Inequalities for the Number of Walks in Graphs

We investigate the growth of the number w _k of walks of length k in undirected graphs as well as related inequalities. In the first part, we deduce the inequality w _2a+c ?w _2(a+b)+c ≤w _2a ?w _2(a+b+c), which we call the Sandwich Theorem. It unifies and generalizes an inequality by Lagarias et al. and an inequality by Dress and Gutman. In the same way, we derive the inequality w _2a+c (v,v)?w _2(a+b)+c (v,v)≤w _2a (v,v)?w _2(a+b+c)(v,v) for the number w _k (v,v) of closed walks of length k starting at a given vertex v. We then use a theorem of Blakley and Dixon to show $w_{2\ell+p}^{k}\leq w_{2\ell+pk}\cdot w_{2\ell}^{k-1}$ , which unifies and generalizes an inequality by Erd?s and Simonovits and, again, the inequality by Dress and Gutman. Both results can be translated directly into the corresponding forms using the higher order densities, which extends former results. In the second part, we provide a new family of lower bounds for the largest eigenvalue λ ₁ of the adjacency matrix based on closed walks. We apply the Sandwich Theorem to show monotonicity in this and a related family of lower bounds of Nikiforov. This leads to generalized upper bounds for the energy of graphs. In the third part, we demonstrate that a further natural generalization of the Sandwich Theorem is not valid for general graphs. We show that the inequality w _a+b ?w _a+b+c ≤w _a ?w _a+2b+c does not hold even in very restricted cases like w ₁?w ₂≤w ₀?w ₃ (i.e., $\bar{d}\cdot w_{2}\leq w_{3}$ ) in the context of bipartite or cycle free graphs. In contrast, we show that surprisingly this inequality is always satisfied for trees and we show how to construct worst-case instances (regarding the difference of both sides of the inequality) for a given degree sequence. We also prove the inequality w ₁?w ₄≤w ₀?w ₅ (i.e., $\bar{d}\cdot w_{4}\leq w_{5}$ ) for trees and conclude with a corresponding conjecture for longer walks.     

Fiber laser induced surface modification/manipulation of an ultrasonically consolidated metal matrix

Ultrasonic Consolidation (UC) is a manufacturing technique based on the ultrasonic joining of a sequence of metal foils. It has been shown to be a suitable method for fiber embedment into metal matrices. However, integration of high volume fractions of fibers requires a method for accurate positioning and secure placement to maintain fiber layouts within the matrices. This paper investigates the use of a fiber laser for microchannel creation in UC samples to allow such fiber layout patterns. A secondary goal, to possibly reduce plastic flow requirements in future embedding processes, is addressed by manipulating the melt generated by the laser to form a shoulder on either side of the channel. The authors studied the influence of laser power, traverse speed and assist gas pressure on the channel formation in aluminium alloy UC samples. It was found that multiple laser passes allowed accurate melt distribution and channel geometry in the micrometre range. An assist gas aided the manipulation of the melted material.     

Temperature-dependent 2-D to 3-D growth transition of ultra-thin Pt films deposited by PLD

During the growth of thin metal films on dielectric substrates at a given deposition temperature T_d, the film’s morphology is conditioned by the magnitude and asymmetry of up- and downhill diffusion. Any severe change of this mechanism leads to a growth instability, which induces an alteration of the thin film morphology. In order to study this mechanism, ultrathin Pt films were deposited via pulsed laser deposition onto yttria-stabilized zirconia single crystals at different deposition temperatures. The morphological evolution of Pt thin films has been investigated by means of scanning electron microscopy, atomic force microscopy and standard image analysis techniques. The experimentally obtained morphologies are compared to simulated thin film structures resulting from a two-dimensional kinetic Monte Carlo approach. Two main observations have been made: (i) thin Pt films deposited onto ZrO₂ undergo a growth transition from two-dimensional to three-dimensional growth at T_d > 573 K. The growth transition and related morphological changes are a function of the deposition temperature; and (ii) a critical cluster size of i¹ = 4 in combination with an asymmetric Ehrlich–Schwoebel barrier favoring the uphill diffusion of atoms allows for a computational reproduction of the experimentally obtained film morphologies.     

Lanthanum nickelate thin films deposited by spray pyrolysis: Crystallization,microstructure and electrochemical properties

Thin films from the La_n+1Ni_nO_3n+1 system exhibit favorable dielectric and electrochemical properties that may prove useful for a variety of devices ranging from ferroelectrics to low-temperature solid oxide fuel cells. The present work covers the compositional, microstructural and electrochemical characterization of thin lanthanum nickelate films deposited by spray pyrolysis. In accordance with the phase diagram, LaNiO_3?δ or La₄Ni₃O_10?δ films were obtained during annealing of spray deposited films at temperatures between 540 °C and 1100 °C. Whereas LaNiO_3?δ films exhibited a high metallic conductivity, La₄Ni₃O_10?δ films were semiconducting. Electrochemical impedance spectroscopy indicated an increase of the area specific oxygen reduction resistance with the annealing temperature. The study highlights how the phase and microstructure of thin films from the La_n+1Ni_nO_3n+1 system can be tailored by annealing of initially amorphous films. LaNiO_3?δ films have a high potential for application in electrochemical devices operating at low temperatures where high electrical conductivity is required.     

