Related papers: On the convergence of cluster expansions for polym…
Size and composition of clusters produced by adiabatic expansion of binary gas mixtures (Ar-Kr, Kr-Xe, and N2-Ar) with various component concentrations are studied by using electron-diffraction technique. The resulting homogeneous and…
Coupled cluster theory produced arguably the most widely used high-accuracy computational quantum chemistry methods. Despite the approach's overall great computational success, its mathematical understanding is so far limited to results…
Group cohomology of polynomial growth is defined for any finitely generated discrete group, using cochains that have polynomial growth with respect to the word length function. We give a geometric condition that guarantees that it agrees…
We show that the abundance and redshift distribution ($dN/dz$) of galaxy clusters in future high--yield cluster surveys, combined with the spatial power spectrum ($P_c(k)$) of the same clusters, can place significant constraints on the…
Possible explanations of the observed accelerated expansion of the Universe are the introduction of a dark energy component or the modifications of gravity at large distances. A particular difference between these scenarios is the dynamics…
We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of `extended quivers' which are oriented hypergraphs. We describe mutations of such…
Linked cluster expansions provide a useful tool both for analytical and numerical investigations of lattice field theories. The expansion parameter is the interaction strength fields at neighboured lattice sites are coupled. They result…
In the cluster expansion framework of Bose liquids we calculate analytical expressions of the two-body, three-body and four-body diagrams contributing to the g.s. energy of an infinite system of neutral alpha-particles at zero-temperature,…
Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoretical model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of…
We prove an effective version of the inverse theorem for the Gowers $U^3$-norm for functions supported on high-rank quadratic level sets in finite vector spaces. For configurations controlled by the $U^3$-norm (complexity-two…
We present a unifying picture of the compact, dense and dilute phases of two-dimensional polymers. The lattice dependence of the scaling exponents for compact polymers is reconciled with their universality in the dense and dilute case. In…
The mathematical foundation of the so-called extended coupled-cluster method for the solution of the many-fermion Schr\"odinger equation is here developed. We prove an existence and uniqueness result, both in the full infinite-dimensional…
In this work we present a coupled-cluster theory for the propagation of multireference electronic systems initiating at general quantum mechanical states. Our formalism is based on the infinitesimal analysis of modified cluster operators,…
We give new bounds on the cosystolic expansion constants of several families of high dimensional expanders, and the known coboundary expansion constants of order complexes of homogeneous geometric lattices, including the spherical building…
We prove combination theorems in the spirit of Klein and Maskit in the context of discrete convergence groups acting geometrically finitely on their limit sets. As special cases, we obtain combination theorems for geometrically finite…
Increasing inhomogeneity due to gravitational clumping reflects increasing gravitational entropy in a time evolving universe. Starting from an ensemble of uniformly distributed particles it is demonstrated that gravitational clustering is…
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…
We give a detailed and refined proof of the Dobrushin-Pechersky uniqueness criterion extended to the case of Gibbs fields on general graphs and single-spin spaces, which in particular need not be locally compact. The exponential decay of…
We propose the implementation of two ingredients in the phenomenological applications of the unitary approach based on the $z$-expansion of hadronic form factors, commonly referred to as the Boyd-Grinstein-Lebed (BGL) $z$-expansion [1-4].…
Clusters of galaxies have been used extensively to determine cosmological parameters. A major difficulty in making best use of Sunyaev-Zel'dovich (SZ) and X-ray observations of clusters for cosmology is that using X-ray observations it is…