Die-swell,splashing drop and a numerical technique for solving the Oldroyd B model for axisymmetric free surface flows

This work deals with the development of a numerical method for simulating viscoelastic axisymmetric free surface flow of an Oldroyd B fluid. A novel formulation is developed for the computation of the non-Newtonian extra-stress components on rigid boundaries and on the symmetry axis. The full free surface stress conditions are employed. The resulting governing equations are solved by finite differences on a Marker-and-cell (MAC) type grid. Validation is provided by simulating a pipe flow problem. The classical die-swell problem is solved and swelling ratios are provided. The height of the splash caused by a falling liquid drop for various Reynolds and Weissenberg numbers is then studied, and the height of the splash is shown to diminish with increasing viscoelasticity.     

On the Riemann–Hilbert problem of the matrix Lakshmanan–Porsezian–Daniel system with a $$4\times4$$ AKNS-type matrix Lax pair

Theoretical and Mathematical Physics - The initial-boundary value problems for the matrix Lakshmanan–Porsezian–Daniel system are studied by utilizing the Fokas unified transform...     

An efficient access to both enantiomers of pipecolic acid

An efficient and convenient synthesis of both enantiomers of pipecolic acid has been developed using the intramolecular cyclization of 2-amino-6-bromohexanoic acid under mild conditions.     

Singularity solutions for ellipsoids in low-Reynolds-number flows: With applications to the calculation of hydrodynamic interactions in suspensions of ellipsoids

The disturbance velocity fields due to translational and rotational motions of an ellipsoid in a uniform stream. constant vorticity and constant rate-of-strain. required in fundamental studies of behavior of suspensions. have been obtained by the singularity method. These solutions extend earlier solutions for prolate spheroids. Although equivalent solutions problems were obtained by Oberbeck. Edwardes and Jeffery by separation of variables in ellipsoidal coordinates. the singularity solutions are far more simple in form. Other significant results obtained by the singularity method include the exposition of the unified structure shared by the three boundary value problems and the construction of new forms of the Faxen laws for ellipsoids through application of the reciprocal theorem. The disturbance solutions and Faxen laws. the basis for Smoluchowski's method-of-reflections technique. are used to calculate hydrodynamic interactions between two or more arbitrarily oriented ellipsoids. In particular. mobility problems are solved directly to orderR⁻⁵. whereR is the centroid-to-centroid separation between the ellipsoids.     

Low dispersion finite volume scheme based on reconstruction with minimized dispersion and controllable dissipation

The reconstruction with minimized dispersion and controllable dissipation(MDCD) optimizes dispersion and dissipation separately and shows desirable properties of both dispersion and dissipation.A low dispersion finite volume scheme based on MDCD reconstruction is proposed which is capable of handling flow discontinuities and resolving a broad range of length scales.Although the proposed scheme is formally second order accurate,the optimized dispersion and dissipation make it very accurate and robust so that the rich flow features encountered in practical engineering applications can be handled properly.A number of test cases are computed to verify the performances of the proposed scheme.     

Tensor force effect on proton shell structure in neutron-rich Ca isotopes

In the framework of the Skyrme-Hartree-Fock approach with 36 sets of the TI J parameterizations,the tensor force effect on the evolution of the single-proton states in the calcium isotopes is systematically investigated.It is shown that the single-proton states with higher angular momenta are influenced significantly by the tensor force and the trend in the evolution of somesingle-particle energy differences with the mass number of the isotopes depends sensitively on a parameter βT associated with the intensity of the tensor force.To understand this phenomenon,we analyze the spin-orbit potentials and the radial wave functions of relevant single-proton orbits in detail.In addition,it is found that some TI J interactions could cause the 2s1/21d3/2 energy level inversion in 48Ca.     

Application of wavelet transform in-ray spectra analysis

The frequency distribution of different ingredients in-ray spectra,e.g.,photo-peak,fluctuations of counts and Compton region,is separately analyzed.After wavelet transform of-ray spectra,the wavelet coefficients of a photo-peak increase with transforming scales and these coefficients show direct proportion with intensity of peak at determinate scale.A novel algorithm based on wavelet transform is proposed and studied.The results indicate that most of the photo-peaks in multi-spectra can be determined accurately,the-rays energy and intensity of the peak can also be determined.This method has the prospect of being applied in on-line multi-spectra analysis in such fields as radioprotection and nuclear safety monitoring.     

Reaction rate theory for supramolecular kinetics: application to protein aggregation

ABSTRACT

Probing reaction mechanisms of supramolecular processes in soft and biological matter, such as protein aggregation, is inherently challenging. This is because these processes involve multiple molecular mechanisms that are associated with the rearrangement of large numbers of weak bonds, resulting in complex free energy landscapes with many kinetic barriers. Reaction rate measurements at different temperatures can offer unprecedented insights into the underlying molecular mechanisms. However, to be able to interpret such measurements, a key challenge is to establish which properties of the complex free energy landscapes are probed by the reaction rate. Here, we present a reaction rate theory for supramolecular kinetics based on Kramers theory of diffusive reactions over multiple kinetic barriers. We find that reaction rates for protein aggregation are of the Arrhenius–Eyring type and that the associated activation energies probe only one relevant barrier along the respective free energy landscapes. We apply this advancement to interpret, in experiments and in coarse-grained computer simulations, reaction rates of amyloid aggregation in terms of molecular mechanisms and associated thermodynamic signatures. These results suggest a practical extension of the concept of rate-determining steps for complex supramolecular processes and establish a general platform for probing the underlying energy landscape using kinetic measurements.