On the Circumference of 3-Connected Cubic Triangle-Free Plane Graphs

The circumference of a graph G is the length of a longest cycle in G , denoted by cir G . For any even number n , let c n = min { cir G | G is a 3-connected cubic triangle-free plane graph with n vertices}. In this paper, we show that an upper bound of c n is n + 1 − 3 ⌊ n / 136 ⌋ for n ≥ 136 .

Exploration of Indoor Barrier-Free Plane Intelligent Lofting System Combining BIM and Multi-Sensors

Lofting is an essential part of construction projects and the high quality of lofting is the basis of efficient construction. However, the most common method of lofting currently which uses the total station in a multi-person cooperative way consumes much manpower and time. With the rapid development of remote sensing and robot technology, using robots instead of manpower can effectively solve this problem, but few scholars study this. How to effectively combine remote sensing and robots with lofting is a challenging problem. In this paper, we propose an intelligent lofting system for indoor barrier-free plane environment, and design a high-flexibility, low-cost autonomous mobile robot platform based on single chip microcomputer, Micro Electro Mechanical Systems-Inertial Measurement Unit (MEMS-IMU), wheel encoder, and magnetometer. The robot also combines Building Information Modeling (BIM) laser lofting instrument and WIFI communication technology to get its own position. To ensure the accuracy of localization, the kinematics model of Mecanum wheel robot is built, and Extended Kalman Filter (EKF) is also used to fuse multi-sensor data. It can be seen from the final experimental results that this system can significantly improve lofting efficiency and reduce manpower.

A General Free Plane Wave Ansatz to The Classcal SU(2) Yang-Mills Theory: with Application to Gravity

In this project, the free plane wave conditions were imposed on the classical SU(2) gauge field to obtain a new general Ansatz. Although afterwards it was found that this Ansatz is similar to a special case of an existing Ansatz[1], there are important differences. The idea of this Ansatz was later applied to the other nonlinear interaction of nature, namely gravity. However, this effort encountered some complications, such as the lack of an exact definition or interpretation of energy and momentum of gravitational waves.

Freeness versus maximal global Tjurina number for plane curves

We give a characterisation of nearly free plane curves in terms of their global Tjurina numbers, similar to the characterisation of free curves as curves with a maximal Tjurina number, given by A. A. du Plessis and C.T.C. Wall. It is also shown that an irreducible plane curve having a 1-dimensional symmetry is nearly free. A new numerical characterisation of free curves and a simple characterisation of nearly free curves in terms of their syzygies conclude this paper.

Analysis of Flow Evolution and Thermal Instabilities in the Near-Nozzle Region of a Free Plane Laminar Jet

This work focuses on the evolution of a free plane laminar jet in the near-nozzle region. The jet is buoyant because it is driven by a continuous addition of both buoyancy and momentum at the source. Buoyancy is given by a temperature difference between the jet and the environment. To study the jet evolution, numerical simulations were performed for two Richardson numbers: the one corresponding to a temperature difference slightly near the validity of the Boussinesq approximation and the other one corresponding to a higher temperature difference. For this purpose, a time dependent numerical model is used to solve the fully dimensional Navier-Stokes equations. Density variations are given by the ideal gas law and flow properties as dynamic viscosity and thermal conductivity are considered nonconstant. Particular attention was paid to the implementation of the boundary conditions to ensure jet stability and flow rates control. The numerical simulations were also reproduced by using the Boussinesq approximation to find out more about its pertinence for this kind of flows. Finally, a stability diagram is also obtained to identify the onset of the unsteady state in the near-nozzle region by varying control parameters of momentum and buoyancy. It is found that, at the onset of the unsteady state, momentum effects decrease almost linearly when buoyancy effects increase.

A Novel Shape-Free Plane Quadratic Polygonal Hybrid Stress-Function Element

A novel plane quadratic shape-free hybrid stress-function (HS-F) polygonal element is developed by employing the principle of minimum complementary energy and the fundamental analytical solutions of the Airy stress function. Without construction of displacement interpolation function, the formulations of the new model are much simpler than those of the displacement-based polygonal elements and can be degenerated into triangular or quadrilateral elements directly. In particular, it is quite insensitive to various mesh distortions and even can keep precision when element shape is concave. Furthermore, the element does not show any spurious zero energy modes. Numerical examples show the excellent performance of the new element, denoted by HSF-AP-19β, in both displacement and stress solutions.

Computational Modeling and Simulations of Isothermal Plane (Linear) Air Jet Velocity Profile for Slot Diffusers

In the present work, computational modeling and simulations of isothermal plane (linear) air jet velocity profile for slot diffusers are performed. Plane air jets are formed by linear slots or rectangular openings with a large aspect ratio. Numerical simulations are performed using the commercial computational fluid dynamics (CFD) code ANSYS FLUENT. Three plane air jet flow simulations will be investigated such as free plane (linear) jets, attached jets, and air flow through a slot diffuser in a room setting. The purpose of simulating the free plane jet through a slot diffuser is to study the behavior of jet velocity profile that is not blocked by side walls or ceilings. The jet velocity profile is modified when obstructed by the walls and the air jet desires to attach to the surfaces along its path. For this reason, attached jet simulations through a slot diffuser will be conducted. The CFD study of plane air jet flows will eventually be extended to jet flows through a slot diffuser to a room to investigate the fluid flow behavior that enters a room under a ceiling. In addition, effects of two-equation turbulence models such as standard, renormalization group (RNG), and realizable k-ε on the CFD simulations will be investigated. Predicted velocity profiles and decays of free plane jet through a slot diffuser will be validated with a semi-empirical model [1]. Predicted velocity profiles of attached jet simulations will also be compared with a semi-empirical expression [2]. The slot diffuser air flow simulations will be compared with experimental data by the work of Chen and Srebric [3]. All simulations will be conducted at a specified inlet air velocity. The effects of grid resolution are also examined. It is established that the standard k-ε turbulence model best simulates attached and free jet flows. The standard k-ε turbulence model is applied to a room setting under isothermal conditions. The results are compared with non-isothermal experimental data [3]. It is shown that temperature which is a passive scalar has less influence on the flow pattern at a high air velocity than at a low air velocity in a room setting.