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This talk discusses a method for creating low-volume versions of massive geophysical data sets that approximately retain high-resolution data structure.
A method has been developed to improve on Witten's binary arithmetic coding procedure of tracking a high value and a low value. The new method approximates the probability of the less probable symbol, which improves the worst-case coding efficiency.
For space missions such as NASA's Magellan mission to Venus and the Cassini mission to Saturn, the communication channel to Earth has a limited channel capacity.
Here, we show that for families of 1d lattice systems in an invertible phase, the cohomology class of the higher Berry curvature can be refined to an integral degree-3 class on the parameter space. Similarly, for families of U(1)-invariant 2d lattice systems in an invertible phase, the higher Thouless pump can be refined to an integral degree-2 class on the parameter space. We show that the 2d Thouless pump can be identified with an excess Berry curvature of a flux insertion.
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The discovery of the integer and fractional quantum Hall effects naturally prompted the question of whether these effects can be realized without a magnetic field. Answering this is fundamentally important and requires a synthesis of the concepts of band topology, quantum geometry and electronic correlations. Here we summarize the basic concepts of both fractional Chern and fractional topological insulators and illustrate them with the theoretical lattice models that support the flat Chern bands in which the states were first predicted. We then examine their experimental realizations in twisted bilayer transition metal dichalcogenides and moiré rhombohedral few-layer graphene. Here, we also discuss the future challenges and opportunities in this research field.
We theoretically investigate the second harmonic generation (SHG) of topological insulator surface states in a perpendicular magnetic field. Our theory is based on the microscopic expression of the second-order magneto-optical conductivity developed from the density matrix formalism, taking into account hexagonal warping effects on the surface states' band structure. Using numerically exact Landau-level energies and wave functions including hexagonal warping, we calculate the spectrum of SHG conductivities under normal incidence for different values of magnetic field and chemical potential. The imaginary parts of the SHG conductivities show prominent resonant peaks corresponding to one-photon and two-photon inter-Landau-level transitions. Treating the hexagonal warping term perturbatively, these transitions are clarified analytically within a perturbation theory from which approximate selection rules for the allowable optical transitions for SHG are determined. Furthermore, our results show extremely high SHG susceptibility that is easily tunable by magnetic field and doping level for topological surface states in the far-infrared regime, exceeding that of many conventional nonlinear materials. This work highlights the key role of hexagonal warping effects in generating second-order optical responses and provides insights into the nonlinear magneto-optical properties of the topological insulators.
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Error analysis and control of analog computer oriented hybrid systems, particularly hybrid computers treating differential equations
Hamiltonian formulation of general relativity
Digital range switching filter for deadband of analog to digital converter for LSI realization
Iterative method for reducing filters required for optimal Kalman filter design maintaining parameter estimation accuracy
Synchrotron radiation rate from deexcitation of electrons in magnetic orbits of low quantum numbers, stressing electrons radiation in intense magnetic fields
A heuristic description is given for a simple harmonic oscillator as a basis for a model of anharmonicity. A formalism is applied in the process, which applies to complex excitation fields involving particle clusters and also facilitates a description of nonequilibrium multibody configurations by classical methods. The heuristic description is based on Streit's results (1965) and is free of linearization requirements in most physically interesting situations.