Deposition Characteristics of Firebrands on and Around Rectangular Cubic Structures

The focus of the present work is on the deposition of firebrands in a flow over a rectangular cubic block representative of a structure in wildland-urban interface (WUI). The study was carried out by physics based modeling where the wind flow turbulence was dealt with by large eddy simulation (LES) and firebrands were treated by Lagrangian tracking. The Lagrangian equations coupled with the flow solver, accounted for both translational and rotational motions as well as thermochemical degradation of firebrands, assumed to be cylindrical. The dimensions of the structure were varied from 3 to 9 m in the simulations for a parametric study. The simulations were carried out by tracking many firebrands randomly released with a uniform distribution from a horizontal plane 35 m above the ground into the computational domain. The coordinates of the deposited firebrands were used to calculate their normalized number density (number of landed firebrands per unit surface area) to quantify their deposition pattern. On the leewardside of the block, an area, referred to as the safe zone, was identified right behind the structure where firebrands never deposit. The size of the safe zone in the direction perpendicular to the wind was nearly identical to the width of the structure. The length of the safe zone in the wind direction was proportional to the height of the structure. The leeward face of the blocks was never hit by a firebrand. The windward face was hit by many more firebrands than the lateral faces but much less than the top face. The distribution of the number density of the deposited firebrands on the top face was found to be correlated with the flow separation and reattachment on this face.

General method for including Stueckelberg fields

A systematic procedure is proposed for inclusion of Stueckelberg fields. The procedure begins with the involutive closure when the original Lagrangian equations are complemented by all the lower order consequences. The Stueckelberg field is introduced for every consequence included into the closure. The generators of the Stueckelberg gauge symmetry begin with the operators generating the closure of original system. These operators are not assumed to be a generators of gauge symmetry of any part of the original action, nor are they supposed to form an on shell integrable distribution. With the most general closure generators, the consistent gauge invariant theory is iteratively constructed, without obstructions at any stage. The Batalin–Vilkovisky form of inclusion of the Stueckelberg fields is worked out and the existence theorem for the Stueckelberg action is proven.

The minimum deformation retract on the wormhole spacetime

In this paper, we investigate the topology of a wormhole from the viewpoint of the theory of retracting and var-folding. We deduce the equatorial geodesics on the line element of the wormhole and discuss the minimum deformation retract related to this space. Using the Lagrangian equations we find that there is a type of minimum retraction of a wormhole with associated topology. We also extend the result to the [Formula: see text]-dimensional wormhole and show that the end limit of var-folding is 0-dimensional wormhole and obtain the relation between limit var-folding and limit retraction. We find a new application in geometric topology and astrophysics.

Bipartite Consensus Control for a Swarm of Robots

This paper studies the bipartite consensus problem of a swarm of robots whose dynamics are formulated by Lagrangian equations. Two distributed bipartite consensus control protocols are proposed for a swarm of robots without a leader or with a virtual leader. For the nonleader case, the networked Lagrangian system can reach static bipartite consensus under the control protocol developed, and the final convergent states can be explicitly determined by the specific structure of the Laplacian matrix associated with the cooperative–competitive network topology. For the virtual leader case, all the followers can track the leader's state in a bipartite formation to realize bipartite tracking consensus. Finally, the simulation results are given to verify the theoretical results.

Lagrangian equations of motion. Conservation laws

This chapter addresses the invariance of the Lagrangian equations of motion under the coordinate to transformation, the transformation of the energy and generalised momenta under the coordinate transformation. The integrals of motion for a particle moving in the field with a given symmetry to the Noether’s theorem, the Lagrangian functions, and the Lagrangian equations of motion for the electromechanical system. The authors also discuss the influence of constraints and friction on the motion of a system, the virial theorem and its generalization in the presents of a magnetic field, and an additional integral of motion for a system of three interacting particles.

Lagrangian equations of motion. Conservation laws

This chapter addresses the invariance of the Lagrangian equations of motion under the coordinate to transformation, the transformation of the energy and generalised momenta under the coordinate transformation. The integrals of motion for a particle moving in the field with a given symmetry to the Noether’s theorem, the Lagrangian functions, and the Lagrangian equations of motion for the electromechanical system. The authors also discuss the influence of constraints and friction on the motion of a system, the virial theorem and its generalization in the presents of a magnetic field, and an additional integral of motion for a system of three interacting particles.