Conventionalism and general relativity

We argue that the geometry of spacetime is a convention that can be freely chosen by the scientist; no experiment can ever determine this geometry of spacetime, only the behavior of matter in space and time. General relativity is then rewritten in terms of an arbitrary conventional geometry of spacetime in which particle trajectories are determined by forces in that geometry, and the forces determined by fields produced by sources in that geometry. As an example, we consider radial trajectories in the field of a single particle expressed in the spacetime of special relativity.     

Generalized Kähler Geometry

Generalized Kähler geometry is the natural analogue of Kähler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We prove that generalized Kähler geometry is equivalent to the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2, 2) supersymmetry. We also prove the existence of natural holomorphic Courant algebroids for each of the underlying complex structures, and that these split into a sum of transverse holomorphic Dirac structures. Finally, we explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kähler geometry.     

锥束CT系统旋转平移轨迹几何参数标定方法

针对锥束CT系统旋转平移（RT）轨迹中几何参数难以直接测量的问题,在单圆轨迹标定方法的基础上,提出了一种适用于RT轨迹的几何参数标定方法。该方法利用定标体模投影轨迹的椭圆参数与系统几何参数建立关系,解析求解出系统的内部参数。在此基础上,外推得到旋转轴所有的位置参数,并求得符合理想轨迹要求的几何参数。所求参数都可以通过解析的公式得到,能有效避免迭代法陷入局部最优的问题。对存在偏差的系统进行了仿真,并利用该方法进行标定,实验结果表明,该方法能有效抑制由于几何参数误差造成的几何伪影,提高图像质量。     

Weyl geometry as a particle geometry

It is shown that a stress-tensor which is a curvature source for a Weyl geometry most contain an antisymmetric component. Otherwise the Weyl geometry is equivalent to a Riemannian geometry via a gauge transformation.     

Synthetic Braided Geometry II

Braided geometry is a natural generalization of supergeometry and is intimately connected with noncommutative geometry. Synthetic differential geometry is a peppy dissident in the stale regime of orthodox differential geometry, just as Grothendieck's category-theoretic revolution in algebraic geometry was in the middle of the 20th century. Our previous paper [Nishimura (1998) International Journal of Theoretical Physics, 37, 2833–2849] was a gambit of our ambitious plan to approach braided geometry from a synthetic viewpoint and to concoct what is supposedly to be called synthetic braided geometry. As its sequel this paper is intended to give a synthetic treatment of braided connections, in which the second Bianchi identity is established. Considerations are confined to the case that the braided monoidal category at issue is a category of vector spaces graded by a finite Abelian group with its nonsymmetric braiding being given by phase factors. Thus the present paper encompasses physical systems amenable to anyonic statistics.     

Logical quantization of differential geometry

In a previous paper we saw that Grothendieck's functorial approach to algebraic geometry and algebraic groups in particular is in consonance with our framework of logical quantization. This paper, as a sequel, consolidates the consonance between functorial geometry and logical quantization by demonstrating that Moerdijk and Reyes' functorial approach to differential geometry can be adequately poised within logical quantization.     

Influence of geometry model approximations on Geant4 simulation results of the Columbus/ISS radiation environment

The influence of geometry model approximations on Geant4 Monte Carlo simulation results of the radiation environment on-board the Columbus module of the International Space Station (ISS) has been investigated. Three geometry models of Columbus with different levels of detail and a geometry model of ISS have been developed. These geometries have been used for Geant4 simulations of the radiation environment inside Columbus induced by trapped protons and Galactic Cosmic Ray protons. Simulated dose rates and particle spectra on-board Columbus for each of the three Columbus models, with or without the ISS geometry model included, are presented and compared.From comparisons of simulated dose rates and particle spectra for the three different geometry models it was found that the most detailed geometry model (750 volumes) produced results similar to a much less detailed model (23 volumes). The most detailed geometry model was concluded to be a sufficiently detailed approximation of the physical Columbus for the purpose of proton induced space radiation studies. The simulated dose rates are compatible with measurements on-board the ISS. The simulation results also show that an increase in shielding thickness decreases the simulated dose rate induced by trapped protons. For Galactic Cosmic Ray protons the dose rate remains unchanged or is slightly increased.     

Semi-Teleparallel Theories of Gravitation

A class of theories of gravitation that naturally incorporates preferred frames of reference is presented. The underlying space-time geometry consists of a partial parallelization of space-time and has properties of Riemann—Cartan as well as teleparallel geometry. Within this geometry, the kinematic quantities of preferred frames are associated with torsion fields. Using a variational method, it is shown in which way action functionals for this geometry can be constructed. For a special action the field equations are derived and the coupling to spinor fields is discussed.     

Odd symplectic geometry types on supermanifolds

Generalization of symplectic geometry on manifolds in a supersymmetric case is examined in the present work. In the even case, this leads either to even symplectic geometry, that is, the geometry on supermanifolds with the nondegenerate Poisson bracket, or to the geometry on the Fedosov even supermanifolds. In the odd case, two different scalar symplectic structures exist (namely, the odd closed differential 2-form and antibracket), which can be used to construct various symplectic geometry types on supermanifolds. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 52–57, February, 2008.     

