We study a (2+1)-dimensional system that can be viewed as an infinite number of O(3) sigma-fields coupled by nearest-neighbour Heisenberg-like interaction. reduce the field equations this model to integrable is closely related two-dimensional relativistic Toda chain and Ablowitz-Ladik equations. Using reduction we obtain dark-soliton solutions our model.

Using a special double-layer membrane to avoid interaction among flow fields generated by different pores, we have, for the first time, observed the predicted discontinuous first-order transition in ultrafiltration of flexible linear polymer chains. Namely, the chain could pass through a pore much smaller than its unperturbed radius only when the flow rate is higher than a certain value. When o...

We study the parametric perturbation of Markov chains with denumerable state spaces. We consider both regular and singular perturbations. By the latter wemean that transition probabilities of aMarkov chain, with several ergodic classes, are perturbed such that (rare) transitions among the different ergodic classes of the unperturbed chain are allowed. Singularly perturbed Markov chains have bee...

We consider the problem of straightening chains in d ≥ 3 dimensions, possibly embedded into higher dimensions, using expansive motions. For any d ≥ 3, we show that there is an open chain in d dimensions that is not straight and not self-touching yet has no expansive motion. Furthermore, for any ∆ > 0 and d ≥ 3, we show that there is an open chain in d dimensions that cannot be straightened usin...

The Schrieffer-Wolff transformation aims to solve degenerate perturbation problems and give an effective Hamiltonian that describes the low-energy dynamics of exact in subspace unperturbed Hamiltonian. This unitary decoupling high-energy subspaces for transformed can be realized by quantum circuits. We a fully algorithm realizing SW transformation. also propose hybrid quantum-classical finding ...