These defects source elastic deformations that direct the assembly of the interfacially trapped colloids into ring-like assemblies, which recapitulate the defect geometry even when the microposts are completely immersed in the nematic. Specifically, by confining the nematic LC in an array of microposts with homeotropic anchoring conditions, we cause defect rings to form at well-defined locations in the bulk of the sample. Here, we report on complex open structures organized via interactions with defects in the bulk. Spherical colloids with homeotropic anchoring trapped at the interface between air and the nematic LC 4-cyano-4′-pentylbiphenyl create quadrupolar distortions in the director field causing particles to repel and consequently form close-packed assemblies with a triangular habit. In the cable this capacitance is between theĪxial wire and shield is analogous to the membrane capacitance of an axon.We exploit the long-ranged elastic fields inherent to confined nematic liquid crystals (LCs) to assemble colloidal particles trapped at the LC interface into reconfigurable structures with complex symmetries and packings. As a voltage signal spreads along the cable or axon, there is a delay and loss of amplitude as current is gradually lost via the capacitance ( Cm) or via leakage through the insulation ( rm). In the axon the external low resistance is the extracellular space). The resistance of the inside wire (or axoplasm) carrying the signal is represented by the string of resistors ( ra) along the top of the diagram.The cable's equivalent circuit is shown as segments representing discrete lengths, perhaps a mile each the junction of each segment is connected to the external low-resistance shield. In the axon this current flows through the ion channels. The current through the insulation itself ( rm), which is proportional to the signal voltage.This current through the capacitance is directly proportional to the rate of change of the signal voltage. In the cable the insulation is the rubber between the two plates of the capacitor (the wire and the external shield of the cable) in the axon, the insulation is the lipid between the two plates of the capacitor (the axoplasm and the extracellular space. The currrent through the capacitance ( Cm) offered by the insulation.The current (here labeled Im) is composed of two parts: The labels on the figure correspond to parts of an axon rather than of a cable. The figure here shows the current along the inside of the wire or axon and also through the cable's insulation or the axon's membrane (which is, of course, its insulation). This equation describing the transmission of a voltage signal along a section of the cable is a \partial differential equation for voltage as a function of time and space.Ī similiar partial differential equation applies equally well to an axon with voltage-sensitive ion channels. Lord Kelvin in 1855 developed what is commonly called the cable equation to describe the attenuation and distortion of signals in the first Atlantic cable.
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