Abstract: A magnetic trap droplet controller is provided that includes a solid substrate, a controller operated by an appropriately programmed computer, a two-dimensional distribution of magnetized domains disposed on a surface of the solid substrate, a fluid chamber disposed above the two-dimensional distribution of magnetized domains, and an active magnet, where the active magnet is disposed to provide a dynamic magnetic field in-plane with the solid substrate, where the dynamic magnetic field controls north and south poles of the two-dimensional distribution of magnetized domains according to the controller, where a fluid under test that is disposed in a carrier fluid that is disposed in the fluid chamber propagates according to the controlled north and south poles of the two-dimensional distribution of the magnetized domains.

Abstract: A magnetic-hydrodynamic force fluid logic controller is provide that includes a solid or flexible or flexible substrate, a fluid chamber disposed above the substrate, where the chamber includes a fluid under test that includes an active magnet, where the active magnet is disposed to control a magnetic north pole of the droplet and a magnetic south pole of the droplet, a two-dimensional distribution of magnetic elements a surface the solid or flexible substrate, where the magnetic elements comprise a magnetization in a magnetic north pole and magnetization in a magnetic south pole, where the magnetic elements are activated by an external magnetic field of the active magnet, where the droplets have a droplet magnetization, where the droplet magnetization is configured for droplet self-interaction by the magnetic elements and the active magnet, where the self-interaction comprises splitting, merging, propagation, logic, storage, memory and all possible combinations of logical circuit operations.

Abstract: A method of forming a three-dimensional object including a continuous sheet of material includes: (a) providing at least one drive roller and a build plate, with the build plate including an optically transparent member, with the optically transparent member including a build surface, and with the build surface at least partially defining a build region and the at least one drive roller adjacent the build region; (b) filling the build region with a polymerizable liquid; (c) irradiating the build region with light through the optically transparent member to form a solid polymer from the polymerizable liquid; and (d) rotating the at least one drive roller to form the three-dimensional object from the solid polymer and/or to advance (or draw) the continuous sheet of material away from the build region.

Abstract: A magnetic-hydrodynamic force fluid logic controller is provide that includes a solid or flexible or flexible substrate, a fluid chamber disposed above the substrate, where the chamber includes a fluid under test that includes an active magnet, where the active magnet is disposed to control a magnetic north pole of the droplet and a magnetic south pole of the droplet, a two-dimensional distribution of magnetic elements a surface the solid or flexible substrate, where the magnetic elements comprise a magnetization in a magnetic north pole and magnetization in a magnetic south pole, where the magnetic elements are activated by an external magnetic field of the active magnet, where the droplets have a droplet magnetization, where the droplet magnetization is configured for droplet self-interaction by the magnetic elements and the active magnet, where the self-interaction comprises splitting, merging, propagation, logic, storage, memory and all possible combinations of logical circuit operations.

Abstract: A magnetohydrodynamic force fluid logic controller is provided including a solid substrate, a fluid chamber disposed above the substrate, containing a fluid under test. It also includes an active magnet such that the active magnet is disposed to control north and south poles on the fluid under test or on the carrier fluid and a two-dimensional distribution of magnetized domains disposed on a surface of the solid substrate. The magnetized domains have poles activated by the above the active magnet, where the different parts of the above the fluid under test self-interact and split, merge or propagate along different directions on the above the substrate subject to their placement on the magnetized domains, whereby the active magnet regulates the self-interaction. The results of the self-interactions are equivalent to physical binary logic operations where “1” is the presence and “0” is the absence of a fluidic volume at a given location.

Abstract: A magnetic trap droplet controller is provided that includes a solid substrate, a controller operated by an appropriately programmed computer, a two-dimensional distribution of magnetized domains disposed on a surface of the solid substrate, a fluid chamber disposed above the two-dimensional distribution of magnetized domains, and an active magnet, where the active magnet is disposed to provide a dynamic magnetic field in-plane with the solid substrate, where the dynamic magnetic field controls north and south poles of the two-dimensional distribution of magnetized domains according to the controller, where a fluid under test that is disposed in a carrier fluid that is disposed in the fluid chamber propagates according to the controlled north and south poles of the two-dimensional distribution of the magnetized domains.