Because of the low convergence efficiency of the typical Vicsek model,a Vicsek with static summoning points(VSSP)algorithm based on the Vicsek model considering static summoning points is proposed.Firstly,the mathemat...Because of the low convergence efficiency of the typical Vicsek model,a Vicsek with static summoning points(VSSP)algorithm based on the Vicsek model considering static summoning points is proposed.Firstly,the mathematical model of the individual movement total cost on each summoning point is established.Then the individual classification rule is designed according to the initial state of the cluster to obtain the subclusters guided by each summoning point.Finally,the summoning factor is introduced to modify the course angle updating formula of the Vicsek model.To verify the effectiveness of the proposed algorithm and study the effect of the cluster summoning factor on the convergence rate,three groups of simulation experiments under different summoning factors are designed in this paper.To verify the superiority of the VSSP algorithm,the performance of the VSSP algorithm is compared with the classic algorithm by designing the algorithm performance comparison verification experiment.The results show that the algorithm proposed in this paper has good convergence and course angle consistency.The summoning factor is the sensitive factor of cluster convergence.This algorithm can provide a reference for efficient cluster segmentation movement.展开更多
In this paper, exact static conditions at the corner points for the bending of thickrectangular ptates are strictly. derived from the theorem of minimum potentialenerg[1].
A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance ...A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.展开更多
A simple method is proposed, for incremental static analysis of a set of inter-colliding particles, simulating 2D flow. Within each step of proposed algorithm, the particles perform small displacements, proportional t...A simple method is proposed, for incremental static analysis of a set of inter-colliding particles, simulating 2D flow. Within each step of proposed algorithm, the particles perform small displacements, proportional to the out-of-balance forces, acting on them. Numerical experiments show that if the liquid is confined within boundaries of a set of inter-communicating vessels, then the proposed method converges to a final equilibrium state. This incremental static analysis approximates dynamic behavior with strong damping and can provide information, as a first approximation to 2D movement of a liquid. In the initial arrangement of particles, a rhombic element is proposed, which assures satisfactory incompressibility of the fluid. Based on the proposed algorithm, a simple and short computer program (a “pocket” program) has been developed, with only about 120 Fortran instructions. This program is first applied to an amount of liquid, contained in a single vessel. A coarse and refined discretization is tried. In final equilibrium state of liquid, the distribution on hydro-static pressure on vessel boundaries, obtained by proposed computational model, is found in satisfactory approximation with corresponding theoretical data. Then, an opening is formed, at the bottom of a vertical boundary of initial vessel, and the liquid is allowed to flow gradually to an adjacent vessel. Almost whole amount of liquid is transferred, from first to second vessel, except of few drops-particles, which remain, in equilibrium, at the bottom of initial vessel. In the final equilibrium state of liquid, in the second vessel, the free surface level of the liquid confirms that the proposed rhombing element assures a satisfactory incompressibility of the fluid.展开更多
Our purpose in this study was to present a method for estimating the specific loss power (SLP) in magnetic hyperthermia in the presence of an external static magnetic field (SMF) and to investigate the SLP values esti...Our purpose in this study was to present a method for estimating the specific loss power (SLP) in magnetic hyperthermia in the presence of an external static magnetic field (SMF) and to investigate the SLP values estimated by this method under various diameters (D) of magnetic nanoparticles (MNPs) and amplitudes (H<sub>0</sub>) and frequencies (f) of an alternating magnetic field (AMF). In our method, the SLP was calculated by solving the magnetization relaxation equation of Shliomis numerically, in which the magnetic field strength at time t (H(t)) was assumed to be given by , with H<sub>s</sub> being the strength of the SMF. We also investigated the SLP values in the case when the SMF with a field-free point (FFP) generated by two solenoid coils was used. The SLP value in the quasi steady state (SLP<sub>qss</sub>) decreased with increasing H<sub>s</sub>. The plot of the SLP<sub>qss</sub> values against the position from the FFP became narrow as the gradient strength of the SMF (G<sub>s</sub>) increased. Conversely, it became broad as G<sub>s</sub> decreased. These results suggest that the temperature rise and the area of local heating in magnetic hyperthermia can be controlled by varying the H<sub>s</sub> and G<sub>s</sub> values, respectively. In conclusion, our method will be useful for estimating the SLP in the presence of both the AMF and SMF and for designing an effective local heating system for magnetic hyperthermia in order to reduce the risk of overheating surrounding healthy tissues.展开更多
基金supported by the National Natural Science Foundation of China(51979193)the China Scholarship Council(201506290080)+1 种基金the China Postdoctoral Science Foundation(2019M653652)the Natural Science Basic Research Plan in Shaanxi Province of China(2019JQ-607).
