Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem

The quasi-geostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimensional inequivalent subalgebras of the maximal Lie invariance algebra is constructed. On the basis of these subalgebras we exhaustively carry out group-invariant reduction and compute various classes of exact solutions. Where possible, reference to the physical meaning of the exact solutions is given. In particular, the well-known baroclinic Rossby wave solutions in the two-layer model are rediscovered.Comment: Extended version, 24 pages, 1 figur

Lie reduction and exact solutions of vorticity equation on rotating sphere

Following our paper [J. Math. Phys. 50 (2009) 123102], we systematically carry out Lie symmetry analysis for the barotropic vorticity equation on the rotating sphere. All finite-dimensional subalgebras of the corresponding maximal Lie invariance algebra, which is infinite-dimensional, are classified. Appropriate subalgebras are then used to exhaustively determine Lie reductions of the equation under consideration. The relevance of the constructed exact solutions for the description of real-world physical processes is discussed. It is shown that the results of the above paper are directly related to the results of the recent letter by N. H. Ibragimov and R. N. Ibragimov [Phys. Lett. A 375 (2011) 3858] in which Lie symmetries and some exact solutions of the nonlinear Euler equations for an atmospheric layer in spherical geometry were determined.Comment: 10 pages, 1 figure, minor corrections and extension

Safety and Immunogenicity of Combined DNA-Polyethylenimine and Oral Bacterial Idiotypic Vaccine for Patients with B-Cell Non-Hodgkin Lymphoma: A Pilot Study

We report, in brief, the results of a phase I, non-randomized study of idiotypic DNA vaccination in patients with B-cell non-Hodgkin's lymphoma (ISRCTN31090206). The DNA sequence of lymphoma-derived immunoglobulin variable regions was used as a tumor-specific antigen fused to the potato virus X coat protein. A conjugate of plasmid DNA with polyethylenimine was used for the intramuscular injections, followed by a boost with an oral live-attenuated Salmonella vaccine carrying the same plasmid. The patients with a complete or partial response to previous chemotherapy received one or two courses of vaccination, including four injections at monthly intervals. The vaccine was well tolerated, with low-grade adverse events. The T-cell immune responses were assessed by ELISpot, at last vaccine, one week and one month post-vaccination, and were detected in 11/14 (78.6%) of the patients. In cases of progression requiring chemotherapy, or the presence of a positive MRD after the first course of vaccination, the patients underwent a second course of vaccination. At the end point, 6/19 vaccinated patients had disease stabilization, while 13/19 were in complete remission. The overall survival was 100% at follow-up, of a median of 2.3 years

American Gut: an Open Platform for Citizen Science Microbiome Research

McDonald D, Hyde E, Debelius JW, et al. American Gut: an Open Platform for Citizen Science Microbiome Research. mSystems. 2018;3(3):e00031-18

Group analysis of the generalized Burnett equations

In this paper group properties of the so-called Generalized Burnett equations are studied. In contrast to the clas-sical Burnett equations these equations are well-posed and therefore can be used in applications. We considerthe one-dimensional version of the generalized Burnett equations for Maxwell molecules in both Eulerian andLagrangian coordinates and perform the complete group analysis of these equations. In particular, this includesfinding and analyzing admitted Lie groups. Our classifications of the Lie symmetries of the Navier-Stokes equa-tions of compressible gas and generalized Burnett equations provide a basis for finding invariant solutions ofthese equations. We also consider representations of all invariant solutions. Some particular classes of invariantsolutions are studied in more detail by both analytical and numerical method

Self-Assembly of Molecular Brushes with Polyimide Backbone and Amphiphilic Block Copolymer Side Chains in Selective Solvents

Three-component molecular brushes with a polyimide backbone and amphiphilic block copolymer side chains with different contents of the “inner” hydrophilic (poly(methacrylic acid)) and “outer” hydrophobic (poly(methyl methacrylate)) blocks were synthesized and characterized by molecular hydrodynamics and optics methods in solutions of chloroform, dimethylformamide, tetrahydrofuran and ethanol. The peculiarity of the studied polymers is the amphiphilic structure of the grafted chains. The molar masses of the molecular brushes were determined by static and dynamic light scattering in chloroform in which polymers form molecularly disperse solutions. Spontaneous self-assembly of macromolecules was detected in dimethylformamide, tetrahydrofuran and ethanol. The aggregates size depended on the thermodynamic quality of the solvent as well as on the macromolecular architectural parameters. In dimethylformamide and tetrahydrofuran, the distribution of hydrodynamic radii of aggregates was bimodal, while in ethanol, it was unimodal. Moreover, in ethanol, an increase in the poly(methyl methacrylate) content caused a decrease in the hydrodynamic radius of aggregates. A significant difference in the nature of the blocks included in the brushes determines the selectivity of the used solvents, since their thermodynamic quality with respect to the blocks is different. The macromolecules of the studied graft copolymers tend to self-organization in selective solvents with formation of a core–shell structure with an insoluble solvophobic core surrounded by the solvophilic shell of side chains

