We demonstrate a dramatic change in the interaction forces between dark solitons nonlocal nonlinear media. present what we believe is first experimental evidence of attraction solitons. Our results indicate that should be observable other systems, such as Bose-Einstein condensates with repulsive long-range interparticle interaction.

We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials nonlocal focusing nonlinearity.We show that nonlocality stabilizes dynamics an otherwise unstable beam.This occurs for either single or higher charge fundamental vortices as well order (multiple ring) solitons.Our results pave way experimental observation stable rings other nonlinear systems including Bose-Einstein condensates pronounced long-range...

We present a semiempirical model for calculating electron transport in atomic-scale devices. The is an extension of the extended H\"uckel method with self-consistent Hartree potential that models effect external bias and corresponding charge rearrangements device. It also possible to include gate potentials continuum dielectric regions used study through organic molecule between gold surfaces, it demonstrated results are closer agreement experiments than ab initio approaches provide. In...

The Wave Function Matching (WFM) technique has recently been developed for the calculation of electronic transport in quantum two-probe systems. In terms efficiency it is comparable with widely used Green's function approach. WFM formalism presented so far requires evaluation all propagating and evanescent bulk modes left right electrodes order to obtain correct coupling between device electrode regions. this paper we will describe a modified approach that allows exclusion vast majority...

Let A 2 be the moduli stack of principally polarized abelian surfaces.Let ‫ޖ‬ a smooth -adic sheaf on associated to an irreducible rational finitedimensional representation Sp(4).We give explicit expression for cohomology in any degree terms Tate-type classes and Galois representations attached elliptic Siegel cusp forms.This confirms conjecture Faber van der Geer.As application we prove dimension formula vector-valued forms Sp(4, ‫)ޚ‬ weight three, which had been conjectured by Ibukiyama.

We construct a spectral sequence associated to stratified space, which computes the compactly supported cohomology groups of an open stratum in terms closed strata and reduced poset strata. Several familiar sequences arise as special cases. The construction is sheaf-theoretic works both for topological spaces \'etale algebraic varieties. As application we prove very general representation stability theorem configuration points.

We show that a certain locus inside the moduli space \mathcal{M}_{g} of hyperbolic surfaces, given by surfaces with “sufficiently many” short geodesics, is classifying handlebody mapping class group. A consequence construction top weight cohomology , studied Chan–Galatius–Payne, maps injectively into

Abstract We give a self‐contained and streamlined rendition of Andrea Bianchi's recent proof the Mumford conjecture using moduli spaces branched covers.

We present a Krylov subspace method for evaluating the self-energy matrices used in Green's function formulation of electron transport nanoscale devices. A procedure based on Arnoldi is employed to obtain solutions quadratic eigenvalue problem associated with infinite layered systems electrodes. One complex and two real shift-and-invert transformations are adopted select interior eigenpairs eigenvalues or vicinity unit circle that correspond propagating evanescent modes most influence...

We prove Getzler’s claims about the cohomology of moduli space stable curves genus one, that is, even ring is spanned by strata classes and all relations between these follow from Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) relation relation. In particular, isomorphic to tautological ring.

We prove that the tautological ring of $M_{2,n}^{ct}$, moduli space n-pointed genus two curves compact type, does not have Poincaré duality for any $n \geq 8$. This result is obtained via a more general study cohomology groups $M_{2,n}^{ct}$. explain how can be decomposed into pieces corresponding to different local systems and identified within this decomposition. Our results allow computation $H^k(M_{2,n}^{ct})$ $k$ $n$ considered both as $S_n$-representation mixed Hodge...

We describe the modular operad structure on moduli spaces of pointed stable curves equipped with an admissible $G$-cover. To do this we are forced to introduce notion colored not by a set but objects category. This construction interpolates in sense between `framed' and `colored' versions operads; hope that it will be independent interest. An algebra over is same thing as $G$-equivariant CohFT, defined Jarvis, Kaufmann Kimura. prove (orbifold) Gromov--Witten invariants global quotients...

Francis Brown introduced a partial compactification M-0,n(delta) of the moduli space M-0,M-n. We prove that gravity cooperad, given by degree-shifted cohomologies spaces M-0,M-n, is ...

Let $X$ be a topological space. We consider certain generalized configuration spaces of points on $X$, obtained from the cartesian product $X^n$ by removing some intersections diagonals. give systematic framework for studying cohomology such using what we call "tcdga models" cochains $X$. prove following theorem: suppose that is "nice" space, $R$ any commutative ring, $H^\bullet_c(X,R)\to H^\bullet(X,R)$ zero map, and $H^\bullet_c(X,R)$ projective $R$-module. Then compact support space...

We consider the loci of d-elliptic curves in $M_2$, and corresponding surfaces $A_2$. show how a description these as quotients product modular can be used to calculate cohomology natural local systems on them, both mixed Hodge structures $\ell$-adic Galois representations. study particular case d=2, compute Euler characteristic moduli space n-pointed bi-elliptic genus 2 Grothendieck group structures.

We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism free braid groups) with coefficients in sequence irreducible algebraic representations arithmetic groups. The novelty is that the stable range independent choice representation. Combined earlier work Bergstr\"om--Diaconu--Petersen--Westerland this proves Conrey--Farmer--Keating--Rubinstein--Snaith predictions all moments family quadratic $L$-functions over function fields,...

Abstract As drilling muds evolve to satisfy well requirements, cementing preflush technologies need change ensure proper mud removal during jobs. A new component—engineering-designed fiber—was added a fluid and tested in the laboratory, with promising results. The system was then implemented Latin America. Obtaining is very important for achieving zonal isolation at technology consists of addition an engineering-designed fiber fluids significantly improve nonaqueous from operations. fibers...

Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only they as associative dg algebras. This answers folklore problem in rational homotopy theory, showing the type space is determined by its algebra cochains. We also Koszul dual statement, under an additional completeness hypothesis: complete Lie whose universal enveloping must themselves be quasi-isomorphic. The latter result applies particular to nilpotent (not...

We prove a comparison isomorphism between singular cohomology and sheaf cohomology.