Influence of a non-condensable gas on mixing of a melt with water in a stratified configuration

The influence of bubbles of hot non-condensable gas formed at the interface between the melt and water on the formation of a mixture of melt with water capable of producing steam explosions is considered. The dynamics of such a bubble in subcooled water is analyzed numerically in a one-dimensional spherically symmetric approximation. It is shown that with significant initial superheat of the bubble relative to the water, a rapid drop in pressure in the bubble occurs due to strong heat removal into the water. This leads to the collapse of the bubble and the appearance of an accompanying flow of water. The results obtained made it possible to approximately describe the stage of collapse of the bubble as the polytropic process and to determine its index. The axisymmetric problem of the impact of the water jet on the surface of a melt during collapse of a gas bubble near the interface between the melt and water is numerically investigated. In this case, the obtained polytropic process equation is used to determine the pressure in the bubble. It is found that the resulting impact on the melt is capable of knocking out melt droplets into the water to a height of several centimeters, which leads to the formation of a layer of water mixed with the melt droplets, which is capable of producing strong steam explosions.

The uniqueness of the best non-symmetric $L_1$-approximant with a weight by $A_{\alpha ,\beta }$-subspace

The questions of the uniqueness of the best non-symmetric $L_1$-approximant with weight in the finite dimensional subspace and the connection of such tasks with $A_{\alpha ,\beta }$-subspaces were considered in this article. This result generalizes the known result of Kroo on the case of non-symmetric approximation.

Approximating Hamiltonian dynamics with the Nyström method

Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation technique whose runtime scales polynomially in the number of qubits and the Frobenius norm of the Hamiltonian. As an immediate application, we show that sample based quantum simulation, a type of evolution where the Hamiltonian is a density matrix, can be efficiently classically simulated under specific structural conditions. Our main technical contribution is a randomized algorithm for approximating Hermitian matrix exponentials. The proof leverages a low-rank, symmetric approximation via the Nyström method. Our results suggest that under strong sampling assumptions there exist classical poly-logarithmic time simulations of quantum computations.

Approximations, ghosts and derived equivalences

Approximation sequences and derived equivalences occur frequently in the research of mutation of tilting objects in representation theory, algebraic geometry and noncommutative geometry. In this paper, we introduce symmetric approximation sequences in additive categories and weakly n-angulated categories which include (higher) Auslander-Reiten sequences (triangles) and mutation sequences in algebra and geometry, and show that such sequences always give rise to derived equivalences between the quotient rings of endomorphism rings of objects in the sequences modulo some ghost and coghost ideals.

Efficient Inference for Untied MLNs

We address the problem of scaling up local-search or sampling-based inference in Markov logic networks (MLNs) that have large shared sub-structures but no (or few) tied weights. Such untied MLNs are ubiquitous in practical applications. However, they have very few symmetries, and as a result lifted inference algorithms--the dominant approach for scaling up inference--perform poorly on them. The key idea in our approach is to reduce the hard, time-consuming sub-task in sampling algorithms, computing the sum of weights of features that satisfy a full assignment, to the problem of computing a set of partition functions of graphical models, each defined over the logical variables in a first-order formula. The importance of this reduction is that when the treewidth of all the graphical models is small, it yields an order of magnitude speedup. When the treewidth is large, we propose an over-symmetric approximation and experimentally demonstrate that it is both fast and accurate.

POLYGONAL APPROXIMATION OF DIGITAL CURVE BASED ON REVERSE ENGINEERING CONCEPT

This paper applies reverse engineering on the Bresenham's line drawing algorithm [J. E. Bresenham, IBM System Journal, 4, 106–111 (1965)] for polygonal approximation of digital curve. The proposed method has a number of features, namely, it is sequential and runs in linear time, produces symmetric approximation from symmetric digital curve, is an automatic algorithm and the approximating polygon has the least non-zero approximation error as compared to other algorithms.