Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

Tuning the charge density wave quantum critical point and the appearance of superconductivity in TiSe2

© 2021 Published by the American Physical Society. The transition metal dichalcogenide is an ideal correlated system for studying the interplay between superconductivity (SC) and a charge density wave (CDW) because both symmetry-breaking phases can be easily controlled by either Cu intercalation or physical pressure. SC appears in proximity to a CDW quantum critical point (QCP) induced by both Cu intercalation and applied pressure, raising the possibility of CDW-driven SC. Here, we report tuning the CDW QCP by simultaneously controlling Cu intercalation and external pressure and the appearance of a SC dome centered on the tunable QCP. When subjected to pressure, CDW ordering of Cu-intercalated is completely suppressed at 2.3 GPa, where the residual resistivity and the resistivity-temperature exponent decrease sharply, indicating the presence of the CDW QCP. The upper critical field of is 3.51 kOe, 16 times larger than that of pristine , and its temperature dependence is linear, indicating that SC of is switched from the two-dimensional- to anisotropic three-dimensional-like by Cu intercalation. These discoveries show that the simultaneous application of Cu intercalation and pressure move the CDW QCP and that the highest SC transition temperature is pinned to the QCP, suggesting that the SC in is strongly correlated with CDW quantum criticality.11Nscopu

Beneficial effects of autologous mesenchymal stem cell transplantation in active progressive multiple sclerosis

In this study (trial registration: NCT02166021), we aimed to evaluate the optimal way of administration, the safety and the clinical efficacy of mesenchymal stem cell (MSC) transplantation in patients with active and progressive multiple sclerosis. Forty-eight patients (28 males and 20 females) with progressive multiple sclerosis (Expanded Disability Status Scale: 3.0-6.5, mean : 5.6 ± 0.8, mean age: 47.5 ± 12.3) and evidence of either clinical worsening or activity during the previous year, were enrolled (between 2015 and 2018). Patients were randomized into three groups and treated intrathecally (IT) or intravenously (IV) with autologous MSCs (1 × 10(6)/kg) or sham injections. After 6 months, half of the patients from the MSC-IT and MSC-IV groups were retreated with MSCs, and the other half with sham injections. Patients initially assigned to sham treatment were divided into two subgroups and treated with either MSC-IT or MSC-IV. The study duration was 14 months. No serious treatment-related safety issues were detected. Significantly fewer patients experienced treatment failure in the MSC-IT and MSC-IV groups compared with those in the sham-treated group (6.7%, 9.7%, and 41.9%, respectively, P = 0.0003 and P = 0.0008). During the 1-year follow-up, 58.6% and 40.6% of patients treated with MSC-IT and MSC-IV, respectively, exhibited no evidence of disease activity compared with 9.7% in the sham-treated group (P < 0.0001 and P < 0.0048, respectively). MSC-IT transplantation induced additional benefits on the relapse rate, on the monthly changes of the T(2) lesion load on MRI, and on the timed 25-foot walking test, 9-hole peg test, optical coherence tomography, functional MRI and cognitive tests. Treatment with MSCs was well-tolerated in progressive multiple sclerosis and induced short-term beneficial effects regarding the primary end points, especially in the patients with active disease. The intrathecal administration was more efficacious than the intravenous in several parameters of the disease. A phase III trial is warranted to confirm these findings