Self-similar solutions to fully nonlinear curvature flows by high powers of curvature

In this paper, we investigate closed strictly convex hypersurfaces in ℝ n + 1 {\mathbb{R}^{n+1}} which shrink self-similarly under a large family of fully nonlinear curvature flows by high powers of curvature. When the speed function is given by powers of a homogeneous of degree 1 and inverse concave function of the principal curvatures with power greater than 1, we prove that the only such hypersurfaces are round spheres. We also prove that slices are the only closed strictly convex self-similar solutions to such curvature flows in the hemisphere 𝕊 + n + 1 {\mathbb{S}^{n+1}_{+}} with power greater than or equal to 1.

The “Backward Looking” Effect in the Continuum Model Considering a New Backward Equilibrium Velocity Function.

In this paper, a new continuum traffic model is developed considering the backward-looking effect through a new positive backward equilibrium speed function. As compared with the conventional full velocity difference model, the backward equilibrium velocity function, which is largely acceptably grounded from mathematical and physical perspectives, plays an important role in significantly enhancing the stability of the traffic flow field. A linear stability condition is derived to demonstrate the flow neutralization capacity of the model, whereas the Korteweg–de Vries–Burgers equation and the attendant analytical solution are deduced using nonlinear analysis to observe the traffic flow behavior near the neutral stability condition. A numerical simulation, used to determine the flow stability enhancement efficiency of the model, is also conducted to verify the theoretical results.

On the edit distance function of the random graph

Given a hereditary property of graphs $\mathcal{H}$ and a $p\in [0,1]$ , the edit distance function $\textrm{ed}_{\mathcal{H}}(p)$ is asymptotically the maximum proportion of edge additions plus edge deletions applied to a graph of edge density p sufficient to ensure that the resulting graph satisfies $\mathcal{H}$ . The edit distance function is directly related to other well-studied quantities such as the speed function for $\mathcal{H}$ and the $\mathcal{H}$ -chromatic number of a random graph. Let $\mathcal{H}$ be the property of forbidding an Erdős–Rényi random graph $F\sim \mathbb{G}(n_0,p_0)$ , and let $\varphi$ represent the golden ratio. In this paper, we show that if $p_0\in [1-1/\varphi,1/\varphi]$ , then a.a.s. as $n_0\to\infty$ , \begin{align*} {\textrm{ed}}_{\mathcal{H}}(p) = (1+o(1))\,\frac{2\log n_0}{n_0} \cdot\min\left\{ \frac{p}{-\log(1-p_0)}, \frac{1-p}{-\log p_0} \right\}. \end{align*} Moreover, this holds for $p\in [1/3,2/3]$ for any $p_0\in (0,1)$ . A primary tool in the proof is the categorization of p-core coloured regularity graphs in the range $p\in[1-1/\varphi,1/\varphi]$ . Such coloured regularity graphs must have the property that the non-grey edges form vertex-disjoint cliques.

Simplified Swarm Optimization for the Heterogeneous Fleet Vehicle Routing Problem with Time-Varying Continuous Speed Function

Transportation planning has been established as a key topic in the literature and practices of social production, especially in urban contexts. To consider traffic environment factors, more and more researchers are taking time-varying factors into account when scheduling their logistic activities. The time-dependent vehicle routing problem (TDVRP) is an extension of the classical Vehicle Routing Problem with Time Windows (VRPTW) by determining a set of optimal routes serving a set of customers within specific time windows. However, few of them use the continuous speed function to express the time-varying. In practice, many vehicle routing problems are addressed by a fleet of heterogeneous vehicles with different capacities and travel costs including fix costs and variable costs. In this study, a Heterogeneous Fleet Vehicle Routing Problem (HFPRP) Time-Varying Continuous Speed Function has been proposed. The objective is to minimize distribution costs, which contained fixed costs of acquiring and variable fuel costs. To address this problem, our research developed a mathematical model and proposed a Simplified Swarm Optimization (SSO) heuristic for HFVRP with Time-Varying Continuous Speed Function.

Development of alternative steering models for ev bus: a preliminary study on the conversion of hydraulic to electric power steering

This study aims to develop alternative steering models for the EV bus. The EV bus uses its energy source from the main 384 VDC 300 Ah battery and the secondary battery with a capacity of 25.8 VDC 100 Ah. The use of energy in this electric bus is divided into the main components, namely the BLDC motor as the main drive of 200 kW, 15 kW of air conditioning, 7.5 kW of hydraulic power steering, a compressor for the air braking system of 4 kW, and accessory components. The other is 2.4 kW. It is expected that this 7.5 kW electric power can be reduced by an electric system by up to 20 %. This research will study the steering system with an electric power system (EPS) to convert the hydraulic steering system (HPS). With this EPS system, it is hoped that controlling the vehicle’s motion towards the steer by wire will be easier. Initially, data were collected from the types of large vehicles from various well-known brands about the steering system used. A large commercial vehicle that purely uses EPS is not yet found. The model developed for EPS on this electric bus is through the reverse engineering method by redrawing all the components involved in the previous steering system. Because this type of EV bus is included in the upper mid-size class, this paper proposes two new EPS models, namely the addition of an assist motor on the drag link and on the steering rack. The links involved in this system are wheel drive, steering column, lower steering column, rack and pinion gear, assist motor, drop link, drag link, drop link extension, drag link extension, tie rod, knuckle, kingpin, tire, axle beam and several others. The values of stiffness, inertia, and damping of each link will affect the driver’s torque and the assist motor as a wheel speed function on this electric bus. The steering structure of the EV bus consists of a truss structure and a frame structure with a kinematic structure consisting of two four-bar linkages joined together

