Theory of local heating in nanoscale conductors

We report first-principles calculations of local heating in nanoscale junctions formed by a single molecule and a gold point contact. Due to a larger heat dissipation, the single molecule heats up less than the gold point contact. We also find, at zero temperature, a threshold bias $V_{onset}$ of about 6 mV and 11 mV for the molecule and the point contact, respectively, is required to excite the smallest vibrational mode and generate heat. The latter estimate is in very good agreement with recent experimental results on the same system. At a given external bias $V$ below $V_{onset}$, heating becomes noticeable when the background temperature is on the order of $\sim e(V_{onset}-V)/k_{B}$. Above $V_{onset}$, local heating increases dramatically with increasing bias but is also considerably suppressed by thermal dissipation into the electrodes. The results provide a microscopic picture of current-induced heat generation in atomic-scale structures.Comment: 4 pages, 4figure

Inelastic effects on the transport properties of alkanethiols

Using first-principles approaches we investigate local heating and the inelastic contribution to the current for various alkanethiols sandwiched between metal electrodes. In the absence of good heat dissipation into the bulk electrodes, we find that the local temperature of the alkanethiols is relatively insensitive to their length. This is due to the rates of heating and cooling processes scaling similarly with length. On the other hand, when considering heat dissipation into the bulk electrodes, the local temperature of alkanethiols decreases as their length increases. We also find that the inelastic scattering profile displays an odd-even effect with length which compares well with experimental results. This effect is due to the alternating direction of the CH3 group motion with respect to current flow with increasing C atoms in the chain, and is very sensitive to the structure of the carbon-sulfur-gold bond. Inelastic scattering profiles can therefore help illuminate the bonding configuration of molecules to metallic surfaces.Comment: 5 pages, 4 figure

Effect of electron-phonon scattering on shot noise in nanoscale junctions

We investigate the effect of electron-phonon inelastic scattering on shot noise in nanoscale junctions in the regime of quasi-ballistic transport. We predict that when the local temperature of the junction is larger than its lowest vibrational mode energy $eV_c$, the inelastic contribution to shot noise (conductance) increases (decreases) with bias as $V$ ($\sqrt{V}$). The corresponding Fano factor thus increases as $\sqrt{V}$. We also show that the inelastic contribution to the Fano factor saturates with increasing thermal current exchanged between the junction and the bulk electrodes to a value which, for $V>>V_c$, is independent of bias. A measurement of shot noise may thus provide information about the local temperature and heat dissipation in nanoscale conductors.Comment: 4 pages, 2 figure

Mixed principal eigenvalues in dimension one

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the $L^{2}$-Poincar\'e inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.Comment: 45 pages; Front. Math. China, 201

A Finite Exact Representation of Register Automata Configurations

A register automaton is a finite automaton with finitely many registers ranging from an infinite alphabet. Since the valuations of registers are infinite, there are infinitely many configurations. We describe a technique to classify infinite register automata configurations into finitely many exact representative configurations. Using the finitary representation, we give an algorithm solving the reachability problem for register automata. We moreover define a computation tree logic for register automata and solve its model checking problem.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

A case of renal cell carcinoma metastasizing to invasive ductal breast carcinoma

Tumor-to-tumor metastasis is an uncommon but well-documented phenomenon. We present a case of a clear cell renal cell carcinoma (RCC) metastasizing to an invasive ductal carcinoma (IDC) of the breast. A 74-year-old woman with a past history of clear cell RCC status after radical nephrectomy underwent right modified radical mastectomy for an enlarging breast mass 3 years after nephrectomy. Histological examination revealed a small focus with distinct morphological features similar to clear cell RCC encased in the otherwise typical IDC. Immunohistochemical studies showed that this focus was positive for CD10 and vimentin, in contrast to the surrounding IDC, which was negative for both markers and positive for Her2/neu. Based on the histological and immunohistochemical features, the patient was diagnosed with metastasis of clear cell RCC to the breast IDC. To the best of our knowledge, this is the first reported case of a breast neoplasm as the recipient tumor in tumor-to-tumor metastasis