Abstract: A gradient method (GM) for constructing and using absorbing boundary conditions (ABCs) for high accuracy numerical computations of various physical phenomena which are governed by partial differential equations (PDEs) is disclosed. The PDEs to which the GM is applicable are for example: the Helmholtz equation (also known as the wave equation in the frequency domain), the elastic wave equation in the frequency domain, Maxwell's equations, and Schrodinger's equation. The GM can be used to develop ABCs for the solution of PDE problems in two or more dimensions. The GM is a tool based on two principles: (1) Any directional derivatives in an ABC must be taken in the direction of the gradient of the unknown function or functions of the PDE, and (2) any ABC using such gradient derivatives may be applied to any domain of a convex shape, even if the ABC was originally developed for domains of a restricted shape.

Abstract: A gradient method (GM) for constructing and using absorbing boundary conditions (ABCs) for high accuracy numerical computations of various physical phenomena which are governed by partial differential equations (PDEs) is disclosed. The PDEs to which the GM is applicable are for example: the Helmholtz equation (also known as the wave equation in the frequency domain), the elastic wave equation in the frequency domain, Maxwell's equations, and Schrodinger's equation. The GM can be used to develop ABCs for the solution of PDE problems in two or more dimensions. The GM is a tool based on two principles: (1) Any directional derivatives in an ABC must be taken in the direction of the gradient of the unknown function or functions of the PDE, and (2) any ABC using such gradient derivatives may be applied to any domain of a convex shape, even if the ABC was originally developed for domains of a restricted shape.

Abstract: A material measurement system (500) includes a THz generator including at least one laser source (111) for emitting optical pulses, the optical pulses coupled to a THz emitter (51) operable for emitting pulsed THz radiation at a sample location on material while being processed (14) by a manufacturing system. A receiver (52) is operable to receive the optical pulses and to detect reflected or transmitted THz radiation from the sample location (14) synchronously with the optical pulses and provide electrical detection signals. Synchronizing optics (112, 113, 114) is operable to receive the optical pulses from said laser and provide the optical pulses to both the receiver (52) and the THz emitter (51).

Abstract: A material measurement system (500) includes a THz generator including at least one laser source (111) for emitting optical pulses, the optical pulses coupled to a THz emitter (51) operable for emitting pulsed THz radiation at a sample location on material while being processed (14) by a manufacturing system. A receiver (52) is operable to receive the optical pulses and to detect reflected or transmitted THz radiation from the sample location (14) synchronously with the optical pulses and provide electrical detection signals. Synchronizing optics (112, 113, 114) is operable to receive the optical pulses from said laser and provide the optical pulses to both the receiver (52) and the THz emitter (51).

Abstract: A stabilizing device having a flexible shaft with a terminal connector and surgical tools used therewith. The flexible shaft is responsive to a tension element connected to a distal end of the shaft and in communication with a proximal end of the shaft. An elastic means interfacing between the proximal end of the tension element and an actuating cam cause the shaft to adapt for differences in activating tension between straight and curved positions. Accordingly, stretching and deformation of the tensioning element is reduced and shaft stiffness upon activation of the tensioning element is repeatable. The terminal connector includes a ball-and-socket arrangement adapted to resiliently absorb movement of an organ during surgery. A bendable suction stabilizer foot adaptable to contours of an organ is also provided as an attachment to the stabilizer device.

Abstract: A stabilizing device having a flexible shaft with a terminal connector and surgical tools used therewith. The flexible shaft is responsive to a tension element connected to a distal end of the shaft and in communication with a proximal end of the shaft. An elastic means interfacing between the proximal end of the tension element and an actuating cam cause the shaft to adapt for differences in activating tension between straight and curved positions. Accordingly, stretching and deformation of the tensioning element is reduced and shaft stiffness upon activation of the tensioning element is repeatable. The terminal connector includes a ball-and-socket arrangement adapted to resiliently absorb movement of an organ during surgery. A bendable suction stabilizer foot adaptable to contours of an organ is also provided as an attachment to the stabilizer device.