Bernoulli Numbers, Wolstenholme's Theorem, and p^5 Variations of Lucas' Theorem

In this note we shall improve some congruences of D.F. Bailey [Two p^3 variations of Lucas' Theorem, JNT 35(1990), pp. 208-215] to higher prime power moduli, by studying the relation between irregular pairs of the form (p,p-3) and refined version of Wolstenholme's theorem.Comment: 7 pages. Final version accepted by J. of Number Theor

Very large magnetoresistance in Fe0.28_{0.28}TaS2_{2} single crystals

Magnetic moments intercalated into layered transition metal dichalcogenides are an excellent system for investigating the rich physics associated with magnetic ordering in a strongly anisotropic, strong spin-orbit coupling environment. We examine electronic transport and magnetization in Fe$_{0.28}$TaS$_{2}$, a highly anisotropic ferromagnet with a Curie temperature $T_{\mathrm{C}} \sim 68.8~$K. We find anomalous Hall data confirming a dominance of spin-orbit coupling in the magnetotransport properties of this material, and a remarkably large field-perpendicular-to-plane MR exceeding 60% at 2 K, much larger than the typical MR for bulk metals, and comparable to state-of-the-art GMR in thin film heterostructures, and smaller only than CMR in Mn perovskites or high mobility semiconductors. Even within the Fe$_x$TaS$_2$ series, for the current $x$ = 0.28 single crystals the MR is nearly $100\times$ higher than that found previously in the commensurate compound Fe$_{0.25}$TaS$_{2}$. After considering alternatives, we argue that the large MR arises from spin disorder scattering in the strong spin-orbit coupling environment, and suggest that this can be a design principle for materials with large MR.Comment: 8 pages, 8 figures, accepted in PR

Log-concavity and lower bounds for arithmetic circuits

One question that we investigate in this paper is, how can we build log-concave polynomials using sparse polynomials as building blocks? More precisely, let $f = \sum\_{i = 0}^d a\_i X^i \in \mathbb{R}^+[X]$ be a polynomial satisfying the log-concavity condition a\_i^2 \textgreater{} \tau a\_{i-1}a\_{i+1} for every $i \in \{1,\ldots,d-1\},$ where \tau \textgreater{} 0. Whenever $f$ can be written under the form $f = \sum\_{i = 1}^k \prod\_{j = 1}^m f\_{i,j}$ where the polynomials $f\_{i,j}$ have at most $t$ monomials, it is clear that $d \leq k t^m$. Assuming that the $f\_{i,j}$ have only non-negative coefficients, we improve this degree bound to $d = \mathcal O(k m^{2/3} t^{2m/3} {\rm log^{2/3}}(kt))$ if \tau \textgreater{} 1, and to $d \leq kmt$ if $\tau = d^{2d}$. This investigation has a complexity-theoretic motivation: we show that a suitable strengthening of the above results would imply a separation of the algebraic complexity classes VP and VNP. As they currently stand, these results are strong enough to provide a new example of a family of polynomials in VNP which cannot be computed by monotone arithmetic circuits of polynomial size

Nanostructure Investigations of Nonlinear Differential Conductance in NdNiO3_3 Thin Films

Transport measurements on thin films of NdNiO$_3$ reveal a crossover to a regime of pronounced nonlinear conduction below the well-known metal-insulator transition temperature. The evolution of the transport properties at temperatures well below this transition appears consistent with a gradual formation of a gap in the hole-like Fermi surface of this strongly correlated system. As $T$ is decreased below the nominal transition temperature, transport becomes increasily non-Ohmic, with a model of Landau-Zener breakdown becoming most suited for describing $I(V)$ characteristics as the temperature approaches 2~K.Comment: 18 pages, 6 figures, accepted for publication in PR

Analytical investigation of the heat-transfer limits of a novel solar loop-heat pipe employing a mini-channel evaporator

© 2018 by the authors. This paper presents an analytical investigation of heat-transfer limits of a novel solar loop-heat pipe developed for space heating and domestic hot water use. In the loop-heat pipe, the condensate liquid returns to the evaporator via small specially designed holes, using a mini-channel evaporator. The study considered the commonly known heat-transfer limits of loop-heat pipes, namely, the viscous, sonic, entrainment, boiling and heat-transfer limits due to the two-phase pressure drop in the loop. The analysis considered the main factors that affect the limits in the mini-channel evaporator: the operating temperature, mini-channel aspect ratio, evaporator length, evaporator inclination angle, evaporator-to-condenser height difference and the dimension of the holes. It was found that the entrainment is the main governing limit of the system operation. With the specified loop design and operational conditions, the solar loop-heat pipe can achieve a heat-transport capacity of 725 W. The analytical model presented in this study can be used to optimise the heat-transfer capacity of the novel solar loop-heat pipe

Energy performance analysis of a novel solar PVT loop heat pipe employing a microchannel heat pipe evaporator and a PCM triple heat exchanger

