ε\varepsilon-factorized differential equations for two-loop non-planar triangle Feynman integrals with elliptic curves

In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the methodology developed in the context of Banana integrals can also be extended to these cases and obtain $\varepsilon$-factorized differential equations for all sectors. The letters are combinations of modular forms on the corresponding elliptic curves and algebraic functions arising from the sub-sectors. With uniform transcendental boundary conditions, we express our results in terms of iterated integrals order-by-order in the dimensional regulator, which can be evaluated efficiently. Our method can be straightforwardly generalized to other elliptic integral families and have important applications to precision physics at current and future high-energy colliders.Comment: Journal version. Add the Lambert series for the Y-invarian

ε\varepsilon-forms for non-planar triangles with elliptic curves at two loops

In this talk, we discuss how to generalize ideas developed for Banana integrals to two two-loop non-planar triangle Feynman integrals involving elliptic curves, which have non-trivial sub-sectors and whose Picard-Fuchs operators share less symmetry than Banana integrals, to obtain the canonical differential equations and to solve them with suitable boundary conditions.Comment: RADCOR202

Fluctuation-driven dynamics in nanoscale thin-film flows : physical insights from numerical investigations

The effects of thermal fluctuations on nanoscale flows are captured by a numerical scheme that is underpinned by fluctuating hydrodynamics. A stochastic lubrication equation (SLE) is solved on non-uniform adaptive grids to study a series of nanoscale thin-film flows. The Fornberg scheme is used for high-resolution spatial discretisation and a fully-implicit time-marching scheme is designed for numerical stability. The accuracy of the numerical method is verified against theoretical results for thermal capillary waves during the linear stage of their development. The framework is then used to study the nonlinear behaviour of three bounded thin-film flows: (i) droplet spreading, where new power laws are derived; (ii) droplet coalescence, where molecular dynamics results are reproduced by the SLE at a fraction of the computational cost and it is discovered that thermal fluctuations decelerate the process, in contrast to previously investigated phenomena; and (iii) thin-film rupture, where, in the regime considered, disjoining pressure dominates the final stages of rupture

Tirofiban for Stroke without Large or Medium-Sized Vessel Occlusion

The effects of the glycoprotein IIb/IIIa receptor inhibitor tirofiban in patients with acute ischemic stroke but who have no evidence of complete occlusion of large or medium-sized vessels have not been extensively studied. In a multicenter trial in China, we enrolled patients with ischemic stroke without occlusion of large or medium-sized vessels and with a National Institutes of Health Stroke Scale score of 5 or more and at least one moderately to severely weak limb. Eligible patients had any of four clinical presentations: ineligible for thrombolysis or thrombectomy and within 24 hours after the patient was last known to be well; progression of stroke symptoms 24 to 96 hours after onset; early neurologic deterioration after thrombolysis; or thrombolysis with no improvement at 4 to 24 hours. Patients were assigned to receive intravenous tirofiban (plus oral placebo) or oral aspirin (100 mg per day, plus intravenous placebo) for 2 days; all patients then received oral aspirin until day 90. The primary efficacy end point was an excellent outcome, defined as a score of 0 or 1 on the modified Rankin scale (range, 0 [no symptoms] to 6 [death]) at 90 days. Secondary end points included functional independence at 90 days and a quality-of-life score. The primary safety end points were death and symptomatic intracranial hemorrhage. A total of 606 patients were assigned to the tirofiban group and 571 to the aspirin group. Most patients had small infarctions that were presumed to be atherosclerotic. The percentage of patients with a score of 0 or 1 on the modified Rankin scale at 90 days was 29.1% with tirofiban and 22.2% with aspirin (adjusted risk ratio, 1.26; 95% confidence interval, 1.04 to 1.53, P = 0.02). Results for secondary end points were generally not consistent with the results of the primary analysis. Mortality was similar in the two groups. The incidence of symptomatic intracranial hemorrhage was 1.0% in the tirofiban group and 0% in the aspirin group. In this trial involving heterogeneous groups of patients with stroke of recent onset or progression of stroke symptoms and nonoccluded large and medium-sized cerebral vessels, intravenous tirofiban was associated with a greater likelihood of an excellent outcome than low-dose aspirin. Incidences of intracranial hemorrhages were low but slightly higher with tirofiban

ε-factorized differential equations for two-loop non-planar triangle Feynman integrals with elliptic curves

Abstract In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the methodology developed in the context of Banana integrals can also be extended to these cases and obtain ε-factorized differential equations for all sectors. The letters are combinations of modular forms on the corresponding elliptic curves and algebraic functions arising from the sub-sectors. With uniform transcendental boundary conditions, we express our results in terms of iterated integrals order-by-order in the dimensional regulator, which can be evaluated efficiently. Our method can be straightforwardly generalized to other elliptic integral families and have important applications to precision physics at current and future high-energy colliders

Thermal capillary waves on bounded nanoscale thin films

The effect of confining walls on the fluctuation of a nanoscale thin film’s free surface is studied using the stochastic thin-film equations (STFE). Two canonical boundary conditions are employed to reveal the influence of the confinement: (i) an imposed contact angle and (ii) a pinned contact line. A linear stability analysis provides the wave eigenmodes, after which thermal-capillary-wave theory predicts the wave fluctuation amplitudes. Molecular dynamics (MD) simulations are performed to test the predictions and a Langevin diffusion model is proposed to capture oscillations of the contact-lines observed in MD. Good agreement between the theoretical predictions and the MD simulation results is recovered, and it is discovered that confinement can influence the entire film. Notably, a constraint on the length scale of wave modes is found to affect fluctuation amplitudes from our theoretical model, especially for 3D films. This opens up new challenges and future lines of inquiry