Long Term Outcome of Patients Undergoing Pancreaticoduodenectomy for Non-Malignant Disease

Symmetry breaking in UCA-based vortex waves

“…In principle, when the source distribution is known, the inhomogeneous wave equations can be solved via the Green function approach, enabling the determination of the radiated fields [22,23,[35][36][37]. In the frequency domain, the outgoing-wave Green function is given by:…”

“…Antenna arrays are configurations of multiple connected antennas, distributed according to a specific geometry, in which the excitation of each radiator can be controlled in amplitude and phase [22,23]. As the electromagnetic waves radiated by the constituent elements combine coherently, affecting the spatial distribution of the transmitted power, antenna arrays represent one of the most manageable and versatile solutions to deal with the synthesis of complex waveforms at the radio frequencies.…”

“…Let us now move to the case of an arbitrary N-element antenna array composed of more realistic radiators. The knowledge of the current term ( ) J r enables the estimation of the electric and magnetic fields via (A.5) and (A.6), from which the corresponding far-field expressions are easily derived [23]. Neglecting all mutual couplings among the antennas, the total electric field radiated by the considered array in a region where r is much greater than the spatial extent of the antennas can be written as: being η the vacuum impedance, I n =I 0 ξ n the supply current to the n-th radiator, where  x Î n is the relative synthesis coefficient and I 0 a constant current term associated to the total input power, whereas q f ( ) h , n represents the n-th antenna vector effective height (see appendix A, equation (A.8)).…”

“…Assuming no coupling, the voltage induced on a p-th receiving element in the absence of noise can be expressed approximately as the dot product between the incoming electric field and the p-th effective height [23]: The matrix elements H pn can of course be interpreted as coupling coefficients between the n-th radiator and the p-th receiving element, whose specific value depends on the type of antennas used (i.e., the explicit form of the effective heights) and on their geometrical arrangement and orientation within the two volumes  T and  R .…”

“…R the resistance of the radiators and having required the normalization condition for the synthesis coefficients. Similarly, the total power collected by the receiving array under ideal circumstances can be written as: are the beamforming weights introduced at the receiver and the network is supposed to be connected to a matched load[23]. The link budget of a communication system is defined as the ratio between the received and the transmitted powers and plays a fundamental role for the characterization of the link; in the present case, from (B.4) and (B.5), the explicit expression of the link budget reads:…”