Renormalization Theory for Interacting Crumpled Manifolds

We consider a continuous model of D-dimensional elastic (polymerized) manifold fluctuating in d-dimensional Euclidean space, interacting with a single impurity via an attractive or repulsive delta-potential (but without self-avoidance interactions). Except for D=1 (the polymer case), this model cannot be mapped onto a local field theory. We show that the use of intrinsic distance geometry allows for a rigorous construction of the high-temperature perturbative expansion and for analytic continuation in the manifold dimension D. We study the renormalization properties of the model for 0<D<2, and show that for d<d* where d*=2D/(2-D) is the upper critical dimension, the perturbative expansion is UV finite, while UV divergences occur as poles at d=d*. The standard proof of perturbative renormalizability for local field theories (the BPH theorem) does not apply to this model. We prove perturbative renormalizability to all orders by constructing a subtraction operator based on a generalization of the Zimmermann forests formalism, and which makes the theory finite at d=d*. This subtraction operation corresponds to a renormalization of the coupling constant of the model (strength of the interaction with the impurity). The existence of a Wilson function, of an epsilon-expansion around the critical dimension, of scaling laws for d<d* in the repulsive case, and of non-trivial critical exponents of the delocalization transition for d>d* in the attractive case is thus established. To our knowledge, this provides the first proof of renormalizability for a model of extended objects, and should be applicable to the study of self-avoidance interactions for random manifolds.Comment: 126 pages (+ 24 figures not included available upon request), harvmac, SPhT/92/12

Ribonucleotide synthesis by NME6 fuels mitochondrial gene expression

Replication of the mitochondrial genome and expression of the genes it encodes both depend on a sufficient supply of nucleotides to mitochondria. Accordingly, dysregulated nucleotide metabolism not only destabilises the mitochondrial genome, but also affects its transcription. Here, we report that a mitochondrial nucleoside diphosphate kinase, NME6, supplies mitochondria with pyrimidine ribonucleotides that are necessary for the transcription of mitochondrial genes. Loss of NME6 function leads to the depletion of mitochondrial transcripts, as well as destabilisation of the electron transport chain and impaired oxidative phosphorylation. These deficiencies are rescued by an exogenous supply of pyrimidine ribonucleosides. Moreover, NME6 is required for the maintenance of mitochondrial DNA when the access to cytosolic pyrimidine deoxyribonucleotides is limited. Our results therefore reveal an important role for ribonucleotide salvage in mitochondrial gene expression

Kritisches Verhalten von Grenzflächen und Membranen

The phase transition of a manifold from a state bound to a surface to an unbound state is considered in this work. The manifold feels an effective external potential which is motivated by the respective physical System. A general classification scheme, based on renormalization group calculations, of this unbinding transition is presented. Within this scheme the phase transition depends on the external potential and on the lateral dimension of the manifold. In the framework of an approximate renormalization calculation one can treat membranes, whose confoLinations are governed by the curvature energy, and interfaces with a finite surface tension simultaneously. The only parameters are the lateral dimension and the roughness of the respective manifold. Two classes of potentials were investigated. Potentials of the first dass contain a hand wall. This hard wall prevents the use of perturbation or linearization methods. However, the approximate renormalization group is nonlinear and the conditions of a hard wall can be considered. lt turns out that the Limit d $\rightarrow$ 3 for interfaces is nonanalytic, since the renormalization group has no fixed points at d = 3 anymore where d = 3 is just the dimension in which the interface is marginal i. e. logarthrnically rough. In d > 3 one expects mean field behaviour of the phase transition. In contrast to bulk critical phenomena one finds a nonanalytic behaviour of the renormalization group when the upper critical dimension is reached. This shows up in a complex bifurcation structure of the fixed points. This Limit is studied in detail for wetting and adhesion phenomena, leading to the concept of 'drifting fixed points'. Symmetrical potentials are the second dass which are considered. The order of the phase transition for this Blass is also investigated. Motivated by the calculations for potentials with a hard wall the Limit d $\rightarrow$ 3 is again studied. An analog bifurcation structure as for unbinding is found, but now one can use linearized methods to derive exact results. A starting point for the investigation of the symmetrie potentials is an exact transfer matrix calculation in d = 1 + 1 which serves also as a Lest for the approximate renormalization group

Kritisches Verhalten von Grenzflaechen und Membranen

SIGLEAvailable from TIB Hannover: RA831(2672) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Diffuse scattering of x rays at grazing angles from near-surface defects in crystals

We derive the cross section for the intensity of diffuse x-ray scattering under conditions of grazing incidence and exit in the vicinity of Bragg reflections induced by near-surface defects. The theoretical results for a simple model are compared with first measurements on Si single crystals implanted with 80-keV As ions. Reasonable agreement is obtained for a profile of a defect distribution corresponding to that of the collision energy deposited by the implanted ions