On the charged-impurity-limited mobility for a very pure semiconductor

The low temperature mobility μ limited by charged impurities in very pure semiconductors (Ge) is interpreted in terms of the Coulomb collision in medium. The theory yields a peculiar dependence in temperature T and charged impurity concentration $\text{n}{}_{\mathrm{s}}\text{: μ ∞n}{}_{\mathrm{s}}{}^{\mathrm{<mtext>-</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$.     

Certain Families of Elliptic Functions Defined by <Emphasis Type="Italic">q</Emphasis>-Series

We introduce certain families of elliptic functions involving the Weierstrass ℘-function via q-series systematically and investigate their analytic and algebraic properties. Especially, we give examples of non-linear algebraic ordinary differential equations satisfied by some such elliptic functions. 2000 Mathematics Subject Classification: Primary–11M36, 33E05     

Hierarchic Natures and Dynamics of Photoinduced Structural Phase Transition in Non-Degenerate Charge Density Wave States Via Successive Photoexcitations

We investigate the adiabatic and dynamical natures of the lattice relaxation of excitons in strongly coupled electron-phonon (e-ph) systems using the extended Peierls-Hubbard model, so as to clarify the possible mechanisms of the photoinduced structural phase transition (PISPT) via multi-photon. Focusing on the growth process of relaxed domains that is induced by multi-photoexcitation, we calculate the adiabatic potential energy surfaces relevant to the nonlinear lattice relaxations of excitons in this process. Calculated potentials lead to an essential model of a multi-stepwise potential-crossing (MSPC) system that is composed of many displaced harmonic oscillators as an elementary process of the domain growth in the strongly coupled e-ph systems. We also investigate the dynamical natures in such MSPC systems calculating the time-developments the excited wave packet in this system using the density operator. It is concluded from calculated results that the system possibly develops from the lowest-energy potential state to the higher ones by the effect of the photoexcitations followed by the lattice relaxations.     

Bounding the distance among longest paths in a connected graph

It is easy to see that in a connected graph any $2$ longest paths have a vertex in common. For $k\ge 7$, Skupień in 1966 obtained a connected graph in which some $k$ longest paths have no common vertex, but every $k?1$ longest paths have a common vertex. It is not known whether every $3$ longest paths in a connected graph have a common vertex and similarly for 4, 5, and $6$ longest path. Fujita et al. in 2015 give an upper bound on distance among $3$ longest paths in a connected graph. In this paper we give a similar upper bound on distance between $4$ longest paths and also for $k$ longest paths, in general.     

Hierarchy of the Selberg Zeta Functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Mathematics Subject Classifications (2000). Primary 11M36, Secondary 33B15     

Ion–ion interactions of LiPF6 and LiBF4 in propylene carbonate solutions

Self-diffusion coefficients of Li⁺ D_Li⁺, PF₆⁻ D_PF6⁻ and solvent propylene carbonate (PC) D_PC in LiPF₆−PC solutions were determined at 298 K by the pulse gradient spin echo (PGSE) NMR technique over the salt concentration range of 0.1–3.0 M (M = mol dm^– 3). The order of the diffusion coefficients was found to be D_Li⁺ < D_PF6⁻ < D_PC over the concentration range examined, and they were monotonically decreased with increasing the salt concentration. Haven ratio Λ/Λ_NMR, where Λ and Λ_NMR represent the ionic conductivity measured electrochemically and that estimated via the Nernst-Einstein equation using the diffusion coefficient, respectively, was evaluated as the measure of the ion–ion interaction in the LiPF₆–PC solutions. Though Λ/Λ_NMR values for LiPF₆-solutions decrease with increasing the salt concentration, they were greater than those for LiBF₄–PC solutions over the whole concentration range examined, which indicates that the ion pair formation ability of PF₆^– ion is weaker than that of the BF₄^– ion. The smaller value of the ionic conductivity for the highly concentrated LiPF₆–PC solution (above 2.0 M) than that of the LiBF₄-solutions can be attributed to the more rapidly increased viscosity relative to the LiBF₄-solution. Classic molecular dynamics (MD) simulations for the respective LiPF₆ and LiBF₄-solution of 0.5 and 1.0 M were also carried out based on the effective pair potentials. Diffusion coefficients, ionic conductivity and Haven ratio for these solutions were calculated from MD trajectories, and they qualitatively agree with those evaluated by experiments. Pair correlation functions g_LiO(r) (for Li⁺–O (PC) pair) and g_LiPF6(r) (for Li⁺–PF₆^– pair) or g_LiBF4(r) (for Li⁺–BF₄^– pair) revealed that the lithium ion weakly forms the contact ion pairs with PF₆^–, whilst strongly with BF₄^–, which supports the present experimental results. Moreover, the simulation results show that both anions in the contact ion pairs predominantly take the monodentate form, which is in contrast to the multidentate coordination predicted by ab initio calculation in gas phase.     

Scanning ion conductance microscopy for imaging biological samples in liquid: a comparative study with atomic force microscopy and scanning electron microscopy

The present study was designed to show the applicability of scanning ion conductance microscopy (SICM) for imaging different types of biological samples. For this purpose, we first applied SICM to image collagen fibrils and showed the usefulness of the approach-retract scanning (ARS)/hopping mode for such samples with steep slopes. Comparison of SICM images with those obtained by AFM revealed that the ARS/hopping SICM mode can probe the surface topography of collagen fibrils and chromosomes at nanoscale resolution under liquid conditions. In addition, we successfully imaged cultured HeLa cells, with 15 μm in height by ARS/hopping SICM mode. Because SICM can obtain non-contact (or force-free) images, delicate cellular projections were visualized on the surface of the fixed cell. SICM imaging of live HeLa cells further demonstrated its applicability to study the morphological dynamics associated with biological processes on the time scale of minutes under liquid conditions. We further applied SICM for imaging the luminal surface of the trachea and succeeded in visualizing the surface of both ciliated and non-ciliated cells. These SICM images were comparable with those obtained by scanning electron microscopy. Although the dynamic mode of AFM provides better resolution than the ARS/hopping mode of SICM in some samples, only the latter can obtain contact-free images of samples with steep slopes, rendering it an important tool for observing live cells as well as unfixed or fixed soft samples with complicated shapes. Taken together, we demonstrate that SICM imaging, especially using an ARS/hopping mode, is a useful technique with unique capabilities for imaging the three-dimensional topography of a range of biological samples under physiologically relevant aqueous conditions.