Advances of phononics in 2012—2022

Due to its great potential applications in thermal management, heat control, and quantum information, phononics has gained increasing attentions since the first publication in Rev. Mod. Phys. 84 1045 (2012). Many theoretical and experimental progresses have been achieved in the past decade. In this paper, we first give a critical review of the progress in thermal diodes and transistors, especially in classical regime. Then, we give a brief introduction to the new developing research directions such as topological phononics and quantum phononics. In the third part, we discuss the potential applications. Last but not least, we point out the outlook and challenges ahead.     

λ-重K_(1,4)-设计到λ-重K_(1,3)-最大填充的变形

令(X,B)为一个u阶的λ-重K_(1,4)-设计.对于每一个区组B=(a:b,c,d,e)∈B,若删去边{a,e},则得到一个K_(1,3)[a:b,c,d].令C为删去B中每一个区组的边{a,e}而得到的K_(1,4)的集合,F为被删去的边构成的集合.若F可以被重组成[λv(v-1)/24]个K_(1,3)的集合D,则(X,CUD)为一个v阶λ-重K_(1,3)-最大填充.称(X,C∪D)为λ-重K_(1,4-)设计(X,B)的变形.本文证明了v阶λ-重K_(1,4)-设计到u阶λ-重K_(1,3)-最大填充的变形存在的充要条件是λv(v-1)≡0(mod 8)且v≥5.     

λ-重C_4+e-设计到λ-重P_5-设计的变形

令(X,B)为一个v阶的λ-重C_4+e-设计.对于每一个区组B=(u,v,w,x:y)∈B,若删去边{u,x},则得到一个P_5[u,v,w,x,y].令C为删去B中每一个区组的边{u,x}而得到的P_5的集合D,F为被删去的边构成的集合.若F可以被重组成λv(v-1)/40个P_5的集合D,则(X,C∪D)为一个v阶λ-重P_5-设计.称(X,C∪D)为λ-重C_4+e-设计(X,B)的变形.v阶λ-重C_4+e-设计到v阶λ-重P_5-设计的变形存在的充要条件是λv(v-1)≡0(mod40)且v≥5.