Heavy-ion conformal irradiation in the shallow-seated tumor therapy terminal at HIRFL

Basic research related to heavy-ion cancer therapy has been done at the Institute of Modern Physics (IMP), Chinese Academy of Sciences since 1995. Now a plan of clinical trial with heavy ions has been launched at IMP. First, superficially placed tumor treatment with heavy ions is expected in the therapy terminal at the Heavy Ion Research Facility in Lanzhou (HIRFL), where carbon ion beams with energy up to 100 MeV/u can be supplied. The shallow-seated tumor therapy terminal at HIRFL is equipped with a passive beam delivery system including two orthogonal dipole magnets, which continuously scan pencil beams laterally and generate a broad and uniform irradiation field, a motor-driven energy degrader and a multi-leaf collimator. Two different types of range modulator, ripple filter and ridge filter with which Guassian-shaped physical dose and uniform biological effective dose Bragg peaks can be shaped for therapeutic ion beams respectively, have been designed and manufactured. Therefore, two-dimensional and three-dimensional conformal irradiations to tumors can be performed with the passive beam delivery system at the earlier therapy terminal. Both the conformal irradiation methods have been verified experimentally and carbon-ion conformal irradiations to patients with superficially placed tumors have been carried out at HIRFL since November 2006.

Conformal irradiation to moving targets in heavy ion radiotherapy with raster-scanning beam delivery system: (II) feasibility experiments

Within the framework of the pilot heavy-ion therapy facility at GSI equipped with an active beam delivery system of advanced raster scanning technique, a feasibility study on actively conformal heavy-ion irradiation to moving tumors has been experimentally conducted. Laterally, real-time corrections to the beam scanning parameters by the raster scanner, leading to an active beam tracing, compensate for the lateral motion of a target volume. Longitudinally, a mechanically driven wedge energy degrader (called depth scanner) is applied to adjust the beam energy so as to locate the high-dose Bragg peak of heavy ion beam to the slice under treatment for the moving target volume. It has been experimentally shown that compensations for lateral target motion by the raster scanner and longitudinal target shift by the depth scanner are feasible.

Non-relativistic conformal symmetries in fluid mechanics

The symmetries of a free incompressible fluid span the Galilei group, augmented with independent dilations of space and time. When the fluid is compressible, the symmetry is enlarged to the expanded Schrodinger group, which also involves, in addition, Schrodinger expansions. While incompressible fluid dynamics can be derived as an appropriate non-relativistic limit of a conformally invariant relativistic theory, the recently discussed conformal Galilei group, obtained by contraction from the relativistic conformal group, is not a symmetry. This is explained by the subtleties of the non-relativistic limit.

Estimation of individual phases from the four-phase structure invariants in the single isomorphous replacement case

The probability distribution of the four-phase invariants in the case of single isomorphous replacement has been developed to estimate some individual phases. An example of its application to obtain the phases having special values of 0, pi or +/-pi /2 is given for a known protein structure in space group P2(1)2(1)2(1). The phasing procedure includes the determination of starting phases and an iterative calculation. The initial values of starting phases, which are required by the formula, can be obtained from the estimate of one-phase seminvariants and by specifying the origin and enantiomorph. In addition, the calculations lead to two sets of possible phases for each type of reflection by assigning arbitrarily an initial phase value. The present method provides a possibility for the multisolution technique to increase greatly the number of known phases while keeping the number of the trials quite small.

Probability distribution of the four-phase structure invariants of isomorphously related structure factors and its applications

The probability distribution of the four-phase structure invariants (4PSIs) involving four pairs of structure factors is derived by integrating the direct methods with isomorphous replacement (IR). A simple expression of the reliability parameter for 16 types of invariant is given in the case of a native protein and a heavy-atom derivative. Test calculations on a protein and its heavy-atom derivative using experimental diffraction data show that the reliability for 4PSI estimates is comparable with that for the three-phase structure invariants (3PSIs), and that a large-modulus invariants method can be used to improve the accuracy.

General expression for probabilistic estimation of multiphase structure invariants in the case of a native protein and multiple derivatives. Application to estimates of the three-phase structure invariants

Concise probabilistic formulae with definite crystallographic implications are obtained from the distribution for eight three-phase structure invariants (3PSIs) in the case of a native protein and a heavy-atom derivative [Hauptman (1982). Acta Cryst. A38, 289-294] and from the distribution for 27 3PSIs in the case of a native and two derivatives [Fortier, Weeks & Hauptman (1984). Acta Cryst. A40, 646-651]. The main results of the probabilistic formulae for the four-phase structure invariants are presented and compared with those for the 3PSIs. The analysis directly leads to a general formula of probabilistic estimation for the n-phase structure invariants in the case of a native and m derivatives. The factors affecting the estimated accuracy of the 3PSIs are examined using the diffraction data from a moderate-sized protein. A method to estimate a set of the large-modulus invariants, each corresponding to one of the eight 3PSIs, that has the largest \Delta\ values and relatively large structure-factor moduli between the native and derivative is suggested, which remarkably improves the accuracy, and thus a phasing procedure making full use of all eight 3PSIs is proposed.

