A unified model for the dynamics of driven ribbon with strain and magnetic order parameters

We develop a unified model to explain the dynamics of driven one dimensional ribbon for materials with strain and magnetic order parameters. We show that the model equations in their most general form explain several results on driven magnetostrictive metallic glass ribbons such as the period doubling route to chaos as a function of a dc magnetic field in the presence of a sinusoidal field, the quasiperiodic route to chaos as a function of the sinusoidal field for a fixed dc field, and induced and suppressed chaos in the presence of an additional low amplitude near resonant sinusoidal field. We also investigate the influence of a low amplitude near resonant field on the period doubling route. The model equations also exhibit symmetry restoring crisis with an exponent close to unity. The model can be adopted to explain certain results on magnetoelastic beam and martensitic ribbon under sinusoidal driving conditions. In the latter case, we find interesting dynamics of a periodic one orbit switching between two equivalent wells as a function of an ac magnetic field that eventually makes a direct transition to chaos under resonant driving condition. The model is also applicable to magnetomartensites and materials with two order parameters.Comment: 11 pages, 18 figure

Projecting Low Dimensional Chaos from Spatio-temporal Dynamics in a Model for Plastic Instability

We investigate the possibility of projecting low dimensional chaos from spatiotemporal dynamics of a model for a kind of plastic instability observed under constant strain rate deformation conditions. We first discuss the relationship between the spatiotemporal patterns of the model reflected in the nature of dislocation bands and the nature of stress serrations. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatiotemporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands.Comment: 9 pages, 19 figure

Elko under spatial rotations

Under a rotation by an angle $\vartheta$, both the right- and left- handed Weyl spinors pick up a phase factor ${\exp(\pm\, i \vartheta/2)}$. The upper sign holds for the positive helicity spinors, while the lower sign for the negative helicity spinors. For $\vartheta = 2\pi$ radians this produces the famous minus sign. However, the four-component spinors are built from a direct sum of the indicated two-component spinors. The effect of the rotation by $2\pi$ radians on the eigenspinors of the parity - that is, the Dirac spinors -- is the same as on Weyl spinors. It is because for these spinors the right- and left- transforming components have the same helicity. And the rotation induced phases, being same, factor out. But for the eigenspinors of the charge conjugation operator, i.e. Elko, the left- and right- transforming components have opposite helicities, and therefore they pick up opposite phases. As a consequence the behaviour of the eigenspinors of the charge conjugation operator (Elko) is more subtle: for $0<\vartheta<2\pi$ a self conjugate spinor becomes a linear combination of the self and antiself conjugate spinors with $\vartheta$ dependent superposition coefficients - and yet the rotation preserves the self/antiself conjugacy of these spinors! This apparently paradoxical situation is fully resolved. This new effect, to the best of our knowledge, has never been reported before. The purpose of this communication is to present this result and to correct an interpretational error of a previous version.Comment: 7 pages, Two new sections, and significantly new material. An error in v1 and v2 correcte

安全かつ持続可能な管理のための廃棄物安定型最終処分場の力学特性及び溶出特性の評価

京都大学0048新制・課程博士博士(地球環境学)甲第22815号地環博第202号新制||地環||39(附属図書館)京都大学大学院地球環境学舎地球環境学専攻(主査)教授 勝見 武, 教授 木村 亮, 准教授 高井 敦史学位規則第4条第1項該当Doctor of Global Environmental StudiesKyoto UniversityDFA

Design and performance evaluation of a low concentrating line-axis dielectric photovoltaic system

This thesis presents a detailed investigation of the design optimisation and performance analysis of a dielectric concentrator for building façade integration at high latitudes (>55°). Considering the seasonal variation of the sun’s position at these latitudes, a concentrating photovoltaic (CPV) system with stationary concentrators of large acceptance angle and low concentration ratio is a suitable alternative to conventional flat plate photovoltaic (PV) modules. A well designed dielectric asymmetric compound parabolic concentrator (ACPC) is a suitable choice to achieve optimum range of acceptance angles and concentration ratio for building façade integration in the Edinburgh and higher latitudes. A theoretical study of the optical performance shows that a truncated dielectric ACPC with acceptance half-angles of 0o and 55o (termed as DiACPC-55) is the optimum design, when compared to the dielectric ACPC designs with acceptance half angles of (0o and 66o) and (0o and 77o) in Edinburgh and higher latitudes. An increase in the range of acceptance angles is achieved by truncating the concentrator profile. Ray tracing simulations show the DiACPC-55 exhibits the widest range of acceptance angles compared to the other designs. The maximum optical efficiency of the DiACPC-55 is found to be 83%. In addition it is found to have a better intensity distribution at the receiver and a higher total annual energy collection, compared to the other designs. Thermal modelling of a CPV system with the DiACPC-55 concentrator shows that the solar cell and rear plate temperature can reach up to 41.6oC for 1000 W/m2 irradiance, when operating with an average ambient temperature of 10oC. The maximum power ratio of the CPV module (fabricated using the DiACPC-55 concentrator) to a similar non-concentrating counterpart is found to be 2.32, when characterised in an indoor controlled environment using a solar simulator. An average electrical conversion efficiency of 9.5% is measured for the entire range of acceptance angles. The optical loss analysis shows that incident light can escape from the parabolic sides and concentrator-encapsulation interface. The outdoor characterisation of the CPV module with the DiACPC-55 concentrator shows that a maximum power ratio of 2.22 can be achieved on a sunny day. In comparison, a maximum power ratio of 1.9 is observed on a rainy day. These results reveal that the designed dielectric concentrator is capable of collecting 68% of the diffuse radiation. The maximum electrical conversion efficiency of the CPV module in outdoor condition is found to be 9.4%. Module degradation due to the delamination of the solar cell is observed in the long term investigation study, which reduces the module efficiency to 8.6% on a clear sunny day. The fabricated CPV system with the DiACPC-55 concentrator is found to be £190.3/m2 cheaper than similar sized conventional glass-glass laminated modules. Therefore the cost of the CPV module is found to be £0.53/Wp cheaper than the conventional glass-glass laminated modules for building facade integration at high latitudes