The complex life of hydrodynamic modes

We study analytic properties of the dispersion relations in classical hydrodynamics by treating them as Puiseux series in complex momentum. The radii of convergence of the series are determined by the critical points of the associated complex spectral curves. For theories that admit a dual gravitational description through holography, the critical points correspond to level-crossings in the quasinormal spectrum of the dual black hole. We illustrate these methods in ${\cal N}=4$ supersymmetric Yang-Mills theory in 3+1 dimensions, in a holographic model with broken translation symmetry in 2+1 dimensions, and in conformal field theory in 1+1 dimensions. We comment on the pole-skipping phenomenon in thermal correlation functions, and show that it is not specific to energy density correlations.Comment: V3: 54 pages, 18 figures. Appendix added. Version to appear in JHE

On the convergence of the gradient expansion in hydrodynamics

Hydrodynamic excitations corresponding to sound and shear modes in fluids are characterised by gapless dispersion relations. In the hydrodynamic gradient expansion, their frequencies are represented by power series in spatial momenta. We investigate the analytic structure and convergence properties of the hydrodynamic series by studying the associated spectral curve in the space of complexified frequency and complexified spatial momentum. For the strongly coupled ${\cal N}=4$ supersymmetric Yang-Mills plasma, we use the holographic duality methods to demonstrate that the derivative expansions have finite non-zero radii of convergence. Obstruction to the convergence of hydrodynamic series arises from level-crossings in the quasinormal spectrum at complex momenta.Comment: V3: 5 pages, 2 figures. Final version. Published in Physical Review Letters with the title "Convergence of the Gradient Expansion in Hydrodynamics

Застосування технологій E-learning в курсі англійської мови для аспірантів у НТУ "ХПІ"

The experience of introduction of E-learning into the English course for post-graduates at NTU "KhPI" is discussed. The major advantages of blended education in studying a foreign language are analyzed. It is concluded that introduction of distance education may be very effective especially for adult learners.Розглядається досвід впровадження технологій E-learning в курс англійської мови для аспірантів в НТУ «ХПІ». Аналізуються основні переваги «змішаного» навчання при вивченні іноземної мови. Робиться висновок, що застосування дистанційної освіти може буди достатньо ефективним, особливо для дорослих студенті

The formation of medical workers subjectity in the patient care institution environment from a position of the eco-psychological approach

The process of the medical worker's subjectity development as the realization of the ability to be a subject of the optional activity in the shape of professional performance in the patient care institution environment is analyse