Diversity of radial spin textures in chiral materials
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The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry ...
The Monge problem (Monge 1781; Taton 1951), as reformulated by Kantorovich (2006a, 2006b) is that of the transportation at a minimum "cost" of a given mass distribution from an initial to a final position during a given time interval. It is an optimal tran ...
In this note we introduce a vector generalization of fractional Brownian motion. Our definition takes into account directional properties of vector fields-such as divergence, rotational behaviour, and interactions with coordinate transformations-that have ...
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Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group o ...
We present a method for determining molecular orientation from second-order nonlinear light scattering experiments. Our modeling shows that there is an optimal angular region, for which the scattering pattern is most sensitive to molecular orientation. We ...
Praseodymium molybdate Pr2(MoO4)3 was synthesized using the standard ceramic route. The crystal structure of the material has been successfully solved in superspace group I2/b(Rβ0)00 with lattice constants a = 5.30284(4), b = 5.32699(3), c = 11.7935(1)A° , ...
In this note we introduce a vector generalization of fractional Brownian motion. Our definition takes into account directional properties of vector fields—such as divergence, rotational behaviour, and interactions with coordinate transformations—that have ...
A modeling framework is proposed for the control of rigid and flexible cable-like systems such as cranes, together with a systematic algorithm for computing flat outputs of mechanical systems for which the flat output is a linear combi- nation of free coor ...
Entirely unlike the arom. closo B6H62- and B12H122- borane dianions, isoelectronic Si62- and Si122- are antiarom. Their Oh and Ih symmetries are responsible, as the other deltahedral silicon dianion clusters do not exhibit this behavior. These high symmetr ...
We consider the comparative statics of solutions to parameterized optimization problems. A geometric method is developed for finding a vector field that, at each point in the parameter space, indicates a direction in which monotone comparative statics obta ...