Primitive Inner Illuminating Systems for Convex Bodies

A set X of boundary points of a (possibly unbounded) convex body KE ^d illuminating K from within is called primitive if no proper subset of X still illuminates K from within. We prove that for such a primitive set X of an unbounded, convex set KE ^d (distinct from a cone) one has X=2 if d=2, X6 if d=3, and that there is no upper bound for X if d4.     

Many body effects in the electronic and optical properties of the (1 1 1) surface of diamond

The (1 1 1) face is the cleavage surface of diamond. Understanding its properties is very important for the growing technological interest on the chemistry of diamond surfaces. Within DFT the most stable reconstruction is the Pandey chain model, the atoms on the chain being neither buckled nor dimerised. However this geometry gives rise to a semi metallic band structure in contrast with experimental findings that show the presence of a gap ranging from 0.5 to 2 eV. Here we show that the same equilibrium geometry and thus the same metallic band structure is found relaxing the surface using screened exchange (sX) or Hartree-Fock (HF) functionals. We will discuss in detail how breaking the equivalence of the atoms on the chain affects the band structure and we will show that a buckling would yield a semiconducting surface, but is energetically unfavorable. A semiconducting character can be restored, within the equilibrium geometry, if quasiparticle corrections are carefully included within an iterative GW scheme. The result of the theoretical reflectance anisotropy spectra (RAS) at a DFT-RPA level are also presented and discussed. As expected, a strong anisotropy signal is found at low energies due to transitions between surface states inside the fundamental gap.     

Simulation of two‐phase flow–body interaction problems using direct forcing/fictitious domain–level set method

In the present paper, a direct forcing/fictitious domain (DF/FD)–level set method is proposed to simulate the twophase flow–body interaction. The DF/FD does not sacrifice accuracy and robustness by employing a discrete δ (Dirac delta) function to transfer quantities between the Eulerian nodes and Lagrangian points explicitly as the immersed boundary method. The advantages of this approach are the simple concept, the easy implementation and the utilization of original governing equation without modification. The main idea is to combine DF/FD method with the level set method in the Cartesian coordinates. We present the results of a number of test cases to illustrate the effectiveness of the proposed method for single‐phase flow–body interaction problem and the two‐phase flows with a stationary body. Eventually, the simulations of various water entry problems have been conducted to validate the capability and the accuracy of the present method on solving the twophase flow–body interaction. Consequently, the present results are found to be in good agreement with those of previous studies. Copyright © 2013 John Wiley & Sons, Ltd.     

Design of an Optimal Grid for Finite Element Methods

ABSTRACT Finite element solutions of improved quality are obtained by optimizing the location of nodes of the finite element grid, while keeping the number of degrees of freedom fixed. The formulation of the grid optimization problem is based on the reduction of error associated with interpolation of the exact solution, using functions from the finite element space. Element sizes are selected as design variables: length in R1 and area in R2. Analytically derived optimality conditions are presented and an approximation to these conditions is introduced to obtain a set of operationally useful equations that can be used as guidelines for construction of improved grids. Example problems are given for illustration.     

ON MEAN CURVATURES OF A PARALLEL CONVEX BODY

In this article, we obtain some results about the mean curvature integrals of the parallel body of a convex set in R^n. These mean curvature integrals are generalizations of the Santalo＇s results.     

Adsorptive refolding of a highly disulfide-bonded inclusion body protein using anion-exchange chromatography

α-Fetoprotein (AFP) is a prospective biopharmaceutical candidate currently undergoing advanced-stage clinical trials for autoimmune indications. The high AFP expression yields in the form of inclusion bodies in Escherichia coli renders the inclusion body route potentially advantageous for process scale commercial manufacture, if high-throughput refolding can be achieved. This study reports the successful development of an ‘anion-exchange chromatography’-based refolding process for recombinant human AFP (rhAFP), which carries the challenges of contaminant spectrum and molecule complexity. rhAFP was readily refolded on-column at rhAFP concentrations unachievable with dilution refolding due to viscosity and solubility constraints. DEAE-FF functioned as a refolding enhancer to achieve rhAFP refolding yield of 28% and product purity of 95% in 3 h, at 1 mg/ml protein refolding concentration. Optimization of both refolding and chromatography column operation parameters (i.e. resin chemistry, column geometry, redox potential and feed conditioning) significantly improved rhAFP refolding efficiency. Compared to dilution refolding, on-column rhAFP refolding productivity was 9-fold higher, while that of off-column refolding was more than an order of magnitude higher. Successful demonstration that a simple anion-exchange column can, in a single step, readily refold and purify semi-crude rhAFP comprising 16 disulfide bonds, will certainly extend the application of column refolding to a myriad of complex industrial inclusion body proteins.     