A new underwater positioning model based on average sound speed

The layout of seafloor datum points is the key to constructing the seafloor geodetic datum network, and a reliable underwater positioning model is the prerequisite for achieving precise deployment of the datum points. The traditional average sound speed positioning model is generally adopted in underwater positioning due to its simple and efficient algorithm, but it is sensitive to incident angle related errors, which lead to unreliable positioning results. Based on the relationship between incident angle and sound speed, the sound speed function model considering the incident angle has been established. Results show that the accuracy of positioning is easily affected by errors related to the incident angle; the new average sound speed correction model based on the incident angle proposed in this paper is used to significantly improve the underwater positioning accuracy.

The “Backward Looking” Effect in the Continuum Model Considering a New Backward Equilibrium Velocity Function

In this paper, a new continuum traffic model is developed considering the backward-looking effect through a new positive backward equilibrium speed function. As compared with the conventional full velocity difference model, the backward equilibrium velocity function, which is largely acceptably grounded from mathematical and physical perspectives, plays an important role in significantly enhancing the stability of the traffic flow field. A linear stability condition is derived to demonstrate the flow neutralization capacity of the model, whereas the Korteweg–de Vries–Burgers equation and the attendant analytical solution are deduced using nonlinear analysis to observe the traffic flow behavior near the neutral stability condition. A numerical simulation, used to determine the flow stability enhancement efficiency of the model, is also conducted to verify the theoretical results.

Energy optimal motion planning of a 14-DOF biped robot on 3D terrain using a new speed function incorporating biped dynamics and terrain geometry

In this paper, a new method is proposed to find a feasible energy-efficient path between an initial point and goal point on uneven terrain and then to optimally traverse the path. The path is planned by integrating the geometric features of the uneven terrain and the biped robot dynamics. This integrated information of biped dynamics and associated cost (energy) for moving toward the goal point is used to define the value of a new speed function at each point on the discretized surface of the terrain. The value is stored as a matrix called the dynamic transport cost (DTC). The path is obtained by solving the Eikonal equation numerically by fast marching method (FMM) on an orthogonal grid, by using the information stored in the DTC matrix. One step of walk on uneven terrain is characterized by 10 footstep parameters (FSPs); these FSPs represent the position of swinging foot at the starting and ending time of the walk, orientation, and state (left or right) of support foot. A walking dataset was created for different walking conditions (FSPs), which the biped robot is likely to encounter when it has to walk on the uneven terrain. The corresponding energy optimal hip and foot trajectory parameters (HFTPs) are obtained by optimization using a genetic algorithm (GA). The created walk dataset is generalized by training a feedforward neural network (NN) using the scaled conjugate gradient (SCG) algorithm. The Foot placement planner gives a sequence of foot positions and orientations along the obtained path, which is followed by the biped robot by generating real-time optimal foot and hip trajectories using the learned NN. Simulation results on different types of uneven terrains validate the proposed method.

Thermodynamic-informed machine learning for pressure-sensitive plasticity model

<p>This talk will present a machine learning framework that builds interpretable macroscopic surrogate elasto-plasticity models inferred from sub-scale direction numerical simulations (DNS) or experiments with limited data. To circumvent the lack of interpretability of the classical black-box neural network, we introduce a higher-order supervised machine learning technique that generates components of elasto-plastic models such as elasticity functional, yield function, hardening mechanisms, and plastic flow. The geometrical interpretation in the principal stress space allows us to use convexity and smoothness to ensure thermodynamic consistency. The speed function from the Hamilton-Jacobi equation is deduced from the DNS data to formulate hardening and non-associative plastic flow rules governed by the evolution of the low-dimensional descriptors. By incorporating a non-cooperative game that determines the necessary data to calibrate material models, the machine learning generated model is continuously tested, calibrated, and improved as new data guided by the adversarial agents are generated. A graph convolutional neural network is used to deduce low-dimensional descriptors that encodes the evolutional of particle topology under path-dependent deformation and are used to replace internal variables. The resultant constitutive laws can be used in a finite element solver or incorporated as a loss function for the physical-informed neural network run physical simulations.</p>

Study of the bullet rifling linear traces matching technology based on deep learning

The practical applications of the bullet rifling linear traces are severely restricted due of the complex shape and strong randomness. We propose a model of position and attitude parameters distribution at the end of specimens based on multimode elastic driving adaptive control method to achieve feature decomposition and error compensation correction of the attitude transformation of the specimen seat. The isolated forest algorithm was employed for abnormal processing of detection signals, non-small features were removed based on variable-scale morphological filtering algorithm, the trace curve profiles were extracted using the multiscale registration framework, and the square speed function optimization elastic shape metric algorithm was used to map the profiles into an embedding. Afterwards, a parametric shared conjoined triple deep learning model suitable for feature tracing and optimization of triplet selection and data augmentation strategies is proposed. This system is trained by minimizing a triplet loss function so that a similarity measure is defined by the L2 distance in this embedding. Finally, the trained model is used to do the similarity matching for the test set, try to solve the technical problems in the manual construction of guns and the inspection of bullet rifling traces.