Dynamic relaxation (DR) is the most widely used approach for static equilibrium analyses. Specifically, DR compels dynamic systems to converge to a static equilibrium through the addition of fictitious damping. DR methods are classified by the method in which fictitious damping is applied. Conventional DR methods use a fictitious mass matrix to increase the fictitious damping while maintaining numerical stability. There are many calculation methods for the fictitious mass matrix; however, it is difficult to select the appropriate method. In addition, these methods require a stiffness matrix of a model, which makes it difficult to apply nonlinear models. To resolve these problems, a new DR method that uses continuous kinetic damping (CKDR) is proposed in this study. The proposed method does not require the fictitious mass matrix and any tuning coefficients, and it possesses a second-order convergence rate. The aforementioned advantages are unique and significant when compared to those of conventional methods. The stability and convergence rate were analyzed by using an eigenvalue analysis and demonstrated by simulating nonlinear models of a pendulum and cable. Simple but representative models were used to clearly demonstrate the features of the proposed DR method and to enable the reproducibility of the verification results.

The slip ratio, which is the ratio of the slip speed to the driving speed, is an essential input in tire models for vehicle-driving analysis. At a driving speed of zero, because the denominator of the slip ratio is zero, singularity is crucial for stable numerical analysis for examining the low-speed dynamic behavior of vehicles. A lagged slip ratio is widely adopted in most commercial software to prevent such failures, but this causes oscillation and requires a tuning parameter. Moreover, it increases the computational complexity because differential equations are employed to define the slip. To overcome this, researchers proposed a modified slip ratio without a differential equation; however, a tuning parameter was still required. Herein, we propose an advanced slip-ratio calculation method that allows stable simulation without the use of a differential equation or tuning parameter in the explicit integration. The accuracy and stability of the proposed slip ratio were verified against other methods via braking simulation. The proposed method showed very stable results compared to conventional methods and did not fail even with explicit integration. Furthermore, in the case of implicit integration, it prevented step-size reduction.

Dynamic relaxation (DR) is a widely used numerical method to determine the static equilibrium of a dynamic system. However, it is difficult to apply conventional DR methods to nonlinear models because they require estimation of a stiffness matrix of the model. To resolve the forementioned problem, a new dynamic relaxation method using continuous kinetic damping (CKDR) was proposed in previous research. The CKDR method does not require any model parameters including the stiffness matrix, and it possesses absolute stability and a second-order convergence rate. However, the convergence rate is proportional to square of the step size, and this may result in a low convergence rate if the selected step size is excessively small. This problem leads to difficulties in the practical use of CKDR. Thus, an adaptive step-size method is proposed in this paper to control the convergence rate of CKDR. The proposed method estimates natural frequency of the model and determines adaptive step size. Static equilibrium simulations were performed for three different models to verify the method. The results revealed that the computational cost of CKDR with a variable step size was very efficient when compared to fixed step sizes and that the convergence rate was also controlled as intended. In addition, the lowest natural frequencies of models in static equilibrium were accurately estimated.

A tire model is essential for vehicle dynamics simulations. The slip ratio of a tire model affects the stability of the simulation. The traditional slip ratio frequently causes numerical problems in low-speed driving simulations when the longitudinal speed approaches zero. To solve this phenomenon, many researchers have proposed various solutions by adding tuning parameters or defining the slip ratio through differential equations. However, these methods have the disadvantages of reducing the reliability of the tire model and increasing the computational complexity. In Part 1 of this paper, we proposed a method to calculate the advanced slip ratio without using tuning parameters or differential equations. This method guarantees the numerical stability of a simulation by limiting the time constant of the wheel dynamics model to be greater than the marginal time constant of the explicit integrator. In Part 1, just the longitudinal slip ratio was considered; thus, the problem of numerical instability of the slip ratio at low speed also occurs in the lateral direction. Therefore, in the second part of this study, the advanced slip ratio is extended to the lateral direction. Furthermore, the proposed method is applied to a bicycle model to verify its performance in a driving simulation. Finally, the simulation results are analyzed to verify the validity and stability of the advanced slip ratio in both directions.

Thirty-nine consecutive patients with symptomatic AV nodal reentrant tachycardia (AVNRT) underwent temperature guided slow AV nodal pathway ablation (group 1). Forty-three consecutive patients undergoing nontemperature guided slow AV nodal pathway ablation late in our experience compose the control population (group 2). Slow pathway ablation was achieved in all patients of both groups. The mean fluoroscopy and ablation times for group 1 were significantly shorter than for group 2 (26.1 +/- 14.9 vs 33.9 +/- 18.9 min, P < 0.05; 19.9 +/- 12.1 vs 30.9 +/- 23.3 min, P < or = 0.02). There were no episodes of coagulum formation in group 1, while there were 15 episodes (7.1% of energy applications) in group 2 (P = 0.0006) despite a significantly higher applied power in group 1 (53.4 +/- 25.1 vs 35.6 +/- 9.5W, P = 0.0001). Successful energy applications were associated with significantly higher temperatures than unsuccessful applications in group 1 (55.6 degrees +/- 5.8 degrees C vs. 52.9 degrees +/- 6.8 degrees C, P < or = 0.03). The minimum temperature required for successful ablation was 48 degrees C for two patients (5%) and was > or = 50 degrees C for the remainder of patients (37/39 [95%]). The catheter ablation system used in this study was safe, effective, and prevented coagulum formation while delivering relatively high power. In addition, shorter ablation times and radiation exposure were seen with this system. Although successful energy applications and the production of junctional rhythm were associated with higher achieved temperatures, temperature alone did not predict either endpoint. Future prospective, randomized trials are needed to confirm these findings and further evaluate the value of temperature monitoring.