THEORETICAL AMPLITUDE AND PERIOD OF PRECURSOR SOLITON GENERATION IN TWO-LAYER FLOW

An fKdV equation of two-layer how and an averaged fKdV equation (AfKdV equation) with respect to phase are derived to determine the theoretical amplitude and period of the precursor solitons in the present paper. In terms of the AfKdV equation derived by the authors, a new theory on the precursor soliton generation based on Lee et al.'s concept is presented. Concepts of asymptotic mean hydraulic fall and level are introduced in our analysis, and the theoretical amplitude and period both depend on the asymptotic mi-an levels and stratified parameters. From the present theoretical results, it is obtained that when the moving velocity of the topography is at the resonant points, there exist two general relations: (1) amplitude relation (A) over circle = 2F, (2) period relation <(tau)over circle> = -8m(1)m(3)(-1)root 6m(4)m(3)(-1)F, in which (A) over circle and <(tau)over circle> are the amplitude and period of the precursor solitons at the resonant points respectively, m(1), m(3) and m(4) are coefficients of the fKdV equation, and F is asymptotic mean half-hydraulic fall at subcritical cutoff points. The theoretical results of this paper are compared with experiments and numerical calculations of two-layer flow over a semicircular topography and all these results are in good agreement. Due to the canonical character of the coefficients of fKdV equations, this theory also holds for any two-dimensional system, which can be reduced to fKdV equations.

Entanglement-enhanced classical communication through generalized amplitude damping channel

The problem of sending a single classical bit through a generalized amplitude damping channel is considered. When two transmissions through the channel arc available as a resource, we find that two entangled transmissions can enhance the capability of receiver＇s judging information correctly under certain conditions compared with two productstate transmissions. In addition, we find a special case in which the two entangled transmissions can always make a classical bit more effectively disable the noise influence.

Geometric discord for non-X states

The level surfaces of geometric discord for a class of two-qubit non-X states are investigated when the Bloch vectors are in arbitrary directions. The level surfaces of constant geometric discord are formed by three intersecting open tubes along three orthogc^nal directions. When Bloch vectors increase, the tubes along one or two directions shrink towards the center and may either totally disappear or the open tubes may become closed tubes when the Bloch vectors reach a critical value. In the generalized amplitude damping channel, the evolution of geometric discord shows double sudden changes when the parameter γ, increases. In the phase damping channel, the freezing phenomenon of geometric discord also exists.

Altered relationship between thickness and intrinsic activity amplitude in generalized tonic–clonic seizures

A thinner cortex has higher potential for binding GABA receptor A which is associated with larger amplitudes of intrinsic brain activity(i BA). However, the relationship between cortical thickness and i BA is unknown in intact and epileptic brains. To this end, we investigated the relationship between cortical thickness measured by highresolution MRI and surface-based i BA derived from resting-state functional MRI in normal controls(n = 82) andpatients with generalized tonic–clonic seizures(GTCS)only(n = 82). We demonstrated that the spatial distribution of cortical thickness negatively correlated with surface-based i BA amplitude at both whole-brain and within independent brain functional networks. In GTCS patients,spatial coupling between thickness and i BA amplitude decreased in the default mode, dorsal attention, and somatomotor networks. In addition, the vertex-wise acrosssubject thickness–i BA amplitude correspondence altered in the frontal and temporal lobes as well as in the precuneus in GTCS patients. The relationship between these two modalities can serve as a brain-based marker for detecting epileptogenic changes.