Spatiotemporal Response of Crystals in X-ray Bragg Diffraction

The spatiotemporal response of crystals in x-ray Bragg diffraction resulting from excitation by an ultra-short, laterally confined x-ray pulse is studied theoretically. The theory presents an extension of the analysis in symmetric reflection geometry [1] to the generic case, which includes Bragg diffraction both in reflection (Bragg) and transmission (Laue) asymmetric scattering geometries. The spatiotemporal response is presented as a product of a crystal-intrinsic plane wave spatiotemporal response function and an envelope function defined by the crystal-independent transverse profile of the incident beam and the scattering geometry. The diffracted wavefields exhibit amplitude modulation perpendicular to the propagation direction due to both angular dispersion and the dispersion due to Bragg's law. The characteristic measure of the spatiotemporal response is expressed in terms of a few parameters: the extinction length, crystal thickness, Bragg angle, asymmetry angle, and the speed of light. Applications to self-seeding of hard x-ray free electron lasers are discussed, with particular emphasis on the relative advantages of using either the Bragg or Laue scattering geometries. Intensity front inclination in asymmetric diffraction can be used to make snapshots of ultra-fast processes with femtosecond resolution

Takagi-Taupin Description of X-ray Dynamical Diffraction from Diffractive Optics with Large Numerical Aperture

We present a formalism of x-ray dynamical diffraction from volume diffractive optics with large numerical aperture and high aspect ratio, in an analogy to the Takagi-Taupin equations for strained single crystals. We derive a set of basic equations for dynamical diffraction from volume diffractive optics, which enable us to study the focusing property of these optics with various grating profiles. We study volume diffractive optics that satisfy the Bragg condition to various degrees, namely flat, tilted and wedged geometries, and derive the curved geometries required for ultimate focusing. We show that the curved geometries satisfy the Bragg condition everywhere and phase requirement for point focusing, and effectively focus hard x-rays to a scale close to the wavelength.Comment: 18 pages, 12 figure

Spontaneous spin bifurcations and ferromagnetic phase transitions in a spinor exciton-polariton condensate

We observe a spontaneous parity breaking bifurcation to a ferromagnetic state in a spatially trapped exciton-polariton condensate. At a critical bifurcation density under nonresonant excitation, the whole condensate spontaneously magnetizes and randomly adopts one of two elliptically polarized (up to 95% circularly polarized) states with opposite handedness of polarization. The magnetized condensate remains stable for many seconds at 5 K, but at higher temperatures, it can flip from one magnetic orientation to another. We optically address these states and demonstrate the inversion of the magnetic state by resonantly injecting 100- fold weaker pulses of opposite spin. Theoretically, these phenomena can be well described as spontaneous symmetry breaking of the spin degree of freedom induced by different loss rates of the linear polarizations.Publisher PDFPeer reviewe

Theory and Applications of X-ray Standing Waves in Real Crystals

Theoretical aspects of x-ray standing wave method for investigation of the real structure of crystals are considered in this review paper. Starting from the general approach of the secondary radiation yield from deformed crystals this theory is applied to different concreat cases. Various models of deformed crystals like: bicrystal model, multilayer model, crystals with extended deformation field are considered in detailes. Peculiarities of x-ray standing wave behavior in different scattering geometries (Bragg, Laue) are analysed in detailes. New possibilities to solve the phase problem with x-ray standing wave method are discussed in the review. General theoretical approaches are illustrated with a big number of experimental results.Comment: 101 pages, 43 figures, 3 table

Olfactory Jump Reflex Habituation in Drosophila and Effects of Classical Conditioning Mutations

Habituation is a nonassociative learning mechanism, in which an initial response toward repeated stimuli gradually wanes. This is amongst the simplest and most widespread forms of behavioral plasticity. So far, neither the underlying molecular mechanisms nor the precise neural networks of habituation are well understood. We have developed a novel paradigm to quantify habituation of the olfactory jump reflex in Drosophila. We present data demonstrating several behavioral properties of this phenomenon, generally observed in other species. We also show that the dunce and rutabaga memory mutants behave abnormally in this assay, suggesting that this assay might be used in behavioral screens for new mutants with defects in this simpler form of behavioral plasticity

Національно-демократичні об'єднання та політичні партії в Україні кінця XIX - початку XX століття

Deep brain stimulation (DBS) has become increasingly important for the treatment and relief of neurological disorders such as Parkinson's disease, tremor, dystonia and psychiatric illness. As DBS implantations and any other stereotactic and functional surgical procedure require accurate, precise and safe targeting of the brain structure, the technical aids for preoperative planning, intervention and postoperative follow-up have become increasingly important. The aim of this paper was to give and overview, from a biomedical engineering perspective, of a typical implantation procedure and current supporting techniques. Furthermore, emerging technical aids not yet clinically established are presented. This includes the state-of-the-art of neuroimaging and navigation, patient-specific simulation of DBS electric field, optical methods for intracerebral guidance, movement pattern analysis, intraoperative data visualisation and trends related to new stimulation devices. As DBS surgery already today is an important technology intensive domain, an "intuitive visualisation" interface for improving management of these data in relation to surgery is suggested

Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations