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M. Otto

Publications and source records attributed to M. Otto.

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Finite approximation of free groups II: the Theorems of Ash, Herwig-Lascar and Ribes-Zalesskii -- revisited and strengthened

Relations and interactions between the theorems of Ash, Herwig--Lascar and Ribes--Zalesskii are discussed and it is shown that these three theorems are equivalent in the sense that each of them can be derived from each other one. Some strengthenings of these theorems are obtained with the use of groups provided by a construction of the third author. Evidence is given that these strengthenings are substantially stronger than the classical results. Yet, it turns out that both kinds of results can be interpreted as different instances of the same common scheme, namely as \emph{finite approximation of free groups}.

math.GR

Finite approximation of free groups I: the $F$-inverse cover problem

For a finite connected graph $\mathcal{E}$ with set of edges $E$, a finite $E$-generated group $G$ is constructed such that the set of relations $p=1$ satisfied by $G$ (with $p$ a word over $E\cup E^{-1}$) is closed under deletion of generators (i.e.~edges). As a consequence, every element $g\in G$ admits a unique minimal set $\mathrm{C}(g)$ of edges (the \emph{content} of $g$) needed to represent $g$ as a word over $\mathrm{C}(g)\cup\mathrm{C}(g)^{-1}$. The crucial property of the group $G$ is that connectivity in the graph $\mathcal{E}$ is encoded in $G$ in the following sense: if a word $p$ forms a path $u\longrightarrow v$ in $\mathcal{E}$ then there exists a $G$-equivalent word $q$ which also forms a path $u\longrightarrow v$ and uses only edges from their content; in particular, the content of the corresponding group element $[p]_G=[q]_G$ spans a connected subgraph of $\mathcal{E}$ containing the vertices $u$ and $v$. As the free group generated by $E$ obviously has these properties, the construction provides another instance of how certain features of free groups can be ``approximated'' or ``simulated'' in finite groups. As an application it is shown that every finite inverse monoid admits a finite $F$-inverse cover. This solves a long-standing problem of Henckell and Rhodes.

math.GR

Graphene-Quantum Dots Hybrid Photodetectors with Low Dark-Current Readout

Graphene-based photodetectors have shown responsivities up to 10$^8$A/W and photoconductive gains up to 10$^{8}$ electrons per photon. These photodetectors rely on a highly absorbing layer in close proximity of graphene, which induces a shift of the graphene chemical potential upon absorption, hence modifying its channel resistance. However, due to the semi-metallic nature of graphene, the readout requires dark currents of hundreds of $μ$A up to mA, leading to high power consumption needed for the device operation. Here we propose a novel approach for highly responsive graphene-based photodetectors with orders of magnitude lower dark current levels. A shift of the graphene chemical potential caused by light absorption in a layer of colloidal quantum dots, induces a variation of the current flowing across a metal-insulator-graphene diode structure. Owing to the low density of states of graphene near the neutrality point, the light-induced shift in chemical potential can be relatively large, dramatically changing the amount of current flowing across the insulating barrier, and giving rise to a novel type of gain mechanism. This readout requires dark currents of hundreds of nA up to few $μ$A, orders of magnitude lower than other graphene-based photodetectors, while keeping responsivities of $\sim$70A/W in the infrared, almost two orders of magnitude higher compared to established germanium on silicon and indium gallium arsenide infrared photodetectors. This makes the device appealing for applications where high responsivity and low power consumption are required.

physics.app-ph

Resistance of Hall Sensors Based on Graphene to Neutron Radiation

An in-situ study of Hall sensors based on single-layered graphene in neutron fluxes of a nuclear reactor to the fluence of 1.5e20 n/sq,m was conducted. The sensitivity of the sensors to the magnetic field remained stable throughout the experiment, while the resistance changes correlated with the increase in sample temperature due to radiation heating. The experiment confirmed the theoretical expectations regarding the high stability of graphene sensors to neutron irradiation. Necessary further improvement of sensor technology to optimize their characteristics, as well as radiation testing to determine the maximum permissible neutron fluence.

physics.app-ph

Nanofilm Materials for Devices of Magnetic Field Measurement in Radiation Environment

The prospects of using nanofilms of indium-containing III-V semiconductors, gold and single-layer graphene in magnetic field sensors, intended for application in radiation environment were evaluated on the results of testing in neutron fluxes. Semiconductor sensors are capable of withstanding radiation levels typical for the ITER-type fusion reactors, while gold sensors are stable even under environment expected in the first fusion power plant DEMO. Graphene is promising for creating sensors that combine high magnetic field sensitivity and high irradiation resistance.

physics.app-ph

Anisotropy in granular media: classical elasticity and directed force chain network

A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic directed force chain networks. Perhaps surprisingly, two-peak response functions can occur even for classical, anisotropic elastic materials, such as triangular networks of springs with different stiffnesses. In such cases, the peak widths grow linearly with the height of the layer, contrary to the diffusive spreading found in `stress-only' hyperbolic models. In principle, directed force chain networks can exhibit the two-peak, diffusively spreading response function of hyperbolic models, but all models in a particular class studied here are found to be in the elliptic regime.

cond-mat.stat-mech

Force chain splitting in granular materials: a mechanism for large scale pseudo-elastic behaviour

We investigate both numerically and analytically the effect of strong disorder on the large scale properties of the hyperbolic equations for stresses proposed in \protect\cite{bcc,wcc}. The physical mechanism that we model is the local splitting of the force chains (the characteristics of the hyperbolic equation) by packing defects. In analogy with the theory of light diffusion in a turbid medium, we propose a Boltzmann-like equation to describe these processes. We show that, for isotropic packings, the resulting large scale effective equations for the stresses have exactly the same structure as those of an elastic body, despite the fact that no displacement field needs to be introduced at all. Correspondingly, the response function evolves from a two peak structure at short scales to a broad hump at large scales. We find, however, that the Poisson ratio is anomalously large and incompatible with classical elasticity theory that requires the reference state to be thermodynamically stable.

cond-mat

Topological interactions in DNA catenanes

The elasticity of DNA catenanes, i.e. multiply linked DNA rings, is investigated using the Gauss invariant as a minimal model for topology conservation. An effective elastic free energy as a function of the distance $R$ between segments located on different rings is obtained. An anharmonic part at large distances, growing as $R^{4}$, if $R\gg R_{G}$ ($R_{G}$ being the radius of gyration of a random walk ring) is found, while for $R\ll R_{G}$ the interaction is strongly repulsive. Treating the attractive interaction as the dominant one, distribution functions for the distance between segments located on different rings for several linking numbers are derived which are in qualitative agreement with distributions functions obtained experimentally from electron micrographs of DNA catenanes (S. D. Levene et al., Biophys.J. 69, 277, 1995).

cond-mat.soft

Elasticity of entangled polymer loops: Olympic gels

In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as $F \propto λ^{5/2}$ where $λ$ is the deformation ratio. Thus a highly non Hookian stress - strain relation is predicted.

cond-mat.soft

The conformation of conducting polymer chains: Hubbard polymers

The conformational and electronic properties of conducting flexible random and self-avoiding walk polymer chains are under investigation. A Hamiltonian for conjugated flexible polymers is introduced and its physical consequences are presented. One important result is that the electronic degrees of freedom greatly affect the conformational statistics of the walks and vice versa. The electronic degrees of freedom extend the size of the chain. The end-to-end distance behaves as $R\propto L^ν$ with $ν=(d+1)/(d+2)$, where $d$ is the spatial dimension.

cond-mat