Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.Comment: 33 pages, 5 figures; submitted to Journal of Nonlinear Scienc

Localization and Coherence in Nonintegrable Systems

We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asympotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved quantities leads naturally to localized and coherent structures. If the phase space is compact, the final equilibrium state is governed by entropy maximization and the final coherent structures are stable lumps. In systems where the phase space is not compact, the coherent structures can be collapses represented in phase space by a heteroclinic connection to infinity.Comment: 41 pages, 15 figure

Giant Magnons and Singular Curves

We obtain the giant magnon of Hofman-Maldacena and its dyonic generalisation on R x S^3 < AdS_5 x S^5 from the general elliptic finite-gap solution by degenerating its elliptic spectral curve into a singular curve. This alternate description of giant magnons as finite-gap solutions associated to singular curves is related through a symplectic transformation to their already established description in terms of condensate cuts developed in hep-th/0606145.Comment: 34 pages, 17 figures, minor change in abstrac

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565

The Effects of Viscosity on the Linear Stability of Damped Stokes Waves, Downshifting, and Rogue Wave Generation

We investigate a higher order nonlinear Schrodinger equation with linear damping and weak viscosity, recently proposed as a model for deep water waves exhibiting frequency downshifting. Through analysis and numerical simulations, we discuss how the viscosity affects the linear stability of the Stokes wave solution, enhances rogue wave formation, and leads to permanent downshift in the spectral peak. In particular, we study the wave evolution over short-to-moderate time scales, when most rogue wave activity occurs, and explain the transition of the perturbed solution from the initial Benjamin-Feir instability to a predominantly oscillatory behavior. Finally, we determine the mechanism and timing of permanent downshift in the spectral peak and its relation to the location of the global minimum of the momentum and the magnitude of its second derivative

Numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger equation

In this article we conduct a broad numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger (NLS) equation, a widely used model of rogue wave generation and dynamics in deep water. NLS breathers rising over an unstable background state are frequently used to model rogue waves. However, the issue of whether these solutions are robust with respect to the kind of random perturbations occurring in physical settings and laboratory experiments has just recently begun to be addressed. Numerical experiments for spatially periodic breathers with one or two modes involving large ensembles of perturbed initial data for six typical random perturbations suggest interesting conclusions. Breathers over an unstable background with N unstable modes are generally unstable to small perturbations in the initial data unless they are "maximal breathers" (i.e., they have N spatial modes). Additionally, among the maximal breathers with two spatial modes, the one of highest amplitude due to coalescence of the modes appears to be the most robust. The numerical observations support and extend to more realistic settings the results of our previous stability analysis, which we hope will provide a useful tool for identifying physically realizable wave forms in experimental and observational studies of rogue waves

Endoscopic failure for foreign body ingestion and food bolus impaction in the upper gastrointestinal tract: An updated analysis in a European tertiary care hospital

Objective Harmfulness of foreign body ingestion and food bolus impaction (FBIs) varies according to geographical area, population, habits, and diet. Therefore, studies may not draw generalizable conclusions. Furthermore, data regarding FBIs management in Europe are limited and outdated. This study aimed to analyze the endoscopic management and outcomes of FBIs in an Italian tertiary care hospital to identify risk factors for endoscopic failure. Methods We retrospectively reviewed patients who underwent upper gastrointestinal endoscopy for FBIs between 2007 and 2017. Baseline, clinical, FBIs, and endoscopic characteristics and outcomes were collected and reported using descriptive statistics and logistic regression analyses. Results Of the 381 endoscopies for FBIs, 288 (75.5%) were emergent endoscopy and 135 (35,4%) included underlying upper gastrointestinal conditions. The study population included 44 pediatric patients (11.5%), 54 prisoners (15.8%), and 283 adults (74.2%). The most common type and location of FBIs were food boluses (52.9%) and upper esophagus (36.5%), respectively. While eight patients (2.1%) developed major adverse events requiring hospital admission, the remainder (97.9%) were discharged after observation. No mortality occurred. Endoscopic success was achieved in 263 of 286 (91.9%) verified FBIs endoscopies. Endoscopic failure (8.04%) was associated with age, bone, disk battery, intentional ingestion, razor blade, prisoners, and stomach in the univariate analysis. Multivariate logistic regression revealed that intentional ingestion was associated with endoscopic failure (odds ratio: 7.31; 95% confidence interval = 2.06-25.99; P = 0.002). Conclusion Endoscopy for FBIs is safe and successful, with low hospital admission rate in children, prisoners, and adults. Intentional ingestion is a risk factor of endoscopic failure

