Rogue waves in a two-component Manakov system with variable coefficients and an external potential

We construct rogue waves (RWs) in a coupled two-mode system with the self-focusing nonlinearity of the Manakov type (equal SPM and XPM coefficients), spatially modulated coefficients, and a specially designed external potential. The system may be realized in nonlinear optics and Bose-Einstein condensates. By means of a similarity transformation, we establish a connection between solutions of the coupled Manakov system with spatially-variable coefficients and the basic Manakov model with constant coefficients. Exact solutions in the form of two-component Peregrine and dromion waves are obtained. The RW dynamics is analyzed for different choices of parameters in the underlying parameter space. Different classes of RW solutions are categorized by means of a naturally introduced control parameter which takes integer values.Comment: 9 pages, 5 figure

Self-trapped bidirectional waveguides in a saturable photorefractive medium

We introduce a time-dependent model for the generation of joint solitary waveguides by counter-propagating light beams in a photorefractive crystal. Depending on initial conditions, beams form stable steady-state structures or display periodic and irregular temporal dynamics. The steady-state solutions are non-uniform in the direction of propagation and represent a general class of self-trapped waveguides, including counterpropagating spatial vector solitons as a particular case.Comment: 4 pages, 5 figure

Anatomy of the Akhmediev breather: Cascading instability, first formation time, and Fermi-Pasta-Ulam recurrence

By invoking Bogoliubov's spectrum, we show that for the nonlinear Schrodinger equation, the modulation instability (MI) of its n = 1 Fourier mode on a finite background automatically triggers a further cascading instability, forcing all the higher modes to grow exponentially in locked-step with the n = 1 mode. This fundamental insight, the enslavement of all higher modes to the n = 1 mode, explains the formation of a triangular-shaped spectrum which generates the Akhmediev breather, predicts its formation time analytically from the initial modulation amplitude, and shows that the Fermi-Pasta-Ulam (FPU) recurrence is just a matter of energy conservation with a period twice the breather's formation time. For higher order MI with more than one initial unstable modes, while most evolutions are expected to be chaotic, we show that it is possible to have isolated cases of "super-recurrence", where the FPU period is much longer than that of a single unstable mode.Comment: 23 pages, 12 figure

Effect of degree of lipomobilization on results of glucose test in dairy cows in heat stress

Cows exposed to heat stress exhibit a decreased ability to mobilize lipids due to increased sensitivity to insulin, which is expressed in a decreased concentration of NEFA. However, certain cows can preserve the level of lipid mobilization after adapting to heat stress. We assumed that cows that have a preserved ability to mobilize lipids are less sensitive to insulin and that they have a lower tolerance for glucose. The aim of this work was to compare the results of an intravenous glucose tolerance test in cows that exhibited, in prolonged heat stress, a decreased (NEFA<0.20 mmol/l) or preserved (NEFA>0.30 mmol/l) ability for lipid mobilization. Glucose concentration and NEFA concentration were measured following intravenous application of glucose. The mean glycaemic index value did not differ statistically significantly between the two groups of cows at 10, 15 and 20 minutes after glucose application (p>0.05), but there was a tendency at 10 and 15 minutes for the glycaemia to be higher in cows with preserved lipomobilization (p<0.1). At 30, 60 and 90 minutes after glucose application, glycaemia was statistically significantly higher (p<0.01; p<0.05 and p<0.05) in the group of cows with preserved lipomobilization. The glycaemic index values (mmol/l) shown in the same order (30, 60 and 90 minutes) were as follows 9.91±0.21: 9.23±0.41; 5.41±0.5: 4.67±0.33 and 4.31±0.39: 3.47±0.37. The mean value for NEFA concentration in samples originating from the two experimental groups of cows did not differ statistically significantly following glucose application. The NEFA concentration showed a tendency to be higher in cows with preserved lipid mobilization in comparison with cows with decreased lipomobilization at 20 and 30 minutes after glucose application (p<0.1). Following the intravenous glucose tolerance test, NEFA and glucose concentrations were in a significant negative correlation, and that correlation was more expressed in cows with decreased lipomobilization. Cows with preserved lipomobilization have a lower tolerance for glucose than cows with a decreased lipomobilization during heat stress. [Projekat Ministarstva nauke Republike Srbije, br. TR 31062

Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator

In this and subsequent paper arXiv:1011.5185 we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte Carlo simulations for path integrals, or to set up various analytic approximation techniques to study properties of quantum systems in time-dependent potentials. The analytically derived results are numerically verified by treating several simple models.Comment: 29 pages, 5 figure

Extra Dimensions: A View from the Top

In models with compact extra dimensions, where the Standard Model fields are confined to a 3+1 dimensional hyperplane, the $t \bar t$ production cross-section at a hadron collider can receive significant contributions from multiple exchange of KK modes of the graviton. These are carefully computed in the well-known ADD and RS scenarios, taking the energy dependence of the sum over graviton propagators into account. Using data from Run-I of the Tevatron, 95% C.L. bounds on the parameter space of both models are derived. For Run-II of the Tevatron and LHC, discovery limits are estimated.Comment: Typos corrected, references added. 12 pages, LaTeX, 2 ps figure

Correction: automated assessment of redox potentials for dyes in dye-sensitized photoelectrochemical cells

Correction for 'Automated assessment of redox potentials for dyes in dye-sensitized photoelectrochemical cells' by Jelena Belić et al., Phys. Chem. Chem. Phys., 2022, 24, 197-210, https://doi.org/10.1039/D1CP04218A.NWO733.000.007Solid state NMR/Biophysical Organic Chemistr