Singularity characteristics for a lip-shaped crack subjected to remote biaxial loading

In this paper, the conformal mapping method was adopted to solve the problem of an infinite plate containing a central lip-shaped crack subjected to remote biaxial loading. A kind of leaf-shaped configuration was also constructed in order to solve the problem. The analytical result showed that the singularity order of the stress field at the tip of a lip-shaped crack remains -1/2, despite the difference in notch-crack width.

Anisotropic thermopiezoelectric solids with an elliptic inclusion or a hole under uniform heat flow

The two-dimensional problem of a thermopiezoelectric material containing an elliptic inclusion or a hole subjected to a remote uniform heat flow is studied. Based on the extended Lekhnitskii formulation for thermopiezoelectricity, conformal mapping and Laurent series expansion, the explicit and closed-form solutions are obtained both inside and outside the inclusion (or hole). For a hole problem, the exact electric boundary conditions on the hole surface are used. The results show that the electroelastic fields inside the inclusion or the electric field inside the hole are linear functions of the coordinates. When the elliptic hole degenerates into a slit crack, the electroelastic fields and the intensity factors are obtained. The effect of the heat how direction and the dielectric constant of air inside the crack on the thermal electroelastic fields are discussed. Comparison is made with two special cases of which the closed solutions exist and it is shown that our results are valid.

Closed form solutions of T-stress in plane elasticity crack problems

The T-stress is considered as an important parameter in linear elastic fracture mechanics. In this paper, several closed form solutions of T-stress in plane elasticity crack problems in an infinite plate are investigated using the complex potential theory. In the line crack case, if the applied loading is the remote stress or the concentrated forces, the T-stress can be derived from the basic field. Here, the basic field is defined as the field caused by the applied loading in the infinite plate without the crack. For the circular are crack, the T-stress can be abstracted from a known solution. For the cusp crack problems, the T-stress can be separated from the obtained stress solution for which the conformal mapping technique is used.

A Cip/Multi-Moment Finite Volume Method For Shallow Water Equations With Source Terms

A novel finite volume method has been presented to solve the shallow water equations. In addition to the volume-integrated average (VIA) for each mesh cell, the surface-integrated average (SIA) is also treated as the model variable and is independently predicted. The numerical reconstruction is conducted based on both the VIA and the SIA. Different approaches are used to update VIA and SIA separately. The SIA is updated by a semi-Lagrangian scheme in terms of the Riemann invariants of the shallow water equations, while the VIA is computed by a flux-based finite volume formulation and is thus exactly conserved. Numerical oscillation can be effectively avoided through the use of a non-oscillatory interpolation function. The numerical formulations for both SIA and VIA moments maintain exactly the balance between the fluxes and the source terms. 1D and 2D numerical formulations are validated with numerical experiments. Copyright (c) 2007 John Wiley & Sons, Ltd.

Complex stress functions and plastic zone sizes for notch cracks subjected to various loading conditions

In this paper, the conformal mapping method is used to solve the plane problem of an infinite plate containing a central lip-shaped notch subjected to biaxial loading at a remote boundary or a surface uniform pressure on the notch. The stress intensity factors KI and KII are obtained by the derived complex stress functions. The simple analytical expressions can be applied to the situation of cracks originating from a circular or an elliptical notch. The plastic zone sizes for such notch cracks are subsequently evaluated in light of the Dugdale strip yield concept. The results are consistent with available numerical data.

Lithography-independent and large scale fabrication of a metal electrode nanogap

A lithography-independent and wafer scale method to fabricate a metal nanogap structure is demon-strated. Polysilicon was first dry etched using photoresist (PR) as the etch mask patterned by photolithography.Then, by depositing conformal SiO_2 on the polysilicon pattern, etching back SiO_2 anisotropically in the perpendic-ular direction and removing the polysilicon with KOH, a sacrificial SiO_2 spacer was obtained. Finally, after metal evaporation and lifting-off of the SiO_2 spacer, an 82 nm metal-gap structure was achieved. The size of the nanogap is not determined by the photolithography, but by the thickness of the SiO_2. The method reported in this paper is compatible with modern semiconductor technology and can be used in mass production.