Related papers: Young wall model for $A_2^{(2)}$-type adjoint crys…
The affine Yangian of $\mathfrak{gl}_1$ is isomorphic to the universal enveloping algebra of $\mathcal{W}_{1+\infty}$ and can serve as a building block in the construction of new vertex operator algebras. In [1], a two-parameter family…
For simply-laced Kac-Moody algebras $\frak g$, Stembridge (2003) proposed a `local' axiomatization of crystal graphs of representations of $U_q(\frak g)$. In this paper we propose axioms for edge-2-colored graphs which characterize the…
The affinity of antibodies (Abs) produced in vivo for their target antigens (Ags) is typically well below the maximum affinity possible. Nearly 25 years ago, Foote and Eisen explained how an 'affinity ceiling' could arise from constraints…
In this paper we construct bases of standard (i.e. integrable highest weight) modules $L(\Lambda)$ for affine Lie algebra of type $B_2\sp{(1)}$ consisting of semi-infinite monomials. The main technical ingredient is a construction of…
Affine Lie algebras admit non-classical highest-weight theories through alternative partitions of the root system. Although significant inroads have been made, much of the classical machinery is inapplicable in this broader context, and…
The surface freezing and surface melting transitions exhibited by a model two-dimensional soft matter system is studied. The behaviour when confined within a wedge is also considered. The system consists of particles interacting via a soft…
When two periodic potentials compete in materials, one may adopt the other, which straightforwardly generates topological defects. Of particular interest are domain walls in charge-, dipole-, and spin-ordered systems, which govern…
Young's moduli of regular two-dimensional truss-like and eye-shape-like structures are simulated by using the finite element method. The structures are the idealizations of soft polymeric materials used in the electret applications. In the…
An important challenge in active matter lies in harnessing useful global work from entities that produce work locally, e.g., via self-propulsion. We investigate here the active matter version of a classical capillary rise effect, by…
In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…
We report on how adjoint zero modes can be used to filter out the topological structures of gauge configurations from the UV fluctuations. We will use the Adjoint Filtering Method (AFM) which relies on the existence of a particular…
The main problem in theoretical analysis of structures with strong confinement is the fact that standard mathematical tools: differential equations and Fourier's transformations are no longer applicable. In this paper we have demonstrated…
A method is proposed to compute the interfacial free energy of a Lennard-Jones system in contact with a structured wall by molecular dynamics simulation. Both the bulk liquid and bulk face-centered-cubic crystal phase along the (111)…
We compare the behavior of a new two-dimensional aqueous colloidal model system with a simple numerical treatment. To the first order the attractive interaction between the colloids induced by an in-plane rotating ac electric field is…
We derive a closed-form false vacuum decay rate at one loop in the thin wall limit, where the true and false vacua are nearly degenerate. We obtain the bounce configuration in $D$ dimensions, together with the Euclidean action with a higher…
We show that Calabi-Yau crystals generate certain Chern-Simons knot invariants, with Lagrangian brane insertions generating the unknot and Hopf link invariants. Further, we make the connection of the crystal brane amplitudes to the…
We demonstrate that highly-ordered two-dimensional crystals of ligand-capped gold nanoparticles display a local photo-mechanical stiffness as high as that of solids such as graphite. In out-of equilibrium electron diffraction experiments, a…
New functional representation for the strongly interacting systems is proposed which contains a new type of the quantum coherent state. As a result the new algebraic structure- so called "tower of algebras" appears which gives the tower (or…
Gas accretion and stellar feedback processes link metal content, star formation, and gas and stellar mass (and the potential depth) in star-forming galaxies. Constraining this hypersurface has been challenging because of the need for…
We classify the simple infinite dimensional integrable modules with finite dimensional weight spaces over the quantized enveloping algebra of an untwisted affine algebra. We prove that these are either highest (lowest) weight integrable…