Galois groups of multivariate Tutte polynomials

The multivariate Tutte polynomial $\hat Z_M$ of a matroid $M$ is a generalization of the standard two-variable version, obtained by assigning a separate variable $v_e$ to each element $e$ of the ground set $E$. It encodes the full structure of $M$. Let \bv = \{v_e\}_{e\in E}, let $K$ be an arbitrary field, and suppose $M$ is connected. We show that $\hat Z_M$ is irreducible over K(\bv), and give three self-contained proofs that the Galois group of $\hat Z_M$ over K(\bv) is the symmetric group of degree $n$, where $n$ is the rank of $M$. An immediate consequence of this result is that the Galois group of the multivariate Tutte polynomial of any matroid is a direct product of symmetric groups. Finally, we conjecture a similar result for the standard Tutte polynomial of a connected matroid.Comment: 8 pages, final version, to appear in J. Alg. Comb. Substantial revisions, including the addition of two alternative proofs of the main resul

Wave Mechanics of a Two Wire Atomic Beamsplitter

We consider the problem of an atomic beam propagating quantum mechanically through an atom beam splitter. Casting the problem in an adiabatic representation (in the spirit of the Born-Oppenheimer approximation in molecular physics) sheds light on explicit effects due to non-adiabatic passage of the atoms through the splitter region. We are thus able to probe the fully three dimensional structure of the beam splitter, gathering quantitative information about mode-mixing, splitting ratios,and reflection and transmission probabilities

Effect of Nanostructured and Open-Porous Particle Morphology on Electrode Processing and Electrochemical Performance of Li-Ion Batteries

A nanostructured, porous NCM cathode material is investigated regarding its behavior during electrode processing and electrochemical performance. The results are related to the densely packed NCM original material from which the nanostructure has been derived. Chemical composition and structural parameters are not affected by the nanostructuring process; changes are limited to the particle morphology in terms of primary particle size, specific surface area, and porosity. Electrodes containing a porous NCM material deliver lower adhesion strength values when adding identical amounts of PVDF binder. Increasing the binder fraction from four to six parts increases also the adhesion strength to an acceptable level without deteriorating the cell capacity. Despite initially high electrode porosities of 65–70%, electrodes with nanostructured NCM are capable of withstanding calendering to 40% porosity without destroying the porous particles. Full-cell tests with 50 mAh pouch cells and graphite anodes reveal substantially improved C-rate capabilities for the nanostructured material in relation to the commercial original NCM. The advantage increases with increasing C-rate and corresponds to shorter diffusion pathways in nanostructured NCM. Remarkably, even at low C-rates (C/20) where diffusion effects are considered secondary, porous NCM lies ahead of the original material. This can be explained by the higher surface area and thereby enlarged interface to the electrolyte, which eases delithiation. Long-term cycling up to 1100 cycles displayed further benefits for the nanostructured active material as one of the most prominent degradation factors, that is, crack formation and particle fragmentation, does not occur throughout the complete cycling procedure—in contrast to the bulk particles of original NCM

Evolution of mud-crack patterns during repeated drying cycles

In mud, crack patterns are frequently seen with either an approximately rectilinear or hexagonal tiling. Here we show, experimentally, how a desiccation crack pattern changes from being dominated by 90° joint angles, to 120° joint angles. Layers of bentonite clay, a few mm thick, were repeatedly wetted and dried. When dried, the layers crack. These cracks visibly close when rewetted, but a similar crack pattern forms when the layer is redried, with cracks forming along the lines of previously open cracks. Time-lapse photography was used to show how the sequence in which individual cracks open is different in each generation of drying. The geometry of the crack pattern was observed after each of 25 generations of wetting and drying. The angles between cracks were found to approach 120°, with a relaxation time of approximately 4 generations. This was accompanied by a gradual change in the position of the crack vertices, as the crack pattern evolved. A simple model of crack behavior in a layer where the positions of previously open cracks define lines of weakness is developed to explain these observations

Morphology‐Dependent Influences on the Performance of Battery Cells with a Hierarchically Structured Positive Electrode**

The rising demand for high-performing batteries requires new technological concepts. To facilitate fast charge and discharge, hierarchically structured electrodes offer short diffusion paths in the active material. However, there are still gaps in understanding the influences on the cell performance of such electrodes. Here, we employed a cell model to demonstrate that the morphology of the hierarchically structured electrode determines which electrochemical processes dictate the cell performance. The potentially limiting processes include electronic conductivity within the porous secondary particles, solid diffusion within the primary particles, and ionic transport in the electrolyte surrounding the secondary particles. Mitigating these limits requires an electronic conductivity in the active material of at least 10−4 S m−1 and a primary particle radius below 100 nm. Our insights enable a goal-oriented tailoring of hierarchically structured electrodes for high-power applications

Role of IFN-gamma and IL-6 in a protective immune response to Yersinia enterocolitica in mice

