New Approach to Nonlinear Dynamics of Fullerenes and Fullerites

New type of nonlinear (anharmonic) excitations -- bushes of vibrational modes -- in physical systems with point or space symmetry are discussed. All infrared active and Raman active bushes for C60 fulerene are found by means of special group-theoretical methods.Comment: LaTeX, 8 pages, to be published in Fizika Tverdogo Tela, 200

Properties of discrete breathers in graphane from ab initio simulations

A density functional theory (DFT) study of the discrete breathers (DBs) in graphane (fully hydrogenated graphene) was performed. To the best of our knowledge, this is the first demonstration of the existence of DBs in a crystalline body from the first-principle simulations. It is found that the DB is a robust, highly localized vibrational mode with one hydrogen atom oscillating with a large amplitude along the direction normal to the graphane plane with all neighboring atoms having much smaller vibration amplitudes. DB frequency decreases with increase in its amplitude, and it can take any value within the phonon gap and can even enter the low-frequency phonon band. The concept of DB is then used to propose an explanation to the recent experimental results on the nontrivial kinetics of graphane dehydrogenation at elevated temperatures.Comment: 20.07.14 Submitted to PhysRev

Stability analysis of dynamical regimes in nonlinear systems with discrete symmetries

We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This theorem suggests a decomposition of the linearized system arising in the standard stability analysis into a number of subsystems whose dimensions can be considerably less than that of the full system. As an example of such simplification, we discuss the stability of bushes of modes (invariant manifolds) for the Fermi-Pasta-Ulam chains and prove another theorem about the maximal dimension of the above mentioned subsystems

Meteorological winter conditions in the Central Arctic according to the drifting stations “North Pole 35-40”

The effect of clouds, wind speed and long-wave radiative balance on the surface and near-surface air temperature in the Arctic during polar night is presented. The most pronounced bimodality in frequency distributions of the cloud fraction corresponding to cloudy and clear-sky situations is found for the stations NP-35 (2007-2008), NP-37 (2009-2010) and NP-38 (2010-2011). A strong impact of the presence or absence of clouds on the air-surface temperature difference is shown. For clear-sky situations nonmonotonic dependency of near-surface air temperature on wind speed is found

Stability of Nonlinear Normal Modes in the FPU-β\beta Chain in the Thermodynamic Limit

All possible symmetry-determined nonlinear normal modes (also called by simple periodic orbits, one-mode solutions etc.) in both hard and soft Fermi-Pasta-Ulam-$\beta$ chains are discussed. A general method for studying their stability in the thermodynamic limit, as well as its application for each of the above nonlinear normal modes are presented

Turbulent structure of the Arctic boundary layer in early summer driven by stability, wind shear and cloud-top radiative cooling: ACLOUD airborne observations

Clouds are assumed to play an important role in the Arctic amplification process. This motivated a detailed investigation of cloud processes, including radiative and turbulent fluxes. Data from the aircraft campaign ACLOUD were analyzed with a focus on the mean and turbulent structure of the cloudy boundary layer over the Fram Strait marginal sea ice zone in late spring and early summer 2017. Vertical profiles of turbulence moments are presented from contrasting atmospheric boundary layers (ABLs) from 4 d. They differ by the magnitude of wind speed, boundary-layer height, stability, the strength of the cloud-top radiative cooling and the number of cloud layers. Turbulence statistics up to third-order moments are presented, which were obtained from horizontal-level flights and from slanted profiles. It is shown that both of these flight patterns complement each other and form a data set that resolves the vertical structure of the ABL turbulence well. The comparison of the 4 d shows that especially during weak wind, even in shallow Arctic ABLs with mixing ratios below 3 g kg−1, cloud-top cooling can serve as a main source of turbulent kinetic energy (TKE). Well-mixed ABLs are generated where TKE is increased and vertical velocity variance shows pronounced maxima in the cloud layer. Negative vertical velocity skewness points then to upside-down convection. Turbulent heat fluxes are directed upward in the cloud layer as a result of cold downdrafts. In two cases with single-layer stratocumulus, turbulent transport of heat flux and of temperature variance are both negative in the cloud layer, suggesting an important role of large eddies. In contrast, in a case with weak cloud-top cooling, these quantities are positive in the ABL due to the heating from the surface. Based on observations and results of a mixed-layer model it is shown that the maxima of turbulent fluxes are, however, smaller than the jump of the net terrestrial radiation flux across the upper part of a cloud due to the (i) shallowness of the mixed layer and (ii) the presence of a downward entrainment heat flux. The mixed-layer model also shows that the buoyancy production of TKE is substantially smaller in stratocumulus over the Arctic sea ice compared to subtropics due to a smaller surface moisture flux and smaller decrease in specific humidity (or even humidity inversions) right above the cloud top. In a case of strong wind, wind shear shapes the ABL turbulent structure, especially over rough sea ice, despite the presence of a strong cloud-top cooling. In the presence of mid-level clouds, cloud-top radiative cooling and thus also TKE in the lowermost cloud layer are strongly reduced, and the ABL turbulent structure becomes governed by stability, i.e., by the surface–air temperature difference and wind speed. A comparison of slightly unstable and weakly stable cases shows a strong reduction of TKE due to increased stability even though the absolute value of wind speed was similar. In summary, the presented study documents vertical profiles of the ABL turbulence with a high resolution in a wide range of conditions. It can serve as a basis for turbulence closure evaluation and process studies in Arctic clouds.</p

Discrete Symmetry and Stability in Hamiltonian Dynamics

In this tutorial we address the existence and stability of periodic and quasiperiodic orbits in N degree of freedom Hamiltonian systems and their connection with discrete symmetries. Of primary importance in our study are the nonlinear normal modes (NNMs), i.e periodic solutions which represent continuations of the system's linear normal modes in the nonlinear regime. We examine the existence of such solutions and discuss different methods for constructing them and studying their stability under fixed and periodic boundary conditions. In the periodic case, we employ group theoretical concepts to identify a special type of NNMs called one-dimensional "bushes". We describe how to use linear combinations such NNMs to construct s(>1)-dimensional bushes of quasiperiodic orbits, for a wide variety of Hamiltonian systems and exploit the symmetries of the linearized equations to simplify the study of their destabilization. Applying this theory to the Fermi Pasta Ulam (FPU) chain, we review a number of interesting results, which have appeared in the recent literature. We then turn to an analytical and numerical construction of quasiperiodic orbits, which does not depend on the symmetries or boundary conditions. We demonstrate that the well-known "paradox" of FPU recurrences may be explained in terms of the exponential localization of the energies Eq of NNM's excited at the low part of the frequency spectrum, i.e. q=1,2,3,.... Thus, we show that the stability of these low-dimensional manifolds called q-tori is related to the persistence or FPU recurrences at low energies. Finally, we discuss a novel approach to the stability of orbits of conservative systems, the GALIk, k=2,...,2N, by means of which one can determine accurately and efficiently the destabilization of q-tori, leading to the breakdown of recurrences and the equipartition of energy, at high values of the total energy E.Comment: 50 pages, 13 figure