This study presents a numerical analysis of the energy efficiency for a novel solar PVT Loop Heat Pipe (PVT-LHP) employing a novel Micro-channel evaporator and a novel PCM heat storage exchanger. It presents a description of the different sub-models in the PVT-LHP system (the PVT model, the microchannel heat collector model and the novel PCM triple heat exchanger model) and the integrated model of the system. The integrated model of the system was solved by ensuring a heat balance at the condenser and the evaporator. A parametric analysis has been performed in order to assess the influence of the environmental parameters (i.e. solar radiation, air temperature, wind velocity), structural parameters (i.e. glazing cover, the number of absorbing microchannel heat pipes, PV cell packing factor), the circulating fluid variables (i.e. cold-water inlet temperature and water mass flow rate) on the energy performance of the system. The novel PVT-LHP has been compared with a onventional Solar PVT-LHP system. It was found that lower solar radiation, lower ambient air temperature, higher wind speed, higher packing factor, lower cold-water inlet temperature and a smaller cover number led to an enhanced electrical efficiency, but a reduced thermal efficiency of the module; whereas a higher coldwater mass flow rate and a greater number of microchannel heat pipes gave rise to both thermal and electrical efficiencies of the module. It was also found that an increase of solar radiation, ambienttemperature, cover number, microchannel heat pipe number and packing factor are favourable factors for the overall COP (Coefficient Of Performance) of the system, whereas an increase of wind velocity and cold water mass flow rate are unfavourable. The study indicated the existence of an optimal cover number, number of microchannel heat pipes and mass flowrate. Under the given design conditions, the electrical, thermal and overall efficiency of the PV/LHP module were 12.2%, 55.6% and 67.8% respectively and the novel system can achieve 28% higher overall energy efficiency and 2.2 times higher COP compared to a conventional system. The integrated computer model developed in this study can be used to design and optimize the novel PVT-LHP heating system

Influence of Spin Orbit Coupling in the Iron-Based Superconductors

We report on the influence of spin-orbit coupling (SOC) in the Fe-based superconductors (FeSCs) via application of circularly-polarized spin and angle-resolved photoemission spectroscopy. We combine this technique in representative members of both the Fe-pnictides and Fe-chalcogenides with ab initio density functional theory and tight-binding calculations to establish an ubiquitous modification of the electronic structure in these materials imbued by SOC. The influence of SOC is found to be concentrated on the hole pockets where the superconducting gap is generally found to be largest. This result contests descriptions of superconductivity in these materials in terms of pure spin-singlet eigenstates, raising questions regarding the possible pairing mechanisms and role of SOC therein.Comment: For supplementary information, see http://qmlab.ubc.ca/ARPES/PUBLICATIONS/articles.htm

Thermally Driven Analog of the Barkhausen Effect at the Metal-Insulator Transition in Vanadium Dioxide

The physics of the metal-insulator transition (MIT) in vanadium dioxide remains a subject of intense interest. Because of the complicating effects of elastic strain on the phase transition, there is interest in comparatively strain-free means of examining VO2 material properties. We report contact-free, low-strain studies of the MIT through an inductive bridge approach sensitive to the magnetic response of VO2 powder. Rather than observing the expected step-like change in susceptibility at the transition, we argue that the measured response is dominated by an analog of the Barkhausen effect, due to the extremely sharp jump in the magnetic response of each grain as a function of time as the material is cycled across the phase boundary. This effect suggests that future measurements could access the dynamics of this and similar phase transitions.Comment: 16 pages, 4 figures. Accepted for publication in Appl. Phys. Let

Hydrogen Diffusion and Stabilization in Single-crystal VO2 Micro/nanobeams by Direct Atomic Hydrogenation

We report measurements of the diffusion of atomic hydrogen in single crystalline VO2 micro/nanobeams by direct exposure to atomic hydrogen, without catalyst. The atomic hydrogen is generated by a hot filament, and the doping process takes place at moderate temperature (373 K). Undoped VO2 has a metal-to-insulator phase transition at ~340 K between a high-temperature, rutile, metallic phase and a low-temperature, monoclinic, insulating phase with a resistance exhibiting a semiconductor-like temperature dependence. Atomic hydrogenation results in stabilization of the metallic phase of VO2 micro/nanobeams down to 2 K, the lowest point we could reach in our measurement setup. Based on observing the movement of the hydrogen diffusion front in single crystalline VO2 beams, we estimate the diffusion constant for hydrogen along the c-axis of the rutile phase to be 6.7 x 10^{-10} cm^2/s at approximately 373 K, exceeding the value in isostructural TiO2 by ~ 38x. Moreover, we find that the diffusion constant along the c-axis of the rutile phase exceeds that along the equivalent a-axis of the monoclinic phase by at least three orders of magnitude. This remarkable change in kinetics must originate from the distortion of the "channels" when the unit cell doubles along this direction upon cooling into the monoclinic structure. Ab initio calculation results are in good agreement with the experimental trends in the relative kinetics of the two phases. This raises the possibility of a switchable membrane for hydrogen transport.Comment: 23 pages, 4 figs + supporting materia