Rigorous envelope approximation for interface wave-packets in Maxwell’s equations in 2D localization

We study transverse magnetic (vector valued) wave-packets in the time dependent Kerr nonlinear Maxwell’s equations at the interface of two inhomogeneous dielectrics with an instantaneous material response. The resulting model is quasilinear. The problem is solved on each side of the interface and the fields are coupled via natural interface conditions. The wave-packet is localized at the interface and propagates in the tangential direction. For a slowly modulated envelope approximation the nonlinear Schrödinger equation is formally derived as an amplitude equation for the envelope. We rigorously justify the approximation in a Sobolev space norm on the corresponding asymptotically large time intervals. The well-posedness result for the quasilinear Maxwell problem builds on the local theory of [R. Schnaubelt und M. Spitz, Local wellposedness of quasilinear Maxwell equations with conservative interface conditions, Commun. Math. Sci., accepted, 2022] and extends this to asymptotically large time intervals for small data using an involved bootstrapping argument

A quasilinear transmission problem with application to Maxwell equations with a divergence-free D-field

Maxwell equations in the absence of free charges require initial data with a divergence-free displacement field D. In materials in which the dependence D=D(E) is nonlinear the quasilinear problem 07 c5D(E)=0 is hence to be solved. In many applications, e.g. in the modelling of wave packets, an approximative asymptotic ansatz of the electric field E is used, which satisfies this divergence condition at t=0 only up to a small residual. We search then for a small correction of the ansatz to enforce 07 c5D(E)=0 at t=0 and choose this correction in the form of a gradient field. In the usual case of a power type nonlinearity in D(E) this leads to the sum of the Laplace and p-Laplace operators. We also allow for the medium to consist of two different materials so that a transmission problem across an interface is produced. We prove the existence of the correction term for a general class of nonlinearities and provide regularity estimates for its derivatives, independent of the L2-norm of the original ansatz. In this way, when applied to the wave packet setting, the correction term is indeed asymptotically smaller than the original ansatz. We also provide numerical experiments to support our analysis

From Petri Dish to Main Dish: The Legal Pathway for Cell-Based Meat

Meat grown outside an animal is no longer simply science fiction, and the market is poised for introduction of a variety of so-called cell-based meat products. Commercializing these products will require a clear regulatory path forward. In this Article, we explore that legal pathway. We introduce the concepts of cellular agriculture and cell-based meat, including the science, the state and history of the industry, and the general regulatory background, in which the USDA and FDA are the major players. Further, we explore in particular regulatory aspects of food safety and labeling in the context of cell-based meat. Overall, we contend that there is a viable pathway forward for cultivated meat companies under the current regulatory scheme. But a nontrivial degree of uncertainty remains, and regulators would do well to be proactive in issuing guidance in this space. Moreover, cell-based meat remains vulnerable to legal challenges

Eosinophilia in patients infected with the human immunodeficiency virus

The prevalence and significance of peripheral blood eosinophilia in patients infected with the human immunodeficiency virus (HIV) were evaluated. Fifteen of 119 consecutive patients had absolute eosinophil counts of > 450/mm3. During a mean follow-up period of 419 days eosinophilia could be identified as secondary to a parasitic infection in only one patient. Correlation with disease stage showed a higher rate of advanced disease in patients with absolute eosinophilia. In a multivariate regression analysis, only low CD4+ cell counts, not the CDC disease stage or the use of antiretroviral therapy or primary prophylaxis, contributed significantly to the prevalence of eosinophilia. It is concluded that expen-sive laboratory investigations in asymptomatic patients with advanced-stage HIV disease are neither necessary nor cost effectiv

Associations Between Hearing Performance and Physiological Measures - An Overview and Outlook

The current paper summarises the research investigating associations between physiological data and hearing performance. An overview of state-of-the-art research and literature is given as well as promising directions for associations between physiological data and data regarding hearing loss and hearing performance. The physiological parameters included in this paper are: electrodermal activity, heart rate variability, blood pressure, blood oxygenation and respiratory rate. Furthermore, the environmental and behavioural measurements of physical activity and body mass index, alcohol consumption and smoking have been included. So far, only electrodermal activity and heart rate variability are physiological signals simultaneously associated with hearing loss or hearing performance. Initial findings suggest blood pressure and respiratory rate to be the most promising physiological measures that relate to hearing loss and hearing performance

Lattice instabilities of cubic NiTi from first principles

The phonon dispersion relation of NiTi in the simple cubic B2 structure is computed using first-principles density-functional perturbation theory with pseudopotentials and a plane-wave basis set. Lattice instabilities are observed to occur across nearly the entire Brillouin zone, excluding three interpenetrating tubes of stability along the (001) directions and small spheres of stability centered at R. The strongest instability is that of the doubly degenerate M5' mode. The atomic displacements of one of the eigenvectors of this mode generate a good approximation to the observed B19' ground-state structure.Comment: 11 pages, 3 figure

Quasi-normal frequencies: Key analytic results

The study of exact quasi-normal modes [QNMs], and their associated quasi-normal frequencies [QNFs], has had a long and convoluted history - replete with many rediscoveries of previously known results. In this article we shall collect and survey a number of known analytic results, and develop several new analytic results - specifically we shall provide several new QNF results and estimates, in a form amenable for comparison with the extant literature. Apart from their intrinsic interest, these exact and approximate results serve as a backdrop and a consistency check on ongoing efforts to find general model-independent estimates for QNFs, and general model-independent bounds on transmission probabilities. Our calculations also provide yet another physics application of the Lambert W function. These ideas have relevance to fields as diverse as black hole physics, (where they are related to the damped oscillations of astrophysical black holes, to greybody factors for the Hawking radiation, and to more speculative state-counting models for the Bekenstein entropy), to quantum field theory (where they are related to Casimir energies in unbounded systems), through to condensed matter physics, (where one may literally be interested in an electron tunelling through a physical barrier).Comment: V1: 29 pages; V2: Reformatted, 31 pages. Title changed to reflect major additions and revisions. Now describes exact QNFs for the double-delta potential in terms of the Lambert W function. V3: Minor edits for clarity. Four references added. No physics changes. Still 31 page

Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics