Cut moments and a generalization of DGLAP equations

We elaborate a cut (truncated) Mellin moments (CMM) approach that is constructed to study deep inelastic scattering in lepton-hadron collisions at the natural kinematic constraints. We show that generalized CMM obtained by multiple integrations of the original parton distribution $f(x,\mu^2)$ as well as ones obtained by multiple differentiations of this $f(x,\mu^2)$ also satisfy the DGLAP equations with the correspondingly transformed evolution kernel $P(z)$. Appropriate classes of CMM for the available experimental kinematic range are suggested and analyzed. Similar relations can be obtained for the structure functions $F(x)$, being the Mellin convolution $F= C \ast f$, where $C$ is the coefficient function of the process.Comment: 11 page

Nonlinear broadening of the plasmon linewidth in a graphene stripe

In contrast to semiconductor structures, the experimentally observed plasma resonances in graphene show an asymmetrical and rather broad linewidth. We show that this can be explained by the linear electron energy dispersion in this material and is related to the violation of the generalized Kohn theorem in graphene.Comment: 5 pages, 3 figure

Noise-induced breakdown of coherent collective motion in swarms

We consider swarms formed by populations of self-propelled particles with attractive long-range interactions. These swarms represent multistable dynamical systems and can be found either in coherent traveling states or in an incoherent oscillatory state where translational motion of the entire swarm is absent. Under increasing the noise intensity, the coherent traveling state of the swarms is destroyed and an abrupt transition to the oscillatory state takes place.Comment: 6 pages, 5 figures; to appear in Phys. Rev.

Nonequilibrium pattern formation in chiral Langmuir monolayers with transmembrane flows

Nonequilibrium Langmuir monolayers including a fraction of chiral molecules and subject to transmembrane flow are considered. The flow induces coherent collective precession of chiral molecules. Our theoretical study shows that splay interactions in this system lead to spatial redistribution of chiral molecules and formation of spiral waves and target patterns observed in experiments

Analysis of some localized boundary-domain integral equations

Some direct segregated localized boundary-domain integral equation (LBDIE) systems associated with the Dirichlet and Neumann boundary value problems (BVP) for a scalar "Laplace" PDE with variable coefficient are formulated and analysed. The parametrix is localized by multiplication with a radial localizing function. Mapping and jump properties of surface and volume integral potentials based on a localized parametrix and constituting the LBDIE systems are studied in a scale of Sobolev (Bessel potential) spaces. The main results established in the paper are the LBDIEs equivalence to the original variable-coefficient BVPs and the invertibility of the LBDIE operators in the corresponding Sobolev spaces

About analysis of some localized boundary-domain integral equations for a variable-coefficient BVPs

Some direct localized boundary-domain integral equations (LBDIEs) associated with the Dirichlet and Neumann boundary value problems for the "Laplace" linear differential equation with a variable coefficient are formulated. The LBDIEs are based on a parametrix localized by a cut-off function. Applying the theory of pseudo-differential operators, invertibility of the localized volume potentials is proved first. This allows then to prove solvability, solution uniqueness and equivalence of the LBDIEs to the original BVP, and investigate the LBDIE operator invertibility in appropriate Sobolev spaces

Localized boundary-domain integral equation formulation for mixed type problems

Copyright @ 2010 Walter de Gruyter GmbHSome modified direct localized boundary-domain integral equations (LBDIEs) systems associated with the mixed boundary value problem (BVP) for a scalar “Laplace” PDE with variable coefficient are formulated and analyzed. The main results established in the paper are the LBDIEs equivalence to the original variable-coefficient BVPs and the invertibility of the corresponding localized boundary-domain integral operators in appropriately chosen function spaces