Periodic orbits around the collinear libration points in the restricted three body problem when the smaller primary is a triaxial rigid body and bigger primary is a source of radiation pressure

Periodic orbits belonging to the stromgren families A, B and C around the collinear libration points in the restricted three body problem have been studied when the smaller primary is a triaxial rigid body and more massive body is a source of radiation pressure. These families are determined in three different cases: (i) classical case, (ii) when bigger primary is a source of radiation pressure, (iii) when smaller primary is a triaxial rigid body and bigger primary is a source of radiation pressure. The Liapunov stability of each periodic solution has also been examined.      

Radiation dose measurements for staff members involved in holmium-166 preclinical trial

AimNeutron-activated holmium-166 (¹⁶⁶Ho) is an excellent radionuclide for internal radiation therapy (Eβmax = 1.84 MeV) with an appropriate half-life (26.8 h), which emits photons (81 keV, 6.2%) suitable to be detected by gamma cameras. Preparing and injecting radiopharmaceuticals containing beta/gamma emitting holmium-166 implies a risk of exceeding the upper limit for skin and hand radiation equivalent doses (500 mSv/an). This study was aimed to estimate the whole body and finger exposure for staff responsible for dose preparation, dose dispensing, and dose injection of holmium-166 therapy.MethodsTo measure the finger dose from external exposure, all staff members wore TLD dosimeters. Personal dose equivalents Hp(10) were measured using electronic personal dosimeters (EPD MK2, Thermo Fischer Scientific) placed on the left side of the chest. During our study, staff members administered more than 40 ¹⁶⁶Ho-based therapies for preclinical trial. Appropriate radiation safety procedures and shielding were applied at each stage.ResultsIn this study, the whole body doses were 2.80 ± 1.56 nSv MBq⁻¹ for one ¹⁶⁶Ho-therapy preparation/formulation, and 2.68 ± 1.70 nSv MBq⁻¹ for one intravenous injection. Maximum finger doses were 2.9 ± 0.2 μSv MBq⁻¹ and 2.5 ± 0.3 μSv MBq⁻¹ for preparation and injection, respectively (activities injected: 72 ± 3 MBq).ConclusionExtrapolated annual doses from 300 ¹⁶⁶Ho radionuclide therapies were lower than the annual limit doses for skin and the whole body, 500 mSv and 20 mSv, respectively, reported in the European Directive EURATOM 96/29 when applying appropriate radiation protection standards. However, these doses have to be added to other diagnostic or therapeutic protocols, performed in preclinical facilities.     

Incompressible SPH simulation of water entry of a free‐falling object

In this paper an incompressible smoothed particle hydrodynamics (Incom‐SPH) model is used to simulate the interactions between the free surface flow and a moving object. Incom‐SPH method is a two‐step semi‐implicit hydrodynamic formulation of the SPH algorithm and is capable of accurately treating the free surface deformations and impact forces during the solid–fluid interactions. For a free‐falling object, its motion is tracked by an additional Lagrangian algorithm based on Newton's law to couple with the Incom‐SPH program. The developed model is employed to investigate the water entry of a free‐falling wedge. The accuracy of the computations is validated by the good agreement in predicting the relevant hydrokinematic and hydrodynamic parameters. Finally, a numerical test is performed to study the influence of spatial resolution on the water entry features. The Incom‐SPH modeling coupled with the solid–fluid interaction algorithm could provide a promising computational tool to predict the slamming problems in coastal and offshore engineering. Copyright © 2008 John Wiley & Sons, Ltd.