Weighted Modulo Orientations of Graphs

This dissertation focuses on the subject of nowhere-zero flow problems on graphs. Tutte\u27s 5-Flow Conjecture (1954) states that every bridgeless graph admits a nowhere-zero 5-flow, and Tutte\u27s 3-Flow Conjecture (1972) states that every 4-edge-connected graph admits a nowhere-zero 3-flow. Extending Tutte\u27s flows conjectures, Jaeger\u27s Circular Flow Conjecture (1981) says every 4k-edge-connected graph admits a modulo (2k+1)-orientation, that is, an orientation such that the indegree is congruent to outdegree modulo (2k+1) at every vertex. Note that the k=1 case of Circular Flow Conjecture coincides with the 3-Flow Conjecture, and the case of k=2 implies the 5-Flow Conjecture. This work is devoted to providing some partial results on these problems. In Chapter 2, we study the problem of modulo 5-orientation for given multigraphic degree sequences. We prove that a multigraphic degree sequence d=(d1,..., dn) has a realization G with a modulo 5-orientation if and only if di≤1,3 for each i. In addition, we show that every multigraphic sequence d=(d1,..., dn) with min{1≤i≤n}di≥9 has a 9-edge-connected realization that admits a modulo 5-orientation for every possible boundary function. Jaeger conjectured that every 9-edge-connected multigraph admits a modulo 5-orientation, whose truth would imply Tutte\u27s 5-Flow Conjecture. Consequently, this supports the conjecture of Jaeger. In Chapter 3, we show that there are essentially finite many exceptions for graphs with bounded matching numbers not admitting any modulo (2k+1)-orientations for any positive integers t. We additionally characterize all infinite many graphs with bounded matching numbers but without a nowhere-zero 3-flow. This partially supports Jaeger\u27s Circular Flow Conjecture and Tutte\u27s 3-Flow Conjecture. In 2018, Esperet, De Verclos, Le and Thomass introduced the problem of weighted modulo orientations of graphs and indicated that this problem is closely related to modulo orientations of graphs, including Tutte\u27s 3-Flow Conjecture. In Chapter 4 and Chapter 5, utilizing properties of additive bases and contractible configurations, we reduced the Esperet et al\u27s edge-connectivity lower bound for some (signed) graphs families including planar graphs, complete graphs, chordal graphs, series-parallel graphs and bipartite graphs, indicating that much lower edge-connectivity bound still guarantees the existence of such orientations for those graph families. In Chapter 6, we show that the assertion of Jaeger\u27s Circular Flow Conjecture with k=2 holds asymptotically almost surely for random 9-regular graphs

Modelling of Temporal‐Spatial Distribution of Airplane Wake Vortex for Scattering Analysis

Aircraft wake vortex is a pair of intensive counter‐rotating airflow generated by a flying aircraft. Wake vortex is one of the most dangerous hazards in aviation because it may cause a following aircraft to roll out of control, particularly during the taking off and landing phases. The real‐time detection of wake vortex is a frontier scientific problem emerging from many fields like aviation safety and atmospheric physics, and the dynamics and scattering characteristics of it remain as key problems to develop corresponding detection technologies. This chapter aims at presenting a simulation scheme for the dynamics of wake vortex under different weather conditions. For wake vortex generated in clear air, changes of the atmospheric dielectric constant produced by the density variation and water vapour variation are analysed; for wake vortex generated in rainy condition, the raindrop distribution in the wake vortex is also analysed. Both of them are essential for further analysing the scattering characteristics and developing new detection algorithms

2-Eth­oxy­ethyl (Z)-2-cyano-3-[(N-phenyl­carbamo­yl)amino]­prop-2-enoate

The crystal structure of the title compound, C15H17N3O4, is stabilized by inter­molecular N—H⋯N hydrogen bonds. An intra­molecular N—H⋯O hydrogen bond also occurs

3-Benzyl­amino-2-cyano-N-[N-(2-fluoro­phenyl)­carbamo­yl]-3-(methyl­sulfanyl)acryl­amide

In the crystal structure of the title compound, C19H17FN4O2S, mol­ecules are linked via pairs of N—H⋯N inter­actions, forming centrosymmetric dimers. Two intra­molecular N—H⋯O hydrogen bonds stabilize the mol­ecular conformation

Bridge’s Overall Structural Scheme Analysis in High Seismic Risk Permafrost Regions

The mechanism of pile-soil reaction in frozen ground is not clear at present, but it is obvious that the reduction of dead weight will be beneficial to the seismic resistance of bridges. In view of the limited bridge engineering practice in high seismic risk permafrost regions, the paper addressed the structural performance of the superstructure and its effect on piles in these special regions. Four superstructures with different dead weights were compared, and bored piles were designed. Numerical simulations were implemented to investigate the refreezing time of the bored pile foundation. The concrete pile cooled rapidly in the first two days. The refreezing times of the GFRP, prestressed concrete T-girder, integrated composite girder, and MVFT girder were 15d, 37d, 39d, and 179d, respectively. The refreezing time of a pile in the same soil layer is mainly affected by the pile’s diameter, and it is significantly correlated to the square of the pile diameter. It reflects that the selection of bridge superstructures in the permafrost region is very important, which has been ignored in previous studies. The pile length and pile diameter of the lighter superstructure can be shorter and smaller to reduce the refreezing time and alleviate the thermal disturbance. Doi: 10.28991/CEJ-2022-08-07-01 Full Text: PD

Thermally Responsive Fluid Behaviors in Hydrophobic Nanopores

A fundamental understanding of the thermal effects on nanofluid behaviors is critical for developing and designing innovative thermally responsive nanodevices. Using molecular dynamics (MD) simulation and experiment, we investigate the temperature-dependent intrusion/adsorption of water molecules into hydrophobic nanopores (carbon nanotubes and nanoporous carbon) and the underlying mechanisms. The critical infiltration pressure is reduced for elevated temperature or increased pore size. The variation of wettability is related to the thermally responsive fluid characteristics, such as the surface tension and contact angle, which arise from the variations of multiple atomic variables including the confined water density, hydrogen bond, and dipole orientation. With thermal perturbation, most of these physical quantities are found to be more significantly influenced in the confined nanoenvironment than in the bulk. By utilizing the prominent thermal effect at the nanoscale, the feasibility and prospective efficiency of employing nanofluidics for energy storage, actuation, and thermal monitoring are discussed

Language Prompt for Autonomous Driving

A new trend in the computer vision community is to capture objects of interest following flexible human command represented by a natural language prompt. However, the progress of using language prompts in driving scenarios is stuck in a bottleneck due to the scarcity of paired prompt-instance data. To address this challenge, we propose the first object-centric language prompt set for driving scenes within 3D, multi-view, and multi-frame space, named NuPrompt. It expands Nuscenes dataset by constructing a total of 35,367 language descriptions, each referring to an average of 5.3 object tracks. Based on the object-text pairs from the new benchmark, we formulate a new prompt-based driving task, \ie, employing a language prompt to predict the described object trajectory across views and frames. Furthermore, we provide a simple end-to-end baseline model based on Transformer, named PromptTrack. Experiments show that our PromptTrack achieves impressive performance on NuPrompt. We hope this work can provide more new insights for the autonomous driving community. Dataset and Code will be made public at \href{https://github.com/wudongming97/Prompt4Driving}{https://github.com/wudongming97/Prompt4Driving}