On the use of the scattering amplitude in coherent X-ray Bragg diffraction imaging

Lens-less imaging of crystals with coherent X-ray diffraction offers some unique possibilities for strain-field characterization. It relies on numerically retrieving the phase of the scattering amplitude from a crystal illuminated with coherent X-rays. In practice, the algorithms encode this amplitude as a discrete Fourier transform of an effective or Bragg electron density. This short article suggests a detailed route from the classical expression of the (continuous) scattering amplitude to this discrete function. The case of a heterogeneous incident field is specifically detailed. Six assumptions are listed and quantitatively discussed when no such analysis was found in the literature. Details are provided for two of them: the fact that the structure factor varies in the vicinity of the probed reciprocal lattice vector, and the polarization factor, which is heterogeneous along the measured diffraction patterns. With progress in X-ray sources, data acquisition and analysis, it is believed that some approximations will prove inappropriate in the near future.

Stocks drift and vortex instability of the potential surface wave

<p>It is shown that in the case of potential surface wave an exact solution of the equations of the nonlinear Lagragian’s dynamics of the fluid particle has the drift velocity as an eigenvalue. The fluid particle trajectory is a circular rotation around a center point moving with a constant drift velocity. The rotation frequency differs from the wave frequency by the Doppler’s shift caused by the drift velocity. The constant drift velocity, for the surface wave of small amplitude, coincides with the classical expression for the Stokes drift velocity.</p><p>It is also shown that in the cases with absence of the Stokes drift and with presence of the Stokes drift the vortex instability of a potential surface wave has the same futures. But the vortex temporal variability in the case of the Stokes drift is affected by the Doppler’s shift caused by the Stokes drift velocity. Hence it allows a conclusion that the vortex instability of a potential surface wave initiates turbulent mixing and Lengmure circulation in the ocean upper layer.      </p><p> </p>

Folklore as sublimation of «soul dialectic» in understanding the stranger («Hadji Murad» by L.N. Tolstoy)

In fact, in the works of L.N. Tolstoy has the best examples of the application of the "dialectic of the soul" to a person of a certain social origin ("Landowner's Morning"), a person of another sex (parting episode in "Anna Karenina"), even a horse ("Screen meter"). However, the understanding of a person of another religion, of another nationality ended up being perhaps the most difficult task. And even in Hadji Murad, the "dialectic of the soul" in its classical expression, when understanding a person, has no other ethnic-confessional culture. Using specific textual examples, we show the possibilities of the Caucasus folk system to describe the protagonist's inner world, understanding the basic meanings of his acts of life. Thus, "Hadji Murad" made a major breakthrough in the psychological portrait of a person of a different national, cultural and religious affiliation, which can hardly be compared to any work of other writers of the nineteenth century.

Folklore as sublimation of «soul dialectic» in understanding the stranger («Hadji Murad» by L.N. Tolstoy)

In fact, in the works of L.N. Tolstoy has the best examples of the application of the "dialectic of the soul" to a person of a certain social origin ("Landowner's Morning"), a person of another sex (parting episode in "Anna Karenina"), even a horse ("Screen meter"). However, the understanding of a person of another religion, of another nationality ended up being perhaps the most difficult task. And even in Hadji Murad, the "dialectic of the soul" in its classical expression, when understanding a person, has no other ethnic-confessional culture. Using specific textual examples, we show the possibilities of the Caucasus folk system to describe the protagonist's inner world, understanding the basic meanings of his acts of life. Thus, "Hadji Murad" made a major breakthrough in the psychological portrait of a person of a different national, cultural and religious affiliation, which can hardly be compared to any work of other writers of the nineteenth century.

On the Physical and Evolutionary Limits to the Rates of Enzyme-Catalyzed Reactions

An existing model for the rate coefficients of enzyme-catalyzed processes involves the regularized gamma function of Euler replacing the exponential dependence of the rate coefficient from the reaction barrier. The application of this model to experimental data, on one hand, validates the model by correctly describing the negative curvature of Eyring plots. On the other hand, this analysis evidences that enzymes never reach the maximum theoretical efficiency, a counterintuitive fact that requires an explanation. This work interprets this evolutionary limit in terms of the necessity of living systems to achieve and maintain homeostasis. Further validation of the expression for the rate coefficients comes from the analysis of the discrepancy between the theoretically predicted energy difference between reactants and products in a chemical equilibrium and the corresponding value obtained by regression to the classical expression for the equilibrium constant. The discrepancy is resolved by making use of the proposed model.

Gonadal, Not Maternal, Acquisition of Duplicated pax6 Orthologs in Megalobrama Amblycephala

: The highly conserved transcription factor Pax6 is involved in the development of the eyes, brain, and pancreas in vertebrates and invertebrates, whereas the additional expression pattern in other organs is still elusive. In this study, we cloned and characterized two pax6 homologs in blunt snout bream (Megalobrama amblycephala), named Mapax6a and Mapax6b. The protein alignment and phylogenetic tree showed that Mapax6a and Mapax6b were highly conserved compared with their counterparts in other species. Genomic information analysis revealed that the synteny conservation of Wilms tumor, Aniridia, genitourinary abnormalities, and mental retardation loci was also maintained in this species. By reverse transcription polymerase chain reaction, the expression of Mapax6a was later than that of Mapax6b which was found in the blastula stage, while the expression of Mapax6a started from the somite stage, and both of them persisted in a subsequent stage during the embryonic development. By RNA and protein detection, Mapax6a and Mapax6b were detected in the eye and brain as canonic patterns, and most importantly, they were also enriched in germ cells of the testis and ovary. Therefore, our findings validate the duplication of pax6 in fish, confirm the classical expression patterns in the brain and eye, and, for the first time, present a new acquisition of Mapax6a and Mapax6b in gonadal germ cells in particular. Therefore, our results enrich the expression pattern and evolutionary relationship of pax6 by suggesting that duplicated Mapax6 is involved in gametogenesis in Megalobrama amblycephala.

Photoconductivity Resonance Tunneling Spectroscopy of the Electron States in the InAs/GaAs Quantum Dot Heterostructures

The electric-field behavior of the resonance features in the photoelectric characteristics of InAs/GaAs heterostructures is studied. We discuss the emission mechanism of the charge carriers excited from InAs quantum dots into the GaAs matrix. It was shown that at the temperature of liquid nitrogen the photocurrent in a strong transverse electric field is only determined by the effect of electron tunneling through the barrier formed at the quantum-dot interfaces. Comparison of the experimental curves with the quasi-classical expression for the tunneling current component and analysis of the potential structure allowed us to specify some parameters of investigated heterostructures. Analysis of the electric-field dependences of the photocurrent-tunneling component revealed resonance peculiarities connected with the local defect states in the vicinity of InAs/GaAs interface.

The Casimir force between an ideal metal plate and a dissipative dielectric slab

In this research, a general formula for the Casimir force between ideal metal plate and a dissipative dielectric slab has been obtained. The dielectric function of the slab is assumed to be an arbitrary complex function of frequency satisfying Kramers–Kronig relations. A classical expression for the radiation pressure of the vacuum fields on the slab is presented by using the Maxwell stress tensor. With the transition to the quantum domain and using the fluctuation dissipation theorem and Kubo's formula, the resulting expression is written in terms of the imaginary part of the vector potential Green functions components of the system. Finally, by computing the Green function, the Casimir force on the slab is obtained. This formalism enables us to calculate the Casimir force without resorting to the explicit form of the field operators. The general expression is confirmed by limiting and comparing with one of the previous works.