A parametric study on buckling of R/C columns exposed to fire

Buckling of concrete columns is a major issue in fire design, since heating of the columns will result in loss of stiffness and strength in the outer concrete layers. In the Dutch concrete code NEN 6720 (NEN, 1995), a quasi-linear theory of elasticity (KLE) method is provided for columns at ambient temperature. However, no literature is available showing whether this method could be adopted for elevated temperatures. Hence, an efficient calculation tool is needed to validate the applicability of this method in case of fire. As a first step, a cross-sectional calculation tool is introduced to calculate interaction curves of columns at ambient temperature. Further, the interaction diagrams obtained with this numerical method as well as the stiffness method provided in (Eurocode, 2004) and the KLE method are compared. Then, an assumed formula in the KLE-method for the nominal stiffness calculation is discussed considering interaction curves of columns in case of an ISO 834 fire. Finally, parameters like the fire duration and the slenderness ratio are investigated

Investigation of strain gradients and magnitudes during microbending

Sheet metal forming of parts with microscale dimensions is gaining importance due to the current trend towards miniaturization, especially in the electronics industry. In microforming although the process dimensions are scaled down, the polycrystalline material stays the same (e.g., the grain size remains constant). When the specimen feature size approaches the grain size, the properties of individual grains begin to affect the overall deformation behavior. This results in inhomogeneous deformation and increased data scatter of the process parameters. In this research, the influence of the specimen size and the grain size on the distribution of plastic deformation through the thickness during 3-point microbending operations is investigated via digital image correlation. Results showed that with miniaturization, a decrease in the strain gradient existed In addition, an analytical model to predict the dislocation density increases, and thus strain gradient hardening, during microbending is presented. The results from this analytical model matched the experimental results and previous research in terms of the feature size where modest and significant strain gradient hardening was observed

Classical Algorithms from Quantum and Arthur-Merlin Communication Protocols

In recent years, the polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times (e.g., R. Williams\u27s n^3 / 2^{Omega(sqrt{log n})} time algorithm for APSP). As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method in algorithm design ultimately rely on certain (probabilistic) low-rank decompositions of the computation matrices corresponding to key subroutines. They suggest that making use of low-rank decompositions directly could lead to more powerful algorithms, as the polynomial method is just one way to derive such a decomposition. Inspired by their observation, in this paper, we study another way of systematically constructing low-rank decompositions of matrices which could be used by algorithms - communication protocols. Since their introduction, it is known that various types of communication protocols lead to certain low-rank decompositions (e.g., P protocols/rank, BQP protocols/approximate rank). These are usually interpreted as approaches for proving communication lower bounds, while in this work we explore the other direction. We have the following two generic algorithmic applications of communication protocols: - Quantum Communication Protocols and Deterministic Approximate Counting. Our first connection is that a fast BQP communication protocol for a function f implies a fast deterministic additive approximate counting algorithm for a related pair counting problem. Applying known BQP communication protocols, we get fast deterministic additive approximate counting algorithms for Count-OV (#OV), Sparse Count-OV and Formula of SYM circuits. In particular, our approximate counting algorithm for #OV runs in near-linear time for all dimensions d = o(log^2 n). Previously, even no truly-subquadratic time algorithm was known for d = omega(log n). - Arthur-Merlin Communication Protocols and Faster Satisfying-Pair Algorithms. Our second connection is that a fast AM^{cc} protocol for a function f implies a faster-than-bruteforce algorithm for f-Satisfying-Pair. Using the classical Goldwasser-Sisper AM protocols for approximating set size, we obtain a new algorithm for approximate Max-IP_{n,c log n} in time n^{2 - 1/O(log c)}, matching the state-of-the-art algorithms in [Chen, CCC 2018]. We also apply our second connection to shed some light on long-standing open problems in communication complexity. We show that if the Longest Common Subsequence (LCS) problem admits a fast (computationally efficient) AM^{cc} protocol (polylog(n) complexity), then polynomial-size Formula-SAT admits a 2^{n - n^{1-delta}} time algorithm for any constant delta > 0, which is conjectured to be unlikely by a recent work [Abboud and Bringmann, ICALP 2018]. The same holds even for a fast (computationally efficient) PH^{cc} protocol

An Improved Algorithm for Incremental DFS Tree in Undirected Graphs

Depth first search (DFS) tree is one of the most well-known data structures for designing efficient graph algorithms. Given an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges, the textbook algorithm takes $O(n+m)$ time to construct a DFS tree. In this paper, we study the problem of maintaining a DFS tree when the graph is undergoing incremental updates. Formally, we show: Given an arbitrary online sequence of edge or vertex insertions, there is an algorithm that reports a DFS tree in $O(n)$ worst case time per operation, and requires $O\left(\min\{m \log n, n^2\}\right)$ preprocessing time. Our result improves the previous $O(n \log^3 n)$ worst case update time algorithm by Baswana et al. and the $O(n \log n)$ time by Nakamura and Sadakane, and matches the trivial $\Omega(n)$ lower bound when it is required to explicitly output a DFS tree. Our result builds on the framework introduced in the breakthrough work by Baswana et al., together with a novel use of a tree-partition lemma by Duan and Zhan, and the celebrated fractional cascading technique by Chazelle and Guibas