Local Impurity Phase Pinning and Pinning Force in Charge Density Waves

Starting from the static Fukuyama-Lee-Rice equation for a three-dimensional incommensurate charge density wave (CDW) in quasi one-dimensional conductors a solvable model for local phase pinning by impurities is defined and studied. We find that average CDW energy and average pinning force show critical behaviour with respect to the pinning parameter $h$. Specifically the pinning force exhibits a threshold at $h=1$ with exponent $\beta=2$. Our model examplifies a general concept of local impurity pinning in which the force exerted by the impurity on the periodic CDW structure becomes multivalued and metastable states appear beyond a threshold. It is found that local impurity pinning becomes less effective at low temperatures and may eventually cease completely. These results are independent of spatial dimensionality as expected for local impurity pinning. Comparison with Larkin's model is also made.Comment: Latex, 16 pages, 3 figure

Global Well-posedness of Strong Solutions to the 3D Primitive Equations with Horizontal Eddy Diffusivity

In this paper, we consider the initial-boundary value problem of the 3D primitive equations for oceanic and atmospheric dynamics with only horizontal diffusion in the temperature equation. Global well-posedness of strong solutions are established with $H^2$ initial data.Comment: arXiv admin note: substantial text overlap with arXiv:1312.603

Linear response and collective oscillations in superconductors with d-wave pairing

Simple and physically transparent equations for the linear response of layered superconductors with d-wave symmetry of the order parameter are derived by means of the quasiclassic kinetic theory of superconductivity. Responses to solenoidal and potential electric fields have different frequency dependencies. The conductivity describing the response to the solenoidal field is limited by the momentum relaxation, like in a normal metal. The response to the potential electric field depends, in addition, on the branch imbalance relaxation rate. The damping of plasma oscillations of superconducting electrons is determined by dielectric relaxation and is small. Relaxation of branch imbalance determined by elastic scattering is large enough to make the Carlson-Goldman mode in d-wave superconductors overdamped.Comment: 11 pages, latex, no figures, submitted to Physical Review

Intrinsic Josephson Effect and Violation of the Josephson Relation in Layered Superconductors

Equations describing the resistive state of a layered superconductor with anisotropic pairing are derived. The similarity with a stack of Josephson junctions is found at small voltages only, when current density in the direction perpendicular to the layers can be interpreted as a sum of the Josephson superconducting, the Ohmic dissipative and the interference currents. In the spatially uniform state differential conductivity at higher voltages becomes negative. Nonuniformity of the current distribution generates the branch imbalance and violates the Josephson relation between frequency and voltage.Comment: 11 pages, no figures, revtex, to be published in Phys. Rev. Let

Threshold electric field in unconventional density waves

As it is well known most of charge density wave (CDW) and spin density wave (SDW) exhibit the nonlinear transport with well defined threshold electric field E_T. Here we study theoretically the threshold electric field of unconventional density waves. We find that the threshold field increases monotonically with temperature without divergent behaviour at T_c, unlike the one in conventional CDW. The present result in the 3D weak pinning limit appears to describe rather well the threshold electric field observed recently in the low-temperature phase (LTP) of alpha-(BEDT-TTF)_2KHg(SCN)_4.Comment: 4 pages, 2 figure

Abstract P-5: Neural Network Approaches to Classify 3D Protein Structures from the Data of X-ray Laser Radiation Diffraction from Single Particles

Background: Protein structure determination using X-ray free-electron laser (XFEL) includes analysis and merging a large number of snapshot diffraction patterns. Convolutional neural networks are widely used to solve numerous computer vision problems, e.g. image classification, and can be used for diffraction pattern analysis. But the task of protein structure determination with the use of CNNs only is not yet solved. Methods: We simulated the diffraction patterns using the Condor software library and obtained more than 1000 diffraction patterns for each structure with simulation parameters resembling real ones. To classify diffraction patterns, we tried two approaches, which are widely known in the area of image classification: a classic VGG network and residual networks. Results: 1. Recognition of a protein class (GPCRs vs globins). Globins and GPCR-like proteins are typical α-helical proteins. Each of these protein families has a large number of representatives (including those with known structure) but we used only 8 structures from every family. 12,000 of diffraction patterns were used for training and 4,000 patterns for testing. Results indicate that all considered networks are able to recognize the protein family type with high accuracy. 2. Recognition of the number of protein molecules in the liposome. We considered the usage of lyposomes as carriers of membrane or globular proteins for sample delivery in XFEL experiments in order to improve the X-ray beam hit rate. Three sets of diffractograms for liposomes of various radius were calculated, including diffractograms for empty liposomes, liposomes loaded with 5 bacteriorhodopsin molecules, and liposomes loaded with 10 bacteriorhodopsin molecules. The training set consisted of 23625 diffraction patterns, and test set of 7875 patterns. We found that all networks used in our study were able to identify the number of protein molecules in liposomes independent of the liposome radius. Our findings make this approach rather promising for the usage of liposomes as protein carriers in XFEL experiments. Conclusion: Thus, the performed numerical experiments show that the use of neural network algorithms for the recognition of diffraction images from single macromolecular particles makes it possible to determine changes in the structure at the angstrom scale