One-sided continuous dependence of maximal solutions

We consider the maximal solution of $\text{u′(s) = ?(s, u(s))}$, where ? satisfies a one-sided variant of Carathéodory's conditions. A best-possible condition is proved for the dependence of u on ?. Also we show that a function v satisfies $\text{v(t) ? v(r) ? ?}{}_{\mathrm{r}}{}^{\mathrm{t}}\text{?(s, v(s))ds}$ if and only if v is dominated by the maximal solution u.     

Quantitative model of price diffusion and market friction based on trading as a mechanistic random process

We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.     

Spin-dependent electron-hole capture kinetics in luminescent conjugated polymers

The recombination of electron-hole pairs injected in extended conjugated systems is modeled as a multistep interconversion relaxation in monoexcited electronic state space, mediated by electron-phonon coupling. The computed ratio of triplet-to-singlet exciton formation times r=tau(T)/tau(S) increases from 0.9 for a model dimer to 2.5 for a 32-unit chain, in good agreement with recent experiments. We rationalize the conjugation-length dependence of r in terms of spin-specific energetics and mutual vibronic coupling of the excited states.     

Pressure-induced phase transitions of lanthanide monoarsenides LaAs and LuAs with a NaCl-type structure

By use of synchrotron radiation the powder X-ray diffraction of lanthanide monoarsenides LaAs and LuAs with a NaCl-type structure has been studied up to 60 GPa at room temperature. First-order phase transitions with the crystallographic change were found at around 20 GPa for LaAs, and 57 GPa for LuAs. The high-pressure form of LaAs is a tetragonal structure and can be viewed as a distorted CsCl-type structure. The atoms in the tetragonal structure are located at La: 0, 0, 0; As: 1/2, 1/2, 1/2. The space group is P4/mmm. The structural change to the tetragonal structure occurs with the volume collapse of about 10%. The structure of these high-pressure phases of LuAs is unknown. The volume vs. pressure curves for LaAs and LuAs are fitted by a Birch equation of state. The bulk moduli of both arsenides are 92±6 GPa for LaAs and 85±3 GPa for LuAs. The high-pressure structural behavior of LaX (X=P, As and Sb) and LnAs (Ln=lanthanide) with the NaCl-type structure is discussed.     

Phase rotation scheme of laser-produced ions for reduction of the energy spread

In order to widely spread out particle beams utilized in cancer therapy, laser-produced ions are developed as the injection beam for an ion synchrotron dedicated for cancer therapy. Such a laser ion source is expected to contribute largely to the realization of compactness of the size and low cost of the cancer therapy accelerator. The energy spectrum of the laser-produced ions, however, has no peak, but their intensities decrease exponentially according to the increase of the energy. For the purpose of modifying such a situation, we have proposed a scheme to rotate the beam in the longitudinal phase space with the use of the RF electric field, which is phase-adjusted with the pulse laser. We aim for a reduction of the energy spread of ± 5% selected by an energy analyzer and slits to ±1% by such phase rotation. For this purpose, a quarter wavelength resonator with two gaps with the same resonant frequency as the source laser has already been fabricated, together with its RF power source. The above phase rotation system and its recent experimental realization are presented.     

Modification of the surface state of rough substrates by two different varnishes and influence on the reflected light

Modification of the visual appearance when a rough surface is covered by a varnish is mostly attributed to the levelling of the substrate surface, which depends on the molecular weight of the varnish. The topography of varnished surfaces, however, has never been measured directly. Surfaces of varnishes applied over glass substrates of varying roughness were studied, therefore, using mechanical profilometry. Two different varnishes made with a low and a high molecular weight resin were studied. Both varnishes lower the r.m.s. roughness of the substrates and filter the high spatial frequencies. These results are amplified for the varnish containing the low molecular weight resin. The light reflected by the varnished samples is modelled from these topographical data. Its angular distribution, calculated from the probability density of slopes is presented, taking into account separately the air/varnish and the varnish/substrate interfaces. These analyses are presented in a back-scattering configuration. They show that varnishing significantly reduces the angular width of the reflected light and that this effect is magnified for the low molecular weight resin. Modelling furthermore shows that the influence of the roughness of the varnish/substrate interface is negligible in the total reflected light.     

Negative differential conductance and hot phonons in suspended nanotube molecular wires

Freely suspended metallic single-walled carbon nanotubes (SWNTs) exhibit reduced current carrying ability compared to those lying on substrates, and striking negative differential conductance at low electric fields. Theoretical analysis reveals significant self-heating effects including electron scattering by hot nonequilibrium optical phonons. Electron transport characteristics under strong self-heating are exploited for the first time to probe the thermal conductivity of individual SWNTs (approximately 3600 W m-1 K-1 at T=300 K) up to approximately 700 K, and reveal a 1/T dependence expected for umklapp phonon scattering at high temperatures.     

Weak decoherence and quantum trajectory graphs

Griffiths' quantum trajectories formalism is extended to describe weak decoherence. The decoherence conditions are shown to severely limit the complexity of histories composed of fine-grained events.