In isolated bimetallic nanoscale systems the limit amount of matter and surface-induced size effects can change the thermodynamics of first-order phase transformation. In this paper we present theoretical modification of Gibbs free energy concept describing first-order phase transformation of binary alloyed nanoparticles taking into account size effects as well as depletion and hysteresis effec...

We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc function representation for the propagators of spin1 2 and spin-1 fields and exploring their properties. We show that the attributes of the spin-0 propagator which allowed us to derive the Sinc function represe...

We present an algorithm for computing exact shortest paths, and consequently distance functions, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex triangulated polyhedral surface. The algorithm is generalized to the case when a set of generalized sites is considered, providing their distance field that implicitly represents the Voronoi diag...

A “total Chern class” invariant of knots is defined. This is a universal Vassiliev invariant which is integral “on the level of Lie algebras” but it is not expressible as an integer sum of diagrams. The construction is motivated by similarities between the Kontsevich integral and the topological Chern character. AMS Classification 57M27; 57R20, 17B10

A one-to-one correspondence is proved between the N -rooted ribbon graphs, or maps, with e edges and the (e−N + 1)-loop Feynman diagrams of a certain quantum field theory. This result is used to obtain explicit expressions and relations for the generating functions of N -rooted maps and for the numbers of N -rooted maps with a given number of edges using the path integral approach applied to th...

Transportation networks model facilities for fast movement on the plane. A transportation network, together with its underlying distance, induces a new distance. Previously, only the Euclidean and the L1 distances have been considered as such underlying distances. However, this paper first considers distances induced by general distances and transportation networks, and present a unifying appro...

We discuss a progress in calculations of Feynman integrals based on the Gegen-bauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most complicated part of O(1/N 3) contributions to critical exponents of φ 4-theory. An illustration of the results obtained with help of above methods is conside...

We have performed multi-canonical chain-growth simulations of a polymer interacting with an adsorbing surface. The polymer, which is not explicitly anchored at the surface, experiences a hierarchy of phase transitions between conformations binding and nonbinding with the substrate. We discuss the phase diagram in the temperature-solubility plane and highlight the transition path through the fre...

We introduce an adic (Bratteli-Vershik) dynamical system based on a diagram whose path counts from the root are the Delannoy numbers. We identify the ergodic invariant measures, prove total ergodicity for each of them, and initiate the study of the dimension group and other dynamical properties.