Discrete moving frames on lattice varieties and lattice based multispace

In this paper, we develop the theory of the discrete moving frame in two different ways. In the first half of the paper, we consider a discrete moving frame defined on a lattice variety and the equivalence classes of global syzygies that result from the first fundamental group of the variety. In the second half, we consider the continuum limit of discrete moving frames as a local lattice coalesces to a point. To achieve a well-defined limit of discrete frames, we construct multispace, a generalization of the jet bundle that also generalizes Olver’s one dimensional construction. Using interpolation to provide coordinates, we prove that it is a manifold containing the usual jet bundle as a submanifold. We show that continuity of a multispace moving frame ensures that the discrete moving frame converges to a continuous one as lattices coalesce. The smooth frame is, at the same time, the restriction of the multispace frame to the embedded jet bundle. We prove further that the discrete invariants and syzygies approximate their smooth counterparts. In effect, a frame on multispace allows smooth frames and their discretisations to be studied simultaneously. In our last chapter we discuss two important applications, one to the discrete variational calculus, and the second to discrete integrable systems. Finally, in an appendix, we discuss a more general result concerning equicontinuous families of discretisations of moving frames, which are consistent with a smooth frame

Rogue waters

In this essay we give an overview on the problem of rogue or freak wave formation in the ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface. These waves cause serious danger for sailing and sea use. A number of huge wave accidents resulted in damages, ship losses and people injuries and deaths are known. Now marine researchers do believe that these waves belong to a specific kind of sea waves, not taken into account by conventional models for sea wind waves. This paper addresses to the nature of the rogue wave problem from the general viewpoint based on the wave process ideas. We start introducing some primitive elements of sea wave physics with the purpose to pave the way for the further discussion. We discuss linear physical mechanisms which are responsible for high wave formation, at first. Then, we proceed with description of different sea conditions, starting from the open deep sea, and approaching the sea cost. Nonlinear effects which are able to cause rogue waves are emphasised. In conclusion we briefly discuss the generality of the physical mechanisms suggested for the rogue wave explanation; they are valid for rogue wave phenomena in other media such as solid matters, superconductors, plasmas and nonlinear opticsComment: will be published in Contemporary Physic

Modest agreement between magnetic resonance and pathological tumor regression after neoadjuvant therapy for rectal cancer in the real world.

Magnetic resonance imaging (MRI) is routinely used for preoperative tumor staging and to assess response to therapy in rectal cancer patients. The aim of our study was to evaluate the accuracy of MRI based restaging after neoadjuvant chemoradiotherapy (CRT) in predicting pathologic response. This multicenter cohort study included adult patients with histologically confirmed locally advanced rectal adenocarcinoma treated with neoadjuvant CRT followed by curative intent elective surgery between January 2014 and December 2019 at four academic high-volume institutions. Magnetic resonance tumor regression grade (mrTRG) and pathologic tumor regression grade (pTRG) were reviewed and compared for all the patients. The agreement between radiologist and pathologist was assessed with the weighted k test. Risk factors for poor agreement were investigated using logistic regression. A total of 309 patients were included. Modest agreement was found between mrTRG and pTRG when regression was classified according to standard five-tier systems (k = 0.386). When only two categories were considered for each regression system, (pTRG 0-3 vs pTRG 4; mrTRG 2-5 vs mrTRG 1) an accuracy of 78% (95% confidence interval [CI] 0.73-0.83) was found between radiologic and pathologic assessment with a k value of 0.185. The logistic regression model revealed that "T3 greater than 5 mm extent" was the only variable significantly impacting on disagreement (OR 0.33, 95% CI 0.15-0.68, P = .0034). Modest agreement exists between mrTRG and pTRG. The chances of appropriate assessment of the regression grade after neoadjuvant CRT appear to be higher in case of a T3 tumor with at least 5 mm extension in the mesorectal fat at the pretreatment MRI