Combined Acoustic Emission and Digital Image Correlation for Early Detection and Measurement of Fatigue Cracks in Rails and Train Parts under Dynamic Loading

Fatigue crack in rails and cyclic-loaded train parts is a contributory factor in multiple railroad accidents. We address the problem of crack detection and measurement at early stages, when total failure has not yet occurred. We propose to combine acoustic emission (AE) testing for prediction of crack growth with digital image correlation (DIC) for its accurate quantitative characterization. In this study, we imitated fatigue crack appearance and growth in samples of railway rail and two train parts by cyclic loading, and applied these two techniques for inspection. Experimental results clearly indicate the efficiency of AE in the early detection of fatigue cracks, and excellent DIC capabilities in terms of geometrical measurements. Combination of these techniques reveals a promising basis for real-time and non-destructive monitoring of rails and train parts

Molecular Brushes with a Polyimide Backbone and Poly(ε-Caprolactone) Side Chains by the Combination of ATRP, ROP, and CuAAC

An approach to the synthesis of the novel molecular brushes with a polyimide (PI) backbone and poly(ε-caprolactone) (PCL) side chains was developed. To obtain such copolymers, a combination of various synthesis methods was used, including polycondensation, atom transfer radical polymerization (ATRP), ring opening polymerization (ROP), and Cu (I)-catalyzed azide-alkyne Huisgen cycloaddition (CuAAC). ATRP of 2-hydroxyethyl methacrylate (HEMA) on PI macroinitiator followed by ROP of ε-caprolactone (CL) provided a “brush on brush” structure PI-g-(PHEMA-g-PCL). For the synthesis of PI-g-PCL two synthetic routes combining ROP and CuAAC were compared: (1) polymer-analogous transformations of a multicenter PI macroinitiator with an initiating hydroxyl group separated from the main chain by a triazole ring followed by ROP of CL, or (2) a separate synthesis of macromonomers with the desirable functional groups (polyimide with azide groups and PCL with terminal alkyne groups), followed by a click reaction. Results showed that the first approach allows to obtain graft copolymers with a PI backbone and relatively short PCL side chains. While the implementation of the second approach leads to a more significant increase in the molecular weight, but unreacted linear PCL remains in the system. Obtained macroinitiators and copolymers were characterized using 1H NMR and IR spectroscopy, their molecular weight characteristics were determined by SEC with triple detection. TGA and DSC were used to determine their thermal properties. X-ray scattering data showed that the introduction of a polyimide block into the polycaprolactone matrix did not change the degree of crystallinity of PCL

Isolation of an escape-resistant SARS-CoV-2 neutralizing nanobody from a novel synthetic nanobody library

The COVID−19 pandemic not only resulted in a global crisis, but also accelerated vaccine development and antibody discovery. Herein we report a synthetic humanized VHH library development pipeline for nanomolar-range affinity VHH binders to SARS-CoV-2 variants of concern (VoC) receptor binding domains (RBD) isolation. Trinucleotide-based randomization of CDRs by Kunkel mutagenesis with the subsequent rolling-cycle amplification resulted in more than 1011 diverse phage display library in a manageable for a single person number of electroporation reactions. We identified a number of nanomolar-range affinity VHH binders to SARS-CoV-2 variants of concern (VoC) receptor binding domains (RBD) by screening a novel synthetic humanized antibody library. In order to explore the most robust and fast method for affinity improvement, we performed affinity maturation by CDR1 and CDR2 shuffling and avidity engineering by multivalent trimeric VHH fusion protein construction. As a result, H7-Fc and G12x3-Fc binders were developed with the affinities in nM and pM range respectively. Importantly, these affinities are weakly influenced by most of SARS-CoV-2 VoC mutations and they retain moderate binding to BA.4\5. The plaque reduction neutralization test (PRNT) resulted in IC50 = 100 ng\ml and 9.6 ng\ml for H7-Fc and G12x3-Fc antibodies, respectively, for the emerging Omicron BA.1 variant. Therefore, these VHH could expand the present landscape of SARS-CoV-2 neutralization binders with the therapeutic potential for present and future SARS-CoV-2 variants