Whitham method for Benjamin-Ono-Burgers equation and dispersive shocks in internal waves in deep fluid

The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of damped Benjamin-Ono equation. The structure of the dispersive shock in internal wave in deep water is considered by this method.Comment: 8 pages, 4 figure

Influence of the focused ion beam parameters on the etching of planar nanosized multigraphene/SiC field emitters

The equipment of the Collective Usage Center “Nanotechnologies” and the Research and Educational Center "Nanotechnologies" of Southern Federal University was used for this study. This work was funded by Internal grant of Southern Federal University No. VnGr-07/2017-26

Whitham systems and deformations

We consider the deformations of Whitham systems including the "dispersion terms" and having the form of Dubrovin-Zhang deformations of Frobenius manifolds. The procedure is connected with B.A. Dubrovin problem of deformations of Frobenius manifolds corresponding to the Whitham systems of integrable hierarchies. Under some non-degeneracy requirements we suggest a general scheme of the deformation of the hyperbolic Whitham systems using the initial non-linear system. The general form of the deformed Whitham system coincides with the form of the "low-dispersion" asymptotic expansions used by B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius manifolds.Comment: 27 pages, Late

Analytic model for a frictional shallow-water undular bore

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by friction. This is derived in Riemann variables using a modified finite-gap integration technique for the AKNS scheme. The Whitham system is then reduced to a simple first-order differential equation which is integrated numerically to obtain an asymptotic profile of the undular bore, with the local oscillatory structure described by the periodic solution of the unperturbed Kaup-Boussinesq system. This solution of the Whitham equations is shown to be consistent with certain jump conditions following directly from conservation laws for the original system. A comparison is made with the recently studied dissipationless case for the same system, where the undular bore is unsteady.Comment: 24 page

Unsteady undular bores in fully nonlinear shallow-water theory

We consider unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the leading-order fully nonlinear dispersive terms. This system contains one horizontal space dimension and time and can be systematically derived from the full Euler equations for irrotational flows with a free surface using a standard long-wave asymptotic expansion. In this context the system was first derived by Su and Gardner. It coincides with the one-dimensional flat-bottom reduction of the Green-Naghdi system and, additionally, has recently found a number of fluid dynamics applications other than the present context of shallow-water gravity waves. We then use the Whitham modulation theory for a one-phase periodic travelling wave to obtain an asymptotic analytical description of an undular bore in the Su-Gardner system for a full range of "depth" ratios across the bore. The positions of the leading and trailing edges of the undular bore and the amplitude of the leading solitary wave of the bore are found as functions of this "depth ratio". The formation of a partial undular bore with a rapidly-varying finite-amplitude trailing wave front is predicted for ``depth ratios'' across the bore exceeding 1.43. The analytical results from the modulation theory are shown to be in excellent agreement with full numerical solutions for the development of an undular bore in the Su-Gardner system.Comment: Revised version accepted for publication in Phys. Fluids, 51 pages, 9 figure

Results of the first tests of the Sidra satellite-borne instrument breadboard model

In this work, the results of the calibration of the solid-state detectors and electronic channels of the SIDRA satelliteborne energetic charged particle spectrometer-telescope breadboard model are presented. The block schemes and experimental equipment used to conduct the thermal vacuum and electromagnetic compatibility tests of the assemblies and modules of the compact satellite equipment are described. The results of the measured thermal conditions of operation of the signal analog and digital processing critical modules of the SIDRA instrument prototype are discussed. Finally, the levels of conducted interference generated by the instrument model in the primary vehicle-borne power circuits are presented.Представлено результати градуювання твердотiльних детекторiв i електронних каналiв лабораторного макету супутникового спектрометру-телескопу енергiйних заряджених частинок SIDRA. Описуються блок-схеми i експериментальне обладнання для здiйснення тепловакуумних випробувань вузлiв i модулiв компактної супутникової апаратури та для проведення випробувань наукових приладiв на електромагнiтну сумiснiсть. Обговорюються результати вимiряних теплових режимiв роботи критичних вузлiв модулiв аналогової i цифрової обробки сигналiв прототипу приладу SIDRA. Нарештi, представленi рiвнi кондуктивних завад, що створює макет приладу в ланцюгах первинного бортового живлення.Представлены результаты градуировки твердотельных детекторов и электронных каналов лабораторного макета спутникового спектрометра-телескопа знергичных заряженных частиц SIDRA. Описываются блок-схемы и экспериментальное оборудование для проведения тепловакуумных испытаний узлов и модулей компактной спутниковой аппаратуры и для осуществления испытаний научных приборов на электромагнитную совместимость. Обсуждаются результаты измеренных тепловых режимов работы критических узлов модулей аналоговой и цифровой обработок сигналов прототипа прибора SIDRA. Наконец, представлены уровни кондуктивных помех, создаваемых макетом прибора в цепях первичного бортового питания

Excimer formation by steric twisting in carbazole and triphenylamine-based host materials

This paper presents a detailed spectroscopic investigation of luminescence properties of 4,4′-Bis(N-carbazolyl)-1,1′-biphenyl (CBP) and N,N,N’,N’-tetraphenylbenzidine (TAD) in solutions and neat films. These compounds are compared to their derivatives CDBP and TDAD that contain methyl groups in the 2 and 2’ position of the biphenyl core. We find that whereas steric twisting in CDBP and TDAD leads to a high triplet energy of about 3.0 and 3.1 eV, respectively, these compounds also tend to form triplet excimers in a neat film, in contrast to CBP and TAD. By comparison with N-phenylcarbazole (NPC) and triphenylamine (TPA), on which these compounds are based, as well as with the rigid spiro analogs to CBP and TAD we show that the reduced excimer formation in CBP and TAD can be attributed to a localization of the excitation onto the central biphenyl part of the molecule.We acknowledge support from the Federal Ministry of Education and Research (BMBF) through the project ‘Trip-Q’, the German Science Foundation (DFG) through the Research and Training Group GRK 1640 and the UK Engineering and Physical Sciences Research Council (grant number EP/G060738/1).This is the final published version. It first appeared at http://pubs.acs.org/doi/abs/10.1021/jp512772j