Roles of PilC and PilE proteins in pilus-mediated adherence of Neisseria gonorrhoeae and Neisseria meningitidis to human erythrocytes and endothelial and epithelial cells

Unlike other type 4 pili, the neisserial pili consist of at least two distinct proteins, the highly variable major subunit PilE forming the pilus fiber and the tip-associated adhesin PilC. PilC protein purified either from gonococci or from Escherichia coli interacted with different human epithelial cell lines, primary epithelial and endothelial cells. The binding of PilC protein efficiently prevented the attachment of piliated Neisseria gonorrhoeae and Neisseria meningitidis to these cell types. Fluorescent beads coated with pili prepared from piliated wild-type N. gonorrhoeae also adhered to these cells, in contrast to beads coated with pili prepared from a piliated PilC-deficient mutant. In the latter case, the binding of fluorescent beads was restored after pretreatment of the pilus-loaded beads with purified PilC. Piliated wild-type N. gonorrhoeae, the piliated PilC-deficient mutant, and N. gonorrhoeae pili assembled in Pseudomonas aeruginosa agglutinated human erythrocytes, while nonpiliated gonococci did not. Consistently, purified PilC did not agglutinate or bind to human erythrocytes, suggesting that N. gonorrhoeae PilE is responsible for pilus-mediated hemagglutination.     

A Living‐Dead Magnetic Layer at the Surface of Ferrimagnetic DyTiO3 Thin Films

When ferromagnetic films become ultrathin, key properties such as the Curie temperature and the saturation magnetization are usually depressed. This effect is thoroughly investigated in magnetic oxides such as half‐metallic manganites, but much less in ferrimagnetic insulating perovskites such as rare‐earth titanates RTiO₃, despite their appeal to design correlated 2D electron gases. Here, the magnetic properties of epitaxial DyTiO₃ thin films are reported. While films thicker than about 50 nm show a bulk‐like response, at low thickness a surprising increase of the saturation magnetization is observed. This behavior is described using a classical model of a “dead layer” but assuming that this layer is actually “living,” that is, it responds to the magnetic field with a strong paramagnetic susceptibility. Through depth‐dependent X‐ray absorption and photoemission spectroscopy, it is shown that the “living‐dead layer” corresponds to surface regions where magnetic (S = 1/2) Ti³⁺ ions are replaced by nonmagnetic Ti⁴⁺ ions. Hysteresis cycles at the Dy M₅ and Ti L₃ edges indicate that the surface Ti⁴⁺ ions decouple the Dy³⁺ ions, thus unleashing their strong paramagnetic response. Finally, it is shown how capping the DyTiO₃ film can help increase the Ti³⁺ content near the surface and thus recover a better ferrimagnetic behavior.     

Solitonic lattice and Yukawa forces in the rare-earth orthoferrite TbFeO3

The random fluctuations of spins give rise to many interesting physical phenomena, such as the 'order-from-disorder' arising in frustrated magnets and unconventional Cooper pairing in magnetic superconductors. Here we show that the exchange of spin waves between extended topological defects, such as domain walls, can result in novel magnetic states. We report the discovery of an unusual incommensurate phase in the orthoferrite TbFeO(3) using neutron diffraction under an applied magnetic field. The magnetic modulation has a very long period of 340?? at 3?K and exhibits an anomalously large number of higher-order harmonics. These domain walls are formed by Ising-like Tb spins. They interact by exchanging magnons propagating through the Fe magnetic sublattice. The resulting force between the domain walls has a rather long range that determines the period of the incommensurate state and is analogous to the pion-mediated Yukawa interaction between protons and neutrons in nuclei.     

Novel anti-reflection technology for GaAs single-junction solar cells using surface patterning and Au nanoparticles

Single-junction GaAs solar cell structures were grown by low-pressure MOCVD on GaAs (100) substrates. Micro-rod arrays with diameters of 2 microm, 5 microm, and 10 microm were fabricated on the surfaces of the GaAs solar cells via photolithography and wet chemical etching. The patterned surfaces were coated with Au nanoparticles using an Au colloidal solution. Characteristics of the GaAs solar cells with and without the micro-rod arrays and Au nanoparticles were investigated. The short-circuit current density of the GaAs solar cell with 2 microm rod arrays and Au nanoparticles increased up to 34.9% compared to that of the reference cell without micro-rod arrays and Au nanoparticles. The conversion efficiency of the GaAs solar cell that was coated with Au nanoparticles on the patterned surface with micro-rod arrays can be improved from 14.1% to 19.9% under 1 sun AM 1.5G illumination. These results show that micro-rod arrays and Au nanoparticle coating can be applied together in surface patterning to achieve a novel cost-effective anti-reflection technology.     

Simultaneous polarized neutron reflectometry and anisotropic magnetoresistance measurements

A novel experimental facility to carry out simultaneous polarized neutron reflectometry (PNR) and anisotropic magnetoresistance (AMR) measurements is presented. Performing both techniques at the same time increases their strength considerably. The proof of concept of this method is demonstrated on a CoO/Co bilayer exchange bias system. Although information on the same phenomena, such as the coercivity or the reversal mechanism, can be separately obtained from either of these techniques, the simultaneous application optimizes the consistency between both. In this way, possible differences in experimental conditions, such as applied magnetic field amplitude and orientation, sample temperature, magnetic history, etc., can be ruled out. Consequently, only differences in the fundamental sensitivities of the techniques can cause discrepancies in the interpretation between the two. The almost instantaneous information obtained from AMR can be used to reveal time-dependent effects during the PNR acquisition. Moreover, the information inferred from the AMR measurements can be used for optimizing the experimental conditions for the PNR measurements in a more efficient way than with the PNR measurements alone.