Two-parametric deformation Up,q[gl(2/1)]U_{p,q}[gl(2/1)] and its induced representations

The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical) finite-dimensional representations of this quantum superalgebra. In spite of some specific features, the present approach is similar to a previously developed method [1] which, as shown here, is applicable not only to the one-parametric quantum deformations but also to the multi-parametric ones.Comment: Latex, 13 pages, no figur

Paradoxien des Digital Turn in der Architektur 1990–2015. Von den Verlockungen des Organischen: digitales Entwerfen zwischen informellem Denken und biomorphem Resultat

Vor dem Hintergrund der Einführung des Computers und der damit verbundenen Digitalisierung in der Architektur mit ihrer breiten Anwendung in den 1990er Jahren geht die Arbeit von der Frage aus, warum es im Formbildungsprozess eine Diskrepanz zwischen informellem Denken und biomorphem Resultat gibt. Es werden Paradoxien aufgedeckt, deren Fehlschlüsse zu einer Vielfalt von digitalen Strömungen bei gleichzeitiger Vereinheitlichung der Ausdrucksmittel führten. Im Mittelpunkt steht eine vergleichende und disziplinübergreifende Gegenüberstellung informeller und biomorpher Ansätze. Der informelle Ansatz findet seinen Ursprung im Konzept des Formlosen bei Georges Bataille in den 1920er Jahren und in der informellen Kunst in den 1950er/1960er Jahren. Der biomorphe Ansatz präsentiert sich in dieser Arbeit durch den Nachweis der Verlockungen, aufgrund derer die Architektur die Natur immer wieder als Vorbild nimmt. Es wird aufgezeigt, wo der aktuelle Architekturdiskurs in der Vermischung beider Ansätze feststeckt. Die Konklusion und der Ausblick bilden den Abschluss, in dem die "Unfreiheit" des Programmierens mit dem Wesen der Unbestimmtheit in einer postdigitalen Ära zusammengedacht wird. Dabei wird eine Antwort auf die Frage gegeben, warum sich das digitale Entwerfen vielfach einer biomorphen Formensprache bedient und wie ein Weg aussehen kann, der aus dieser Sackgasse herausführt

Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states

The evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wave length and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wave length with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by X-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.Comment: 50 pages, 17 postscript files including 18 figures, to be published in Phys. Rev.

Epithelial-to-Mesenchymal Transition in Pancreatic Ductal Adenocarcinoma and Pancreatic Tumor Cell Lines: The Role of Neutrophils and Neutrophil-Derived Elastase

Pancreatic ductal adenocarcinoma (PDAC) is frequently associated with fibrosis and a prominent inflammatory infiltrate in the desmoplastic stroma. Moreover, in PDAC, an epithelial-to-mesenchymal transition (EMT) is observed. To explore a possible connection between the infiltrating cells, particularly the polymorphonuclear neutrophils (PMN) and the tumor cell transition, biopsies of patients with PDAC (n=115) were analysed with regard to PMN infiltration and nuclear expression of β-catenin and of ZEB1, well-established indicators of EMT. In biopsies with a dense PMN infiltrate, a nuclear accumulation of β-catenin and of ZEB1 was observed. To address the question whether PMN could induce EMT, they were isolated from healthy donors and were cocultivated with pancreatic tumor cells grown as monolayers. Rapid dyshesion of the tumor cells was seen, most likely due to an elastase-mediated degradation of E-cadherin. In parallel, the transcription factor TWIST was upregulated, β-catenin translocated into the nucleus, ZEB1 appeared in the nucleus, and keratins were downregulated. EMT was also induced when the tumor cells were grown under conditions preventing attachment to the culture plates. Here, also in the absence of elastase, E-cadherin was downmodulated. PMN as well as prevention of adhesion induced EMT also in liver cancer cell line. In conclusion, PMN via elastase induce EMT in vitro, most likely due to the loss of cell-to-cell contact. Because in pancreatic cancers the transition to a mesenchymal phenotype coincides with the PMN infiltrate, a contribution of the inflammatory response to the induction of EMT and—by implication—to tumor progression is possible

Frustration and sound attenuation in structural glasses

Three classes of harmonic disorder systems (Lennard-Jones like glasses, percolators above threshold, and spring disordered lattices) have been numerically investigated in order to clarify the effect of different types of disorder on the mechanism of high frequency sound attenuation. We introduce the concept of frustration in structural glasses as a measure of the internal stress, and find a strong correlation between the degree of frustration and the exponent alpha that characterizes the momentum dependence of the sound attenuation $Gamma(Q)$$\simeq$$Q^\alpha$. In particular, alpha decreases from about d+1 in low-frustration systems (where d is the spectral dimension), to about 2 for high frustration systems like the realistic glasses examined.Comment: Revtex, 4 pages including 4 figure

Nature of vibrational eigenmodes in topologically disordered solids

We use a local projectional analysis method to investigate the effect of topological disorder on the vibrational dynamics in a model glass simulated by molecular dynamics. Evidence is presented that the vibrational eigenmodes in the glass are generically related to the corresponding eigenmodes of its crystalline counterpart via disorder-induced level-repelling and hybridization effects. It is argued that the effect of topological disorder in the glass on the dynamical matrix can be simulated by introducing positional disorder in a crystalline counterpart.Comment: 7 pages, 6 figures, PRB, to be publishe

Scaling of phononic transport with connectivity in amorphous solids

The effect of coordination on transport is investigated theoretically using random networks of springs as model systems. An effective medium approximation is made to compute the density of states of the vibrational modes, their energy diffusivity (a spectral measure of transport) and their spatial correlations as the network coordination $z$ is varied. Critical behaviors are obtained as $z\to z_c$ where these networks lose rigidity. A sharp cross-over from a regime where modes are plane-wave-like toward a regime of extended but strongly-scattered modes occurs at some frequency $\omega^*\sim z-z_c$, which does not correspond to the Ioffe-Regel criterion. Above $\omega^*$ both the density of states and the diffusivity are nearly constant. These results agree remarkably with recent numerical observations of repulsive particles near the jamming threshold \cite{ning}. The analysis further predicts that the length scale characterizing the correlation of displacements of the scattered modes decays as $1/\sqrt{\omega}$ with frequency, whereas for $\omega<<\omega^*$ Rayleigh scattering is found with a scattering length $l_s\sim (z-z_c)^3/\omega^4$. It is argued that this description applies to silica glass where it compares well with thermal conductivity data, and to transverse ultrasound propagation in granular matter

Density of states in random lattices with translational invariance

We propose a random matrix approach to describe vibrational excitations in disordered systems. The dynamical matrix M is taken in the form M=AA^T where A is some real (not generally symmetric) random matrix. It guaranties that M is a positive definite matrix which is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. We found that for certain type of disorder phonons cannot propagate through the lattice and the density of states g(w) is a constant at small w. The reason is a breakdown of affine assumptions and inapplicability of the elasticity theory. Young modulus goes to zero in the thermodynamic limit. It strongly reminds of the properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B v.79, 1715 (1999).Comment: 4 pages, 5 figure

On the high-density expansion for Euclidean Random Matrices

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows to group the diagrams in a small number of topological classes, providing a simple way to determine the infrared (small momenta) behavior of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.Comment: 29 page