相关论文: Realizations of Crystals
A new scheme for amplification of coherent gamma rays is proposed. The key elements are crystalline undulators - single crystals with periodically bent crystallographic planes exposed to a high energy beam of charged particles undergoing…
A permutative matrix is a square matrix such that every row is a permutation of the first row. A constructive version of a result attributed to Suleimanova is given via permutative matrices. In addition, we strengthen a well-known result by…
We will show that the complex shapes of snow crystals can be explained from a simple basic mechanism that is also responsible for the appearance of many others structures in nature. We expect that this new physical mechanism, that follows…
We prove the finiteness of crystalline cohomology of higher level. An important ingredient is a "higher de Rham complex" and a kind of Poincar\'e lemma for it.
We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial…
In the preceding paper, we formulated a conjecture on the relations between certain classes of irreducible representations of affine Hecke algebras of type B and symmetric crystals for $\gl_\infty$. In the present paper, we prove the…
The polyhedral realizations for crystal bases of the integrable highest weight modules of $U_q(\mathfrak{g})$ have been introduced in ([T.Nakashima, J. Algebra, vol.219, no. 2, (1999)]), which describe the crystal bases as sets of lattice…
We perform extensive monomer-resolved computer simulations of suitably-designed amphiphilic dendritic macromolecules over a broad range of densities, proving the existence and stability of cluster crystals formed in these systems, as…
General realizations, star products and plane waves for kappa-Minkowski spacetime are considered. Systematic construction of general hermitian realization is presented, with special emphasis on noncommutative plane waves and hermitian star…
We construct a crystalline measure on the real line, which is not a Fourier Quasicrystal.
It is show that in group representation by non-traditionally determining by the Maxwell equations, instead of wave, linear differential operator of momentous type from the common point of view the transformation of electromagnetic and…
In this paper, we give geometric realizations of Lusztig's symmetries. We also give projective resolutions of a kind of standard modules. By using the geometric realizations and the projective resolutions, we obtain the categorification of…
Finite-dimensional subalgebras of a Lie algebra of smooth vector fields on a circle, as well as piecewise-smooth global transformations of a circle on itself, are considered. A canonical forms of realizations of two- and three-dimensional…
In this thesis, four realizations of the Onsager algebra are explored. We begin with its original definition as introduced by Lars Onsager. We then examine how the Onsager algebra can be presented as a Lie algebra with two generators and…
Crystallization from an amorphous atomic structure is usually seen as a spontaneous process in pursuit of a lower energy state, but for alloy systems it is often hard to elucidate because of the intrinsic structural and compositional…
The vertices of any (combinatorial) Kashiwara crystal graph carry a natural monoid structure given by identifying words labelling vertices that appear in the same position of isomorphic components of the crystal. Working on a purely…
We extend the recently developed classical theory for the optical response of a single-layer crystal to bilayers. We account for the interaction between the two atomic planes and the multiple reflections inside the crystals. We show how to…
Let $(A, I)$ be a bounded prism, and $X$ be a smooth $p$-adic formal scheme over $\Spf(A/I)$. We consider the notion of crystals on Bhatt--Scholze's prismatic site $(X/A)_{\prism}$ of $X$ relative to $A$. We prove that if $X$ is proper over…
Bose-Einstein condensates of sodium atoms have been prepared in optical and magnetic traps in which the energy-level spacing in one or two dimensions exceeds the interaction energy between atoms, realizing condensates of lower…
Optimizing the free energy under a mass constraint may generate a convex crystal subject to assumptions on the potential $g(0)=0$, $g \ge 0$. The general problem classically attributed to Almgren is to infer if this is the case assuming the…