Evolution of unstable system.

Scenario of appearance and development of instability in problem of a flow around a solid sphere at rest is discussed. The scenario was created by solutions to the multimoment hydrodynamics equations, which were applied to investigate the unstable phenomena. These solutions allow interpreting Stokes flow, periodic pulsations of the recirculating zone in the wake behind the sphere, the phenomenon of vortex shedding observed experimentally. In accordance with the scenario, system loses its stability when entropy outflow through surface confining the system cannot be compensated by entropy produced within the system. The system does not find a new stable position after losing its stability, that is, the system remains further unstable. As Reynolds number grows, one unstable flow regime is replaced by another. The replacement is governed tendency of the system to discover fastest path to depart from the state of statistical equilibrium. This striving, however, does not lead the system to disintegration. Periodically, reverse solutions to the multimoment hydrodynamics equations change the nature of evolution and guide the unstable system in a highly unlikely direction. In case of unstable system, unlikely path meets the direction of approaching the state of statistical equilibrium. Such behavior of the system contradicts the scenario created by solutions to the classic hydrodynamics equations. Unstable solutions to the classic hydrodynamics equations are not fairly prolonged along time to interpret experiment. Stable solutions satisfactorily reproduce all observed stable medium states. As Reynolds number grows one stable solution is replaced by another. They are, however, incapable of reproducing any of unstable regimes recorded experimentally. In particular, stable solutions to the classic hydrodynamics equations cannot put anything in correspondence to any of observed vortex shedding modes. In accordance with our interpretation, the reason for this is the classic hydrodynamics equations themselves

N-derivatives of formaldimines: the reason for the high nitrogen inversion barriers in N-methyl- and N-chloroimines

The energy and electronic parameters of the nitrogen inversion in imines Н2С=NХНn (ХНn = СН3, NH2, OH, F, SiH3, PH2, SH, Cl) have been calculated with the DFT method (B3LYP 6-311+G(d,p)) in terms of natural bond orbital. It has been established that the interactions of the nitrogen lone pair (LP) with the bond orbitals at the imino carbon atom are practically independent of the X atom and contribute to the decrease of the inversion barriers (ΔЕі≠). While nN→σ*X–H, nN↔σX–H and nN↔nX interactions substantially depend on the heteroatom type and promote the increase in the ΔЕі≠ values with the rise in electronegativity of the X atom. The contribution of the interactions of the nitrogen LP with the Rydberg orbitals of the C=N–X group atoms is small and they cannot be the main reason of the decrease in the ΔЕі≠ values when X atoms of the second period are replaced by atoms of the third period of the same group. The interactions of the LP of the X atoms and the X–H bond orbitals with the C=N bond orbitals have the main influence on the inversion barriers. The contribution of nX→π*C=N interactions to the ΔЕі≠ values is dominant. The main reason of the “anomalous” inversion barriers of N-methyl- and Nchloroformaldimines is the destabilization of inversion transition states because of the reduction in the energies of σX–H →π*C=N and nX→π*C=N interactions and the rise in the energies of nN↔nСl interactions. The contributions of electronegativity of ХНn substituents and energies of intramolecular interactions to the ΔЕі≠ values have been determined

About Appearance of the Irreversibility

The inevitability of arising in equations of kinetics and hydrodynamics irreversibility not contained in original equations of classic mechanics is substantiated. It is established that transfer of information about the direction of system evolution from initial conditions to resulting equations is the consequence of losing information about the position of an individual particle in space, which takes place at roughening description. It is shown that the roughening with respect to impact parameters of colliding particles is responsible for appearance of the irreversibility in resulting equations. Direct equations of kinetics and hydrodynamics are the result of roughening distribution functions with respect to impact parameters of particles, which have not yet reached the domain of their interaction. The direct equations are valid for the progressive direction of timing on the time axis pointing from the past to the future. Reverse equations of kinetics and hydrodynamics are the result of roughening distribution functions with respect to impact parameters of particles, which have already left the domain of their interaction. The reverse equations are valid for the progressive direction of timing on the time axis pointing from the future to the past

The case for an EIC Theory Alliance: Theoretical Challenges of the EIC

44 pages, ReVTeX, White Paper on EIC Theory AllianceWe outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance