Similarity analytical solutions for the Schrӧdinger equation with the Riesz fractional derivative in quantum mechanics

The present article deals with the similarity method to tackle the fractional Schrӧdinger equation where the derivative is defined in the Riesz sense. Moreover, the procedure of reducing a fractional partial differential equation (FPDE) into an ordinary differential equation (ODE) has been efficiently displayed by means of suitable scaled transform to the proposed fractional equation. Furthermore, the ODEs are treated effectively via the Fourier transform. The graphical solutions are also depicted for different fractional derivatives α .     

J/ψ gluonic dissociation revisited: III. Effects of transverse hydrodynamic flow

In a recent paper [B.K. Patra, V.J. Menon, Eur. Phys. J. C 44, 567 (2005)] we developed a very general formulation to take into account explicitly the effects of the hydrodynamic flow profile on the gluonic breakup of J/ψs produced in an equilibrating quark–gluon plasma. Here we apply that formulation to the case when the medium is undergoing a cylindrically symmetric transverse expansion starting from RHIC or LHC initial conditions. Our algebraic and numerical estimates demonstrate that the transverse expansion causes enhancement of the local gluon number density n_g, affects the p_T-dependence of the average dissociation rate through a partial-wave interference mechanism and makes the survival probability S(p_T) to change with p_T very slowly. Compared to the previous case of a longitudinal expansion the new graph of S(p_T) is pushed up at LHC but develops a rich structure at RHIC, due to a competition between the transverse catch-up time and the plasma lifetime.PACS 12.38.Mh     

Crystal plasticity-based constitutive modelling of irradiated bcc structures

A constitutive crystal plasticity model is proposed and developed for the inelastic deformation of irradiated bcc ferritic/martensitic steels. Defects found in these irradiated materials are used as substructure variables in the model. Insights from lower length- and time-scale simulations are used to frame the kinematic and substructure evolution relations of the governing deformation mechanisms. Models for evolution of mobile and immobile dislocations, as well as interstitial loops (formed due to irradiation), are developed. A rate theory-based approach is used to model the evolution of point defects generated during irradiation. The model is used to simulate the quasi-static tensile and creep response of a martensitic steel over a range of loading histories.     

Crystal plasticity modeling of irradiation growth in Zircaloy-2

Abstract

A physically based reaction-diffusion model is implemented in the visco-plastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. The reaction-diffusion model accounts for the defects produced by the cascade of displaced atoms, their diffusion to lattice sinks and the contribution to crystallographic strain at the level of single crystals. The VPSC framework accounts for intergranular interactions and irradiation creep, and calculates the strain in the polycrystalline ensemble. A novel scheme is proposed to model the simultaneous evolution of both, number density and radius, of irradiation-induced dislocation loops directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behaviour of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture and external stress on the coupled irradiation growth and creep behaviour are also studied and compared with available experimental data.     

Maximizing the distance between center,centroid and characteristic set of a tree

Consider a tree P_n-g,g , n≥ 2, 1≤ g≤ n-1 on n vertices which is obtained from a path on [1,2,?…?,n-g] vertices by adding g pendant vertices to the pendant vertex n-g. We prove that over all trees on n?≥?5 vertices, the distance between center and characteristic set, centroid and characteristic set, and center and centroid is maximized by trees of the form P_n-g,g , 2?≤?g?≤?n-3. For n≥ 5, we also supply the precise location of the characteristic set of the tree P_n-g,g , 2?≤?g?≤?n-3.     

Photochemical Conjugation and One‐Pot Radiolabelling of Antibodies for Immuno‐PET

Monoclonal antibodies (mAbs), immunoglobulin fragments, and other proteins are important scaffolds in the development of radiopharmaceuticals for diagnostic immuno‐positron emission tomography (immuno‐PET) and targeted radioimmunotherapy (RIT). Conventional methods for radiolabelling proteins with metal ions such as ⁶⁸Ga, ⁶⁴Cu, ⁸⁹Zr, and ⁹⁰Y require multi‐step procedures involving pre‐purification, functionalisation with a chelate, and subsequent radiolabelling. Standard coupling chemistries are time‐consuming, difficult to automate, and involve synthesis, isolation, and storage of an intermediate, new molecular entity (the conjugated mAb) whose biochemical properties can differ from those of the parent protein. To circumvent these issues, we developed a photoradiochemical approach that uses fast, chemoselective, light‐induced protein modification under mild conditions with novel metal‐ion‐binding chelates derivatised with aryl azide (ArN₃) groups. Experiments show that one‐pot photochemical conjugation and radiolabelling of formulated mAbs can be achieved in <20 min.     

Room-Temperature Synthesis of Germanium Oxide Nanofilaments and Their Potential Use as Luminescent Self-Cleaning Surfaces

Germanium oxide nanofilaments (GNFs) have been synthesized under ambient conditions from the gas phase using germanium tetrachloride as a precursor. Non-crystalline GNFs synthesized by this procedure are 1–10 μm in length and 80–110 nm in diameter applying Droplet Assisted Growth and Shaping (DAGS) Chemistry. The relative humidity has been adjusted at various values in order to demonstrate the crucial role of humidity in the gas phase for the nanofilament synthesis. The novel GNFs show a strong luminescence emission in the ultra-violet and light blue region. In addition, a self-cleaning and superhydrophobic properties could be introduced in the luminescent GNF nanofilaments by simple treatment with silane molecules.     

Poly(3,4-ethylenedioxyselenophene)

The first highly conductive polyselenophene, namely, poly(3,4-ethylenedioxyselenophene) (PEDOS), was synthesized by taking advantage of a novel method for efficiently contracting the selenophene ring. PEDOS shows a relatively low band gap (1.4 eV), very high stability in the oxidized state, and a well-defined spectroelectrochemistry.     

Potential of mean force calculations of ligand binding to ion channels from Jarzynski's equality and umbrella sampling

Potential of mean force (PMF) calculations provide a reliable method for determination of the absolute binding free energies for protein-ligand systems. The common method used for this purpose -- umbrella sampling with weighted histogram analysis -- is computationally very laborious, which limits its applications. Recently, a much simpler alternative for PMF calculations has become available, namely, using Jarzynski's equality in steered molecular dynamics simulations. So far, there have been a few comparisons of the two methods and mostly in simple systems that do not reflect the complexities of protein-ligand systems. Here, we use both methods to calculate the PMF for ion permeation and ligand binding to ion channels. Comparison of results indicate that Jarzynski's method suffers from relaxation problems in complex systems and would require much longer simulation times to yield reliable PMFs for protein-ligand systems.