Quantum censorship in two dimensions

It is pointed out that increasingly attractive interactions, represented by partially concave local potential in the Lagrangian, may lead to the degeneracy of the blocked, renormalized action at the gliding cutoff scale by tree-level renormalization. A quantum counterpart of this mechanism is presented in the two-dimensional sine-Gordon model. The presence of Quantum Censorship is conjectured which makes the loop contributions pile up during the renormalization and thereby realize an approximate semiclassical effect.Comment: 12 pages, 4 figures. Final versio

Interplay of fixed points in scalar models

We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that can be identified with the correlation length. This enables one to identify the type of the phase transition which shows similarity to the one appearing in the crossover scale. The critical exponent $\nu$ of the correlation length also proved to be equal in the crossover and the infrared scaling regimes.Comment: 11 pages, 4 figure

Unit Killing Vector Fields on Nearly Kahler Manifolds

We study 6-dimensional nearly Kahler manifolds admitting a Killing vector field of unit length. In the compact case it is shown that up to a finite cover there is only one geometry possible, that of the 3--symmetric space $S^3 \times S^3$

Resilience and risk analysis of fault-tolerant control design in continuous pharmaceutical manufacturing

PresentationThe effects of the paradigm shift from batch to continuous manufacturing on pharmaceutical industry, in terms of process safety and product quality, e.g., danger of dust explosions and risk of off-spec products, are of major concerns in the recent research progress in control system design. Specifically, a fault-tolerant control of critical process parameters (CPPs) and critical quality attributes (CQAs) is of paramount importance for the continuous operation with built-in safety and quality. In this study, a systematic framework for fault-tolerant control design, analysis, and evaluation for continuous pharmaceutical solid-dosage manufacturing is proposed, consisting of system identification, control design and analysis (controllability, stability, resilience, etc.), hierarchical three-layer control structures (model predictive control, state estimation, data reconciliation, etc.), risk mapping, assessment and planning (Risk MAP) strategies, and control performance evaluation. The key idea of the proposed framework is to identify the potential risks in the control design, material variance, and process uncertainties, under which the control strategies are evaluated. The framework is applied to a continuous direct compaction process, specifically the feeding-blending system wherein the major source of variance in the process operation and product quality arises. It can be demonstrated that the process operation failures and product quality variances in the feeding-blending system can be mitigated and managed through the proposed systematic fault-tolerant control system design and risk analysis framework

Locating Depots for Capacitated Vehicle Routing

We study a location-routing problem in the context of capacitated vehicle routing. The input is a set of demand locations in a metric space and a fleet of k vehicles each of capacity Q. The objective is to locate k depots, one for each vehicle, and compute routes for the vehicles so that all demands are satisfied and the total cost is minimized. Our main result is a constant-factor approximation algorithm for this problem. To achieve this result, we reduce to the k-median-forest problem, which generalizes both k-median and minimum spanning tree, and which might be of independent interest. We give a (3+c)-approximation algorithm for k-median-forest, which leads to a (12+c)-approximation algorithm for the above location-routing problem, for any constant c>0. The algorithm for k-median-forest is just t-swap local search, and we prove that it has locality gap 3+2/t; this generalizes the corresponding result known for k-median. Finally we consider the "non-uniform" k-median-forest problem which has different cost functions for the MST and k-median parts. We show that the locality gap for this problem is unbounded even under multi-swaps, which contrasts with the uniform case. Nevertheless, we obtain a constant-factor approximation algorithm, using an LP based approach.Comment: 12 pages, 1 figur