential size in the data. Thus, as soon as he works with real data, the size of the concept lattice is a fundamental problem. In this chapter, we propose to investigate factor…
A popular approximation in lattice gauge theory is an extrapolation in the number of fermion species away from the four fold degeneracy natural with the staggered fermions formulation. I show that at finite lattice spacing and for an odd…
Woven shell structures are beneficial for applications requiring lightweight, damage resilience, and design tunability, such as in wearable devices, soft robotics, and aerospace systems. A fundamental component of woven structures is the…
Cohesive interactions between filamentous molecules have broad implications for a range of biological and synthetic materials. While long-standing theoretical approaches have addressed the problem of inter-filament forces from the limit of…
The paper deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem…
Predicting protein secondary structure using lattice model is one of the most studied computational problem in bioinformatics. Here secondary structure or three dimensional structure of protein is predicted from its amino acid sequence.…
An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Frechetness, strong Frechetness,…
In strange metals, a strong and anomalous scattering effect exists and increases linearly with temperature. In FeSe, we observed that the temperature dependence of resistivity exhibits non-Fermi liquid behavior in two regions below and…
We investigate the dispersion relations of TE resonances in different graphene-dielectric structures. Previous work has shown that when a graphene layer is brought into contact with a dielectric material, a gap can appear in its electric…
Throughout biology, hierarchy is a recurrent theme in the geometry of structures where strength is achieved with minimal use of material. Acting over vast timescales, evolution has brought about beautiful solutions to problems of…
Third order amplitude equations on hexagonal lattices can be used for predicting the existence and stability of stripes, up- and down-hexagons in pattern forming systems. These amplitude equations predict the nonexistence of bistable ranges…
Using selection rules imposed by the Pauli principle, we classify pairing correlations according to their symmetry properties with respect to spin, momentum, and energy. We observe that inhomogeneity always leads to mixing of even- and…
Finite element methods are used to study non-adhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with load at small loads. The mean pressure in the contact…
We consider the link between fragility and elasticity that follows from analysis of the data for a set of soft-colloid materials consisting of deformable spheres reported by Mattsson et. al., in Nature vol 462, 83 (2009). Fragility index…