Symmetries, Quantum Geometry, and the Fundamental Interactions

A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making these relations dynamical implies the nonlocal effect of the fundamental interactions on the wave function, as in the Aharonov–Bohm effect and its generalizations to non-Abelian gauge fields and gravity. The usual space–time geometry is obtained as the classical limit of this quantum geometry using the quantum-state space metric.     

Characterization of PSD of activated carbons by using slit and triangular pore geometries

A mixed geometry model for activated carbons, representing the porous space as a collection of an undetermined proportion of slit and triangular pores, is developed, evaluated theoretically and applied to the characterization of a controlled series of samples of activated carbon obtained from the same precursor material. A method is proposed for the determination of the Pore Size Distribution (PSD) for such a mixed geometry model, leading to the unique determination of the proportion of pores of the two geometries fitting adsorption data. By using the Grand Canonical Monte Carlo (GCMC) simulation method in the continuum space, families of N2 adsorption isotherms are generated both for slit and triangular geometry corresponding to different pore sizes. The problem of the uniqueness in the determination of the PSD by fitting an adsorption isotherm using the mixed geometry model is then discussed and the effects of the addition of triangular pores on the PSD are analyzed by performing a test where the adsorption isotherm corresponding to the known PSD is generated and used as the “experimental” isotherm. It is found that a pure slit geometry model would widen the PSD and shift it to smaller sizes, whereas a pure triangular geometry model would produce the opposite effect. The slit and triangular geometry families of isotherms are finally used to the fit experimental N₂ adsorption data corresponding to a family of activated carbons obtained from coconut shells through a one-step chemical activation process with phosphoric acid in air, allowing for the determination of the micropore volume, the proportion of slit and triangular pores and the PSD corresponding to the mixed geometry. The same experimental data were fit using both the conventional slit pore model and the mixed geometry model. From the analysis of the effect of different preparation procedures on the resulting PSDs, it is concluded that the proposed mixed geometry model may probably better capture the morphology and energetics of activated carbons prepared by chemical activation under mild temperatures.     

90°全息记录衍射效率分析与提高

对光折变全息记录特别是双中心全息记录中90°记录结构下较低的衍射效率进行了研究,采用局域衍射理论对90°记录结构的衍射进行了分析,表明在同样的折射率变化和2 mm的光束宽度的情况下,只有当折射率光栅振幅大于10^-4时,90°记录结构衍射效率才能够与小角度透射记录结构的衍射效率大致相当。针对环境干扰导致的干涉条纹振动影响光栅记录,提出了有效调制度概念,根据分析90°记录结构的干涉条纹间距很小,容易受外界环境干扰而导致低的折射率变化率,因此应采用主动条纹锁定系统。此外在双中心全息记录中,微观光学参量的优化对衍射效率影响也很重要。     

Geometry of quadrilateral nets: Second Hamiltonian form

Discrete Darboux–Manakov–Zakharov systems possess two distinct Hamiltonian forms (by this term we mean that equations of motion are discrete time extensions of Hamiltonian equations of motion). In the framework of discrete-differential geometry one Hamiltonian form appears in a geometry of a circular net. In this paper a geometry of the second form is identified.     

Spectral photosensitivity of an organic semiconductor in a submicron metal grating

The photoelectric effect in films of the copper phthalocyanine organic semiconductor (α-CuPc) has been experimentally studied for two fundamentally different geometries. A sample in the first, normal geometry is fabricated in the form of a sandwich with an α-CuPc film between a transparent SnO₂ electrode on a substrate and an upper reflecting Al electrode. In the second case of the planar geometry, the semiconductor is deposited on the substrate with a system of submicron chromium interdigital electrodes. It has been found that the effective photoconductivity in the planar geometry is more than two orders of magnitude higher than that in the normal geometry. In addition to the classical model (without excitons), a simple exciton model has been proposed within which a relation has been obtained between the probability of the formation of electron–hole pairs and the characteristic recombination and dissociation times of excitons. An increase in the photoconductivity in the planar geometry has been explained within the exciton model by an increase in the rate of dissociation of excitons into electron–hole pairs owing to acceptor oxygen molecules, which diffuse more efficiently into the film in the case of the planar geometry where the upper electrode is absent.     

Differentiating the shape of stellarator coils with respect to the plasma boundary

The task of designing the geometry of a set of current-carrying coils that produce the magnetic field required to confine a given plasma equilibrium in stellarators is expressed as a minimization principle, namely that the coils minimize a suitably defined error expressed as a surface integral, which is recognized as the quadratic-flux. A penalty on the coil length is included to avoid pathological solutions. A simple expression for how the quadratic-flux and coil length vary as the coil geometry varies is derived, and an expression describing how this varies with variations in the surface geometry is derived. These expressions allow efficient coil-design algorithms to be implemented, and also enable efficient algorithms for varying the shape of the plasma surface in order to simplify the coil geometry, and a numerical illustration of this is given.