Zur Theorie des in einem Eisenkörper inducirten Magnetismus

Abstract

Theorie des in einem Eisenkorper in& cirten Jnagaetisnius ; von K i I* c R h off. I . K i n Fall, i n deui die voii P o i s s o n aufgestellte Tlieorie des in weichein Eiseii iirtlricirteil Magnetisnius Rich sehr leicht durchfiiliim Ialst. der. aiicli i i i exp~?rimrnteller Hinsicht Iuteresse datbietet uod, soviel icli weirs, bisher theoretisdi nicht behaudclt ist, ist drr Fall eiiics Kiiigcsoder, um es bestirninter auszudrucbeu, eines Rotatioiiskiirpers, der von dtbr Kotalioiisaxe nicht getroffrn wirdvan Eiseo, der durch eioen elekttischen Stroin inagnetisirt ist, dessen Wiudungen eiuen, cleri Eisenliiii per' umschliefseiider~, hohlen King bilden, tlec-init diesein eine g~~~nc~insctiaftliclie Rotationsaxe tiat. Die Theorie dieses Falles sol1 tiier eiitwickelt werden. Die P o i s s o ii'sche Theorie setzt voraus, dafs'die magiietisirenden Krafte ein Potential haben : es Fey dieses, bezogen arif eirien Punkt, drr die rechtwinliligeti Coordinaten x, y, a hat, = Y ; es ecsyen ferner r ( , p , y die magnetischen Momente in dem Punktv-z, y, z, der Eisenlnasse, hezogen auf die Voiuineneinheit ; die GrGCsen ar, g, y sind dann eindeutig bestimint durcb die folgenden Gleichungen, die fiir alle Punkte der Eisenmasse erfullt werden iniissen : a = % -, 8P p = x r , BY y--xz& -81p 8 X dY o = V + y j + Q Hier bedeat,et x die M a~~i~t i~i r i~n~s c o n r ; t a n t e des Eisens, d S eiii Element der Oberfllicbe dessell,en, N die uach dem Innrrn gerichtete Noiniale von d S ond r die Entferniing Poggendorffs Ann. Erganzungsbd. V.

Eigenvalue spectrum of transition matrix of dual Sierpinski gaskets and its applications

“…It has been established that for a connected network G with N nodes, the number of its spanning trees, N st (G), is related to the N − 1 nonzero eigenvalues of its normalized Laplacian matrix [6,7]. Let N st (H d,g ) denote the number of spanning trees in H d,g , and let L g represent its normalized Laplacian matrix defined by…”

“…In addition to random walks, the transition matrix of a network is also relevant in structural and other aspects of a network. In structure, the spectra of the transition matrix of a connected network determine the number of spanning trees in the network as well as the resistance distance of its corresponding resistor network [6,7]. With respect to other aspects of networks, the transition matrix is closely related to the self-organized criticality of the Oslo sandpile model [8], recommendation model [9], community detection [10] and so on.…”

Wide-angle camouflage detectors by manipulating emissivity using a non-reciprocal metasurface array

“…4,5 Recently, Chamoli et al proposed the use of phase change materials 36,37 to control emissivity in two different phases through reconfigurable radiative metasurface designs [38][39][40][41] Kirchhoff's law is the governing principle of thermal emission, which dictates that all objects have equal emission and absorption, or more precisely, they follow Lorentz reciprocity. 4,42 All of the previously proposed nanophotonics camouflage designs comply with this law. However, this law is not valid once the reciprocity has been broken in a system, 32,35 and it is now possible to produce a nonreciprocal thermal emitter that contrasts emissivity and absorptivity.…”