<p>Abstract</p> <p>Background</p> <p><it>Yersinia </it>outer protein (Yop) H is a secreted virulence factor of <it>Yersinia enterocolitica </it>(Ye), which inhibits phagocytosis of Ye and contributes to the virulence of Ye in mice. The aim of this study was to address whether and how YopH affects the innate immune response to Ye in mice.</p> <p>Results</p> <p>For this purpose, mice were infected with wild type Ye (pYV⁺) or a YopH-deficient Ye mutant strain (Δ<it>yopH</it>). CD11b⁺cells were isolated from the infected spleen and subjected to gene expression analysis using microarrays. Despite the attenuation of Δ<it>yopH in vivo</it>, by variation of infection doses we were able to achieve conditions that allow comparison of gene expression in pYV⁺and Δ<it>yopH </it>infection, using either comparable infection courses or splenic bacterial burden. Gene expression analysis provided evidence that expression levels of several immune response genes, including IFN-γ and IL-6, are high after pYV⁺infection but low after sublethal Δ<it>yopH </it>infection. In line with these findings, infection of IFN-γR^-/-and IL-6^-/-mice with pYV⁺or Δ<it>yopH </it>revealed that these cytokines are not necessarily required for control of Δ<it>yopH</it>, but are essential for defense against infection with the more virulent pYV⁺. Consistently, IFN-γ pretreatment of bone marrow derived macrophages (BMDM) strongly enhanced their ability in killing intracellular Ye bacteria.</p> <p>Conclusion</p> <p>In conclusion, this data suggests that IFN-γ-mediated effector mechanisms can partially compensate virulence exerted by YopH. These results shed new light on the protective role of IFN-γ in Ye wild type infections.</p

Morphology-Dependent Influences on the Performance of Battery Cells with a Hierarchically Structured Positive Electrode

The rising demand for high-performing batteries requires new technological concepts. To facilitate fast charge and discharge, hierarchically structured electrodes offer short diffusion paths in the active material. However, there are still gaps in understanding the influences on the cell performance of such electrodes. Here, we employed a cell model to demonstrate that the morphology of the hierarchically structured electrode determines which electrochemical processes dictate the cell performance. The potentially limiting processes include electronic conductivity within the porous secondary particles, solid diffusion within the primary particles, and ionic transport in the electrolyte surrounding the secondary particles. Our insights enable a goal-oriented tailoring of hierarchically structured electrodes for high-power applications

Drying of NCM Cathode Electrodes with Porous, Nanostructured Particles Versus Compact Solid Particles: Comparative Study of Binder Migration as a Function of Drying Conditions

Porous, nanostructured Li(NiₓCo$_{y}$Mn)O₂ (NCM) achieves an improvement in the fast-charging capability and the durability of lithium-ion batteries. This improvement is attributed to an extended electrolyte—active material interface, where the electrochemical reactions take place and thus shorter diffusion paths inside the active material particles are necessary for charge transfer. Due to the porous particle morphology, new processing challenges arise compared to compact solid NCM. Herein, the properties of the slurries and the electrodes made of the two active materials and, in particular, the influence of the drying process on the binder distribution, are comparatively investigated. For the same composition of the slurries, a significantly lower dependence of adhesion force and discharge capacity at higher C-rates on the drying rate is shown when using porous, nanostructured particles instead of solid particles. Binder migration and thus an inhomogeneous concentration distribution of the polyvinylidene fluoride binder is less pronounced for these electrodes during faster drying. Cell tests with half cells show that after increasing the drying rate by more than 350%, the discharge capacity of the electrodes consisting of solid NCM is reduced by about 63% at 5C while for the electrodes made of porous material no reduction is measured

Drying of Compact and Porous NCM Cathode Electrodes in Different Multilayer Architectures: Influence of Layer Configuration and Drying Rate on Electrode Properties

Porous, nanostructured particles ensure the wetting of electrolyte up to the particle core and shortened diffusion paths, which is relevant not only for lithium-ion batteries but also for postlithium systems like sodium-ion batteries. The porous structure leads to a high C-rate capability. However, compared to conventional compact NCM, porous NCM shows a reduced adhesion force but no or only slight negative influence on C-rate capability by binder migration at higher drying rates. Herein, a multilayer concept is used to increase the adhesion force with equal or better electrochemical performance compared to single-layer electrodes. Compact particles of high volumetric energy density and porous particles with high C-rate capability are combined in a simultaneously coated multilayer electrode. Multilayers with compact NCM toward the current collector and porous NCM with reduced binder content toward the separator side show an about 16-times higher adhesion force at lower drying rate and an about ten-times higher adhesion force at increased drying rate compared to electrodes produced of porous NCM only. The specific discharge capacity of the multilayers is increased by 88% at the lower and 67% at the higher drying rate for a discharge rate of 3C compared to a single layer with compact NCM