文摘Because of the low convergence efficiency of the typical Vicsek model,a Vicsek with static summoning points(VSSP)algorithm based on the Vicsek model considering static summoning points is proposed.Firstly,the mathematical model of the individual movement total cost on each summoning point is established.Then the individual classification rule is designed according to the initial state of the cluster to obtain the subclusters guided by each summoning point.Finally,the summoning factor is introduced to modify the course angle updating formula of the Vicsek model.To verify the effectiveness of the proposed algorithm and study the effect of the cluster summoning factor on the convergence rate,three groups of simulation experiments under different summoning factors are designed in this paper.To verify the superiority of the VSSP algorithm,the performance of the VSSP algorithm is compared with the classic algorithm by designing the algorithm performance comparison verification experiment.The results show that the algorithm proposed in this paper has good convergence and course angle consistency.The summoning factor is the sensitive factor of cluster convergence.This algorithm can provide a reference for efficient cluster segmentation movement.
文摘In this paper, exact static conditions at the corner points for the bending of thickrectangular ptates are strictly. derived from the theorem of minimum potentialenerg[1].
文摘A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.
文摘A simple method is proposed, for incremental static analysis of a set of inter-colliding particles, simulating 2D flow. Within each step of proposed algorithm, the particles perform small displacements, proportional to the out-of-balance forces, acting on them. Numerical experiments show that if the liquid is confined within boundaries of a set of inter-communicating vessels, then the proposed method converges to a final equilibrium state. This incremental static analysis approximates dynamic behavior with strong damping and can provide information, as a first approximation to 2D movement of a liquid. In the initial arrangement of particles, a rhombic element is proposed, which assures satisfactory incompressibility of the fluid. Based on the proposed algorithm, a simple and short computer program (a “pocket” program) has been developed, with only about 120 Fortran instructions. This program is first applied to an amount of liquid, contained in a single vessel. A coarse and refined discretization is tried. In final equilibrium state of liquid, the distribution on hydro-static pressure on vessel boundaries, obtained by proposed computational model, is found in satisfactory approximation with corresponding theoretical data. Then, an opening is formed, at the bottom of a vertical boundary of initial vessel, and the liquid is allowed to flow gradually to an adjacent vessel. Almost whole amount of liquid is transferred, from first to second vessel, except of few drops-particles, which remain, in equilibrium, at the bottom of initial vessel. In the final equilibrium state of liquid, in the second vessel, the free surface level of the liquid confirms that the proposed rhombing element assures a satisfactory incompressibility of the fluid.
文摘Our purpose in this study was to present a method for estimating the specific loss power (SLP) in magnetic hyperthermia in the presence of an external static magnetic field (SMF) and to investigate the SLP values estimated by this method under various diameters (D) of magnetic nanoparticles (MNPs) and amplitudes (H<sub>0</sub>) and frequencies (f) of an alternating magnetic field (AMF). In our method, the SLP was calculated by solving the magnetization relaxation equation of Shliomis numerically, in which the magnetic field strength at time t (H(t)) was assumed to be given by , with H<sub>s</sub> being the strength of the SMF. We also investigated the SLP values in the case when the SMF with a field-free point (FFP) generated by two solenoid coils was used. The SLP value in the quasi steady state (SLP<sub>qss</sub>) decreased with increasing H<sub>s</sub>. The plot of the SLP<sub>qss</sub> values against the position from the FFP became narrow as the gradient strength of the SMF (G<sub>s</sub>) increased. Conversely, it became broad as G<sub>s</sub> decreased. These results suggest that the temperature rise and the area of local heating in magnetic hyperthermia can be controlled by varying the H<sub>s</sub> and G<sub>s</sub> values, respectively. In conclusion, our method will be useful for estimating the SLP in the presence of both the AMF and SMF and for designing an effective local heating system for magnetic hyperthermia in order to reduce the risk of overheating surrounding healthy tissues.
