Search results for "PD"
showing 10 items of 1971 documents
On a rough perturbation of the Navier-Stokes system and its vorticity formulation
2019
We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In particular, we define an intrinsic notion of solution based on ideas from the rough path theory and study the system in an equivalent vorticity formulation. In two space dimensions, we prove that well-posedness and enstrophy balance holds. Moreover, we derive rough path continuity of the equation, which yields a Wong-Zakai result for Brownian driving paths, and show that for a large class of driving signals, the system generates a continuous rando…
Extremal polynomials in stratified groups
2018
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.
Lévy processes in bounded domains: path-wise reflection scenarios and signatures of confinement
2022
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line is secured by a two-sided reflection. Depending on the specific reflection "mechanism", the inferred jump-type processes differ in their spectral and statistical characteristics, like e.g. relaxation properties, and functional shapes of invariant (equilibrium, or asymptotic near-equilibrium) probability density functions in the interval. The analysis is carried out in conjunction with attempts to give meaning to the notion of a reflecting L\'{e}vy process…
Anomalous diffusion and nonlinear relaxation phenomena in stochastic models of interdisciplinary physics
2020
The study of nonlinear dynamical systems in the presence of both Gaussian and non-Gaussian noise sources is the topic of this research work. In particular, after shortly present new theoretical results for statistical characteristics in the framework of Markovian theory, we analyse four different physical systems in the presence of Levy noise source. (a) The residence time problem of a particle subject to a non-Gaussian noise source in arbitrary potential profile was analyzed and the exact analytical results for the statistical characteristics of the residence time for anomalous diffusion in the form of Levy flights in fully unstable potential profile was obtained. Noise enhanced stability …
tBuLi-Mediated One-Pot Direct Highly Selective Cross-Coupling of Two Distinct Aryl Bromides.
2015
A Pd-catalyzed direct cross-coupling of two distinct aryl bromides mediated by tBuLi is described. The use of [Pd-PEPPSI-IPr] or [Pd-PEPPSI-IPent] as catalyst allows for the efficient one-pot synthesis of unsymmetrical biaryls at room temperature. The key for this selective cross-coupling is the use of an ortho-substituted bromide that undergoes lithium-halogen exchange preferentially.
Application of palladium complexes bearing acyclic amino(hydrazido)carbene ligands as catalysts for copper-free Sonogashira cross-coupling
2015
Abstract Metal-mediated coupling of one isocyanide in cis-[PdCl2(CNR1)2] (R1 = C6H11 (Cy) 1, tBu 2, 2,6-Me2C6H3 (Xyl) 3, 2-Cl-6-MeC6H3 4) and various carbohydrazides R2CONHNH2 [R2 = Ph 5, 4-ClC6H4 6, 3-NO2C6H4 7, 4-NO2C6H4 8, 4-CH3C6H4 9, 3,4-(MeO)2C6H3 10, naphth-1-yl 11, fur-2-yl 12, 4-NO2C6H4CH2 13, Cy 14, 1-(4-fluorophenyl)-5-oxopyrrolidine-3-yl 15, (pyrrolidin-1-yl)C(O) 16, 3-(3,5-di-tert-butyl-4-hydroxyphenyl)propane-1-yl 17, EtNHC(O) 18] or sulfohydrazides R3SO2NHNH2 [R3 = Ph 19, 4-MeC6H4 20] led to a series of (hydrazido)(amino)carbene complexes cis-[PdCl2{ C (NHNHX) N(H)R1}(CNR1)]; X = COR2, SO2R3 (21–48, isolated yields 60–96%). All prepared species were characterized by elemental…
Long-distance magnetic coupling in dinuclear copper(II) complexes with oligo-para-phenylenediamine bridging ligands
2010
Abstract Two novel dinuclear copper(II) complexes of formulae [Cu2(tren)2(bpda)](ClO4)4 (2) and [Cu2(tren)2(tpda)](ClO4)4 (3) containing the tripodal tris(2-aminoethyl)amine (tren) terminal ligand and the 4,4′-biphenylenediamine (bpda) and 4,4″-p-terphenylenediamine (tpda) bridging ligands have been synthesized and structurally, spectroscopically, and magnetically characterized. Their experimentally available electronic spectroscopic and magnetic properties have been reasonably reproduced by DFT and TDDFT calculations. Single crystal X-ray diffraction analysis of 2 shows the presence of dicopper(II) cations where the bpda bridging ligand adopts a bismonodentate coordination mode toward two …
Stilizētu dzīvnieku motīvi audumu apdrukā
2018
Darba autore, LU PPMF 4. kursa studente Nadīna Mansurova, ir izveidojusi diplomdarbu ar nosaukumu ,,Stilizētu dzīvnieku motīvi audumu apdrukā’’, kurš sastāv no 3 daļām: teorētiskās, empīriskās un radošās daļas. Teorētiskā daļa sastāv no četrām nodaļām. Teoretiskajā daļā autore izpētija motīva un ornamenta kā mākslas sastāvdaļas raksturojumu un tā veidojošos komponentus, apģērbu un tekstīlizstrādājumu vēsturisko attīstību, dzīvnieku motīvu vēsturisko attīstību un apdrukas meistarus Latvijā. Šī darba izstrādes mērķos tika izmantoti dažādi literatūras avoti, tai skaitā krievu valodā. Empīriskajā daļā autore veica pētījumu par dzīvnieku motīvu pielotojumu apģērbu apdrukā un veica dizaina paraug…
Hydrodynamics and Stochastic Differential Equation with Sobolev Coefficients
2013
In this chapter, we will explain how the Brenier’s relaxed variational principle for Euler equation makes involved the ordinary differential equations with Sobolev coefficients and how the investigation on stochastic differential equations (SDE) with Sobolev coefficients is useful to establish variational principles for Navier–Stokes equations. We will survey recent results on this topic.
The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow
2008
We propose a mathematical derivation of Brinkman's force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Omega subset of R-3 for the velocity field u of an incompressible fluid with kinematic viscosity v and density 1. Brinkman's force consists of a source term 6 pi rvj where j is the current density of the particles, and of a friction term 6 pi vpu where rho is the number density of particles. These additional terms in the motion equation for the fluid are obtained from the Stokes or steady Navier-Stokes equations set in Omega minus the disjoint union of N balls of radius epsilo…