Behavior of Direct Tower Foundation on Improved Soil

The paper presents the foundation behaviour of a 146-m telecommunications tower situated near Verona in Italy, with foundation soils characterized as a thick deposit of alluvial gravels and sands. In order to limit total and differential settlements of the tower it was decided to improve the foundation soil with jet-grouting columns. Predictions on the behaviour of the structure and the foundation soil were performed with an axisymmetric finite-element model adopting an elastic linear constitutive law. Soil moduli were obtained from the results of a cross-hole test and from Standard Penetration Tests; jet-grouting columns behaviour was estimated from load and borehole tests. Calculated settlements in the construction stages are compared with the measured ones

On the center of quiver-Hecke algebras

We compute the equivariant cohomology ring of the moduli space of framed instantons over the affine plane. It is a Rees algebra associated with the center of cyclotomic degenerate affine Hecke algebras of type A. We also give some related results on the center of quiver Hecke algebras and cohomology of quiver varieties.Comment: 72 page

Stick-Slip Sliding of Water Drops on Chemically Heterogeneous Surfaces

We present a comprehensive study of water drops sliding down chemically heterogeneous surfaces formed by a periodic pattern of alternating hydrophobic and hydrophilic stripes. Drops are found to undergo a stick-slip motion whose average speed is an order of magnitude smaller than that measured on a homogeneous surface having the same static contact angle. This motion is the result of the periodic deformations of the drop interface when crossing the stripes. Numerical simulations confirm this view and are used to elucidate the principles underlying the experimental observations

Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A

We are interested in the structure of the crystal graph of level $l$ Fock spaces representations of $\mathcal{U}_q (\widehat{\mathfrak{sl}_e})$. Since the work of Shan [26], we know that this graph encodes the modular branching rule for a corresponding cyclotomic rational Cherednik algebra. Besides, it appears to be closely related to the Harish-Chandra branching graph for the appropriate finite unitary group, according to [8]. In this paper, we make explicit a particular isomorphism between connected components of the crystal graphs of Fock spaces. This so-called "canonical" crystal isomorphism turns out to be expressible only in terms of: - Schensted's classic bumping procedure, - the cyclage isomorphism defined in [13], - a new crystal isomorphism, easy to describe, acting on cylindric multipartitions. We explain how this can be seen as an analogue of the bumping algorithm for affine type $A$. Moreover, it yields a combinatorial characterisation of the vertices of any connected component of the crystal of the Fock space

Some combinatorial identities related to commuting varieties and Hilbert schemes

In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane

Drop motion induced by vertical vibrations

We have studied the motion of liquid drops on an inclined plate subject to vertical vibrations. The liquids comprised distilled water and different aqueous solutions of glycerol, ethanol and isopropanol spanning the range 1–39 mm2 s−1 in kinematic viscosities and 40–72 mN m−1 in surface tension. At sufficiently low oscillating amplitudes, the drops are always pinned to the surface. Vibrating the plate above a certain amplitude yields sliding of the drop. Further increasing the oscillating amplitude drives the drop upward against gravity. In the case of the most hydrophilic aqueous solutions, this motion is not observed and the drop only slides downward. Images taken with a fast camera show that the drop profile evolves in a different way during sliding and climbing. In particular, the climbing drop experiences a much bigger variation in its profile during an oscillating period. Complementary numerical simulations of 2D drops based on a diffuse interface approach confirm the experimental findings. The overall qualitative behavior is reproduced suggesting that the contact line pinning due to contact angle hysteresis is not necessary to explain the drop climbing

Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras

Let Uq(ghat) be the quantum affine algebra associated to a simply-laced simple Lie algebra g. We examine the relationship between Dorey's rule, which is a geometrical statement about Coxeter orbits of g-weights, and the structure of q-characters of fundamental representations V_{i,a} of Uq(ghat). In particular, we prove, without recourse to the ADE classification, that the rule provides a necessary and sufficient condition for the monomial 1 to appear in the q-character of a three-fold tensor product V_{i,a} x V_{j,b} x V_{k,c}.Comment: 30 pages, latex; v2, to appear in Communications in Mathematical Physic

Doped MXenes—A new paradigm in 2D systems: Synthesis, properties and applications

Since 2011, 2D transition metal carbides, carbonitrides and nitrides known as MXenes have gained huge attention due to their attractive chemical and electronic properties. The diverse functionalities of MXenes make them a promising candidate for multitude of applications. Recently, doping MXene with metallic and non-metallic elements has emerged as an exciting new approach to endow new properties to this 2D systems, opening a new paradigm of theoretical and experimental studies. In this review, we present a comprehensive overview on the recent progress in this emerging field of doped MXenes. We compare the different doping strategies; techniques used for their characterization and discuss the enhanced properties. The distinct advantages of doping in applications such as electrocatalysis, energy storage, photovoltaics, electronics, photonics, environmental remediation, sensors, and biomedical applications is elaborated. Additionally, theoretical developments in the field of electrocatalysis, energy storage, photovoltaics, and electronics are explored to provide key specific advantages of doping along with the underlying mechanisms. Lastly, we present the advantages and challenges of doped MXenes to take this thriving field forward

Multiplicative slices, relativistic Toda and shifted quantum affine algebras

We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on the equivariant $K$-theory of parabolic Laumon spaces. In type $A_1$, they are closely related to the open relativistic quantum Toda lattice of type $A$.Comment: 125 pages. v2: references updated; in section 11 the third local Lax matrix is introduced. v3: references updated. v4=v5: 131 pages, minor corrections, table of contents added, Conjecture 10.25 is now replaced by Theorem 10.25 (whose proof is based on the shuffle approach and is presented in a new Appendix). v6: Final version as published, references updated, footnote 4 adde

On minimal affinizations of representations of quantum groups

In this paper we study minimal affinizations of representations of quantum groups (generalizations of Kirillov-Reshetikhin modules of quantum affine algebras introduced by Chari). We prove that all minimal affinizations in types A, B, G are special in the sense of monomials. Although this property is not satisfied in general, we also prove an analog property for a large class of minimal affinization in types C, D, F. As an application, the Frenkel-Mukhin algorithm works for these modules. For minimal affinizations of type A, B we prove the thin property (the l-weight spaces are of dimension 1) and a conjecture of Nakai-Nakanishi (already known for type A). The proof of the special property is extended uniformly for more general quantum affinizations of quantum Kac-Moody algebras.Comment: 38 pages; references and additional results added. Accepted for publication in Communications in Mathematical Physic