Soliton X-junctions with controllable transmission

We propose new planar X-junctions and multi-port devices written by spatial solitons, which are composed of two (or more) nonlinearly coupled components in Kerr-type media. Such devices have no radiation losses at a given wavelength. We demonstrate that, for the same relative angle between the channels of the X-junctions, one can vary the transmission coefficients into the output channels by adjusting the polarizations of multi-component solitons. We determine analytically the transmission properties and suggest two types of experimental embodiments of the proposed device.Comment: 3 pages, 2 figure

Hegemonization of Whiteness in the LatinX Community

In this literature review, I aim to explore the discourse on how whiteness engages with the LatinX community. The majority of the literature asserts that whiteness is hegemonized in the LatinX community. I address the claims made for how these two groups intersect, drawing on a variety of prevalent research and experts in the field. This review is situated within the social science field, with an emphasis on communications, psychology, and sociology. I explore the current power dynamics between these two groups through a variety of lenses including the assimilation and racial boundary paradigms. I also, address areas in the research that deviate from this assertion and possible directions for future research to expand on this intersection

More then simply iron: Macro- to microscopic cellular iron distribution in the brain determines MR contrast

Myelin and iron are the major source of MR contrast in the brain. Iron dominates R2*, R2 and QSM in the cortex as well as in subcortical areas and contributes to white matter contrast. To exploit this contrast for cortical parcellation, myeloarchitecture mapping, or iron quantification, significant theoretical and experimental efforts were devoted to the understanding of iron-induced contrast. However, the impact of the cellular and subcellular iron distribution is not well understood. Frequently, it is described by a simple linear dependence of the MRI contrast parameters on iron concentration, largely disregarding the inhomogeneous distribution of iron in the brain. A major reason for this simplification is a lack of quantitative knowledge on the cellular iron distribution. Moreover, the interplay between the microscopic iron distribution and diffusion in creating MR contrast in static de-phasing, motional narrowing or intermediate regime is not fully understood. We set out to address this lack in knowledge and modelling by combining state of the art quantitative 7T MRI with cutting-edge quantitative iron and myelin mapping on post mortem brain samples. Quantitative R2*, R2, R1 and QSM maps were obtained for the human cortex, the subcortical and the deep white matter as well as for brain nuclei before and after de-ironing. Laser Ablation Inductively Coupled Plasma Mass Spectroscopic Imaging (LA ICP MSI) yielded quantitative iron maps with a mesoscopic resolution of 60x120μm. Proton Induced X-ray Emission (PIXE) provided quantitative iron maps with a cellular resolution down to 1μm. MSI and PIXE demonstrated the inhomogenous distribution of iron in both grey and white matter at different spatial scales. In grey matter iron rich fibers, and small (1-3μm) micro-, astro- and oligodendroglia contained most of the iron and were sparsely distributed. In superficial and deep white matter, however, oligodendrocytes somas with the sizes of 5±1.5μm (distance between cells of 20±5μm) and iron rich fibers contained most of the iron. In addition, patches of enhanced iron concentration around small vessels with a typical size of 100-200μm contribute to up to 20% of R2* and QSM and their orientation dependence in white matter. A different contrast mechanism prevailed in brain nuclei where densely packed 20μm large iron loaded neurons dominated the MR contrast. These results provide an important basis for understanding the iron induced MR-contrast and its microstructural underpinnings. Based on these measured microscopic iron distributions and a Gaussian diffusion model we are now in the process of simulating the MR contrast mechanisms in different tissue types

Exact soliton solutions, shape changing collisions and partially coherent solitons in coupled nonlinear Schroedinger equations

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schroedinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general $N$-coupled nonlinear Schroedinger equations (N-CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among the modes. We also analyse the various possibilities and conditions for such collisions to occur. Further, we report the significant fact that the various partial coherent solitons (PCS) discussed in the literature are special cases of the higher order bright soliton solutions of the N-CNLS equations.Comment: 4 pages, RevTex, 1 EPS figure To appear in Physical Review Letter

Exact soliton solutions of coupled nonlinear Schr\"odinger equations: Shape changing collisions, logic gates and partially coherent solitons

The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{\"o}dinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by explicitly constructing multisoliton solutions (upto four-soliton solutions) for two coupled and arbitrary $N$-coupled nonlinear Schr{\"o}dinger equations using the Hirota bilinearization method, we bring out clearly the various features underlying the fascinating shape changing (intensity redistribution) collisions of solitons, including changes in amplitudes, phases and relative separation distances, and the very many possibilities of energy redistributions among the modes of solitons. However in this multisoliton collision process the pair-wise collision nature is shown to be preserved in spite of the changes in the amplitudes and phases of the solitons. Detailed asymptotic analysis also shows that when solitons undergo multiple collisions, there exists the exciting possibility of shape restoration of atleast one soliton during interactions of more than two solitons represented by three and higher order soliton solutions. From application point of view, we have shown from the asymptotic expressions how the amplitude (intensity) redistribution can be written as a generalized linear fractional transformation for the $N$-component case. Also we indicate how the multisolitons can be reinterpreted as various logic gates for suitable choices of the soliton parameters, leading to possible multistate logic. In addition, we point out that the various recently studied partially coherent solitons are just special cases of the bright soliton solutions exhibiting shape changing collisions, thereby explaining their variable profile and shape variation in collision process.Comment: 50 Pages, 13 .jpg figures. To appear in PR

Isotropic wave turbulence with simplified kernels: Existence, uniqueness, and mean-field limit for a class of instantaneous coagulation-fragmentation processes

The isotropic 4-wave kinetic equation is considered in its weak formulation using model (simplified) homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting where the kernels have a rate of growth at most linear. We also consider finite stochastic particle systems undergoing instantaneous coagulation-fragmentation phenomena and give conditions in which this system approximates the solution of the equation (mean-field limit)