Related papers: An experiment of the complexity of sliding block p…
A sliding puzzle is a combination puzzle where a player slide pieces along certain routes on a board to reach a certain end-configuration. In this paper, we propose a novel measurement of complexity of massive sliding puzzles with…
The harmonic map heat flow is a geometric flow well known to produce solutions whose gradient blows up in finite time. A popular model for investigating the blow-up is the heat flow for maps $\mathbb R^{d}\to S^{d}$, restricted to…
Multimaterial heat diffusion can be a challenging numerical problem when the material boundaries are misaligned with the numerical grid. Even when the boundaries start out aligned, they typically become misaligned through hydrodynamic…
We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single…
We introduce and study a conformal heat flow of harmonic maps defined by an evolution equation for a pair consisting of a map and a conformal factor of metric on the two-dimensional domain. This flow is designed to postpone finite time…
This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these…
We build up a decomposition for the flow generated by the heat equation with a real analytic memory kernel. It consists of three components: The first one is of parabolic nature; the second one gathers the hyperbolic component of the…
High power density systems require efficient cooling to maintain their thermal performance. Despite this, as systems get larger and more complex, human practice and insight may not suffice to determine the desired thermal management system…
This paper presents our 2nd place solution for the NuPlan Challenge 2023. Autonomous driving in real-world scenarios is highly complex and uncertain. Achieving safe planning in the complex multimodal scenarios is a highly challenging task.…
Microfluidic cooling has been recognized as one of the most promising solutions to achieve efficient thermal management for three-dimensional integrated circuits (3DICs). It enables more opportunities to architect 3DICs with different die…
Clustering methods must be tailored to the dataset it operates on, as there is no objective or universal definition of ``cluster,'' but nevertheless arbitrariness in the clustering method must be minimized. This paper develops a…
We present a novel hybrid incompressible flow/material point method solver for simulating the combustion of flammable solids. Our approach utilizes a sparse grid representation of solid materials in the material point method portion of the…
Simulations are reported to investigate solid superheating and liquid supercooling of two-dimensional (2D) systems with a Yukawa interparticle potential. Motivated by experiments where a dusty plasma is heated and then cooled suddenly, we…
We present a new explicit and stable numerical algorithm to solve the homogeneous heat equation. We illustrate the performance of the new method in the cases of two 2D systems with highly inhomogeneous random parameters. Spatial…
We analyze the finite-time blow-up of solutions of the heat flow for $k$-corotational maps $\mathbb R^d\to S^d$. For each dimension $d>2+k(2+2\sqrt{2})$ we construct a countable family of blow-up solutions via a method of matched…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
Motivated by applications to 3D printing, this paper presents two algorithms for calculating an ensemble of solutions to heat conduction problems. The ensemble average is the most likely temperature distribution and its variance gives an…
This paper is concerned with the popular Sudoku problem. We proposed a warm restart strategy for solving Sudoku puzzles, based on the sparse optimization technique. Furthermore, we defined a new difficulty level for Sudoku puzzles. The…
In this paper, we use stochastic polynomial optimization to derive high-performance operating strategies for heating networks with uncertain or variable demand. The heat flow in district heating networks can be regulated by varying the…
I use a simple analytical model to show that simple heat conduction models cannot significantly suppress cluster cooling flows. I build a static medium where heat conduction globally balances radiative cooling, and then perturb it. I show…