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Starting with Gauss and Kelvin, knots in fields were postulated to behave like particles, but experimentally they were found only as transient features or required complex boundary conditions to exist and could not self-assemble into three-dimensional crystals. We introduce energetically stable, micrometer-sized knots in helical fields of chiral liquid crystals. While spatially localized and freely diffusing in all directions, they resemble colloidal particles and atoms, self-assembling into crystalline lattices with open and closed structures. These knots are robust and topologically distinct from the host medium, though they can be morphed and reconfigured by weak stimuli under conditions such as those in displays. A combination of energy-minimizing numerical modeling and optical imaging uncovers the internal structure and topology of individual helical field knots and the various hierarchical crystalline organizations that they form.
This article was published in the following journal.
Name: Science (New York, N.Y.)
To investigate why security of identical knot sequences is variable and how to avoid occasionally insecure knots.
The free swelling of knots and the directional motion of knots under tension were studied in vertically vibrated bead chains. A metastable state of swelling was observed in the strongly vibrated two-e...
Organic semiconducting single crystals are ideal candidates both for fundamental and application-oriented researches due to their advantages of free grain boundaries, few defects, minimal traps and im...
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The separation of haloalkene cis-trans isomers is difficult to achieve, yet highly desired in the chemical industry. Here, we report an energy-efficient adsorptive separation of 1,4-dichloro-2-butene ...
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The COR-KNOT technology (LSI SOLUTIONS, Victor, New York USA) was developed to replace suture tying with a faster procedure during surgery. While preclinical studies confirmed the speed of...
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Echocardiography amplified by the addition of depth to the conventional two-dimensional ECHOCARDIOGRAPHY visualizing only the length and width of the heart. Three-dimensional ultrasound imaging was first described in 1961 but its application to echocardiography did not take place until 1974. (Mayo Clin Proc 1993;68:221-40)
The process of generating three-dimensional images by electronic, photographic, or other methods. For example, three-dimensional images can be generated by assembling multiple tomographic images with the aid of a computer, while photographic 3-D images (HOLOGRAPHY) can be made by exposing film to the interference pattern created when two laser light sources shine on an object.
Three-dimensional computed tomographic imaging with the added dimension of time, to follow motion during imaging.
Methods of comparing two or more samples on the same two-dimensional gel electrophoresis gel.
Dynamic three-dimensional echocardiography using the added dimension of time to impart the cinematic perception of motion. (Mayo Clin Proc 1993;68:221-40)