For the local catenary path of yarn in steady motion fre-quently encountered in textile processing,this paper studiesthe mathematical expression of its geometrical configurationand tension variation,as well as the cur...For the local catenary path of yarn in steady motion fre-quently encountered in textile processing,this paper studiesthe mathematical expression of its geometrical configurationand tension variation,as well as the curve inclination angleand its maximum suspending deflection.The final math-ematical equations and graphical curves are all presented indimensionless forms,as they are more general and universalthan dimensional expressions and graphs.On the otherhand,we can also find out the catenary yarn tension fromexperimentally measured geometrical parameters by calcula-tions based on these graphs or mathematical expressions asgiven in the paper.展开更多
Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution PnL for the winding number n and the partition function...Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution PnL for the winding number n and the partition function PL of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.展开更多
文摘For the local catenary path of yarn in steady motion fre-quently encountered in textile processing,this paper studiesthe mathematical expression of its geometrical configurationand tension variation,as well as the curve inclination angleand its maximum suspending deflection.The final math-ematical equations and graphical curves are all presented indimensionless forms,as they are more general and universalthan dimensional expressions and graphs.On the otherhand,we can also find out the catenary yarn tension fromexperimentally measured geometrical parameters by calcula-tions based on these graphs or mathematical expressions asgiven in the paper.
文摘Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution PnL for the winding number n and the partition function PL of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.
