Global well-posedness for a slightly supercritical surface quasi-geostrophic equation

We use a nonlocal maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velocity field $u$ is obtained from the active scalar $\theta$ by a Fourier multiplier with symbol $i k^\perp |k|^{-1} m(k|)$, where $m$ is a smooth increasing function that grows slower than $\log \log |k|$ as $|k|\rightarrow \infty$.Comment: 11 pages, second version with slightly stronger resul

Investigation of vibratory drilling model with adaptive control. Part 2: mixed control of peak-to-peak vibration displacement and cutting continuity index

Chip segmentation is important condition for deep drilling efficiency improving. Chip segmentation could be ensured by sustaining stable axial self-excited vibrations of a drill. Vibrations are excited by regenerative effect when cutting edges move along the surface formed by previous passes. The conditions required for reliable chip segmentation could be created by using of a special vibratory head with an elastic element, providing tool additional axial flexibility. To maintain stable vibro-process with amplitude sufficient for chip segmentation, it’s suggested to use the vibratory head with a special actuator for adaptive feedback control proportional to a tool vibration velocity. Two algorithms of the feedback gain adaptation are proposed in the present paper: the adaptation by peak-to-peak displacement and the mixed adaptation by peak-to-peak displacement with cutting continuity index. The investigation of effectiveness of the proposed algorithms applicable to the model, described in [9], is also presented

The working zone in the interpolar area of the Faraday balance: an approach to testing the magnetic force factor stability criterion

Due to rapid development of the scientific and applied research in magnetic control and magnetophoresis of ferro- and ferromagnetic disperse fraction of various technological, natural and industry-specific media, the Faraday method is again in high demand as it is mainly aimed at defining magnetic susceptibility of solid and heterogeneous samples of small volumes. Based on the appearing (and then measured) ponderomotive force impacting the sample, the method allows accurate determining of single particles magnetic susceptibility by using the data of the sample represented by a conglomerate of the particles of such a fraction. In addition, it is mentioned that to date there is still a great gap in the methodology of the Faraday method as there are no exact recommendations on choosing both the form of the polar pieces of the Faraday balance and the positioning of the sample (the location of the working zone) in the interpolar area. Owing to these drawbacks, the well-known and long-time used Faraday method cannot be considered substantiated to a satisfactory degree. Thus, in our point of view, the treatment of the results obtained earlier with the help of the method should be cautious. In our work, we experimentally defined and substantiated an approach to identifying a working (local) zone, viz. the zone with stable values of the magnetic force factor – the product of the field intensity and induction by its gradient. The approach features the relative phenomenological analysis and is exemplified by polar pieces of non-traditional spherical form. It has been demonstrated that in order to state the fact of mere existence of this zone (and its location) in the interpolar area, the coordinate (usually nonlinear one) characteristic of intensity or induction, which is obligatorily obtained in an experiment, should have an inflexion, which guarantees a functionally extreme view of the following coordinate characteristics both of the gradient and that of the force factor. We also established the coordinates and the length of the working zone in a specific interpolar area

Asymptotic analysis of operator families and applications to resonant media

We give an overview of operator-theoretic tools that have recently proved useful in the analysis of boundary-value and transmission problems for second-order partial differential equations, with a view to addressing, in particular, the asymptotic behaviour of resolvents of physically motivated parameter-dependent operator families. We demonstrate the links of this rich area, on the one hand, to functional frameworks developed by S. N. Naboko and his students, and on the other hand, to concrete applications of current interest in the physics and engineering communities.Comment: 60 pages, 2 figures; a survey of recent results in the area, see also arXiv:2010.13318, arXiv:1808.03961, arXiv:1703.06220, arXiv:1510.0336

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.Comment: 14 pages, 20 figures, revtex4, submitted to Combustion Theory and Modellin

Laser based synchrotron radiation

Beams of x rays in the kiloelectronvolt energy range have been produced from laser-matter interaction. Here, energetic electrons are accelerated by a laser wakefield, and experience betatron oscillations in an ion channel formed in the wake of the intense femtosecond laser pulse. Experiments using a 50 TW laser (30 fs duration) are described, as well as comparisons with numerical simulations. These results pave the way of a new generation of radiation in the x-ray spectral range, with a high collimation and an ultrafast pulse duration, produced by the use of compact laser system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87767/2/023101_1.pd

Telemedicine and international disaster response: Medical consultation to Armenia and Russia via a telemedicine spacebridge

The Telemedicine Spacebridge, a satellite mediated audio-video-fax link between four U.S. and two Armenian and Russian medical centers, permitted remote American consultants to assist Armenian and Russian physicians in the management of medical problems following the December 1988 earthquake in Armenia and the June 1989 gas explosion near Ufa. During 12 weeks of operations, 247 Armenian and Russian and 175 American medical professionals participated in 34 half-day clinical conferences. 209 patients were discussed, requiring expertise in 20 specialty areas. Telemedicine consultations resulted in altered diagnoses for 54, new diagnostic studies for 70, altered diagnostic processes for 47, and modified treatment plans for 47 of 185 Armenian patients presented. Simultaneous participation of several U.S. medical centers was judged beneficial; quality of data transmission was judged excellent. These results suggest that interactive consultation by remote specialists can provide valuable assistance to onsite physicians and favorably influence clinical decisions in the aftermath of major disasters