Exponential asymptotics and Stokes lines in a partial differential equation

A singularly perturbed linear partial differential equation motivated by the geometrical model for crystal growth is considered. A steepest descent analysis of the Fourier transform solution identifies asymptotic contributions from saddle points, end points and poles, and the Stokes lines across which these may be switched on and off. These results are then derived directly from the equation by optimally truncating the naïve perturbation expansion and smoothing the Stokes discontinuities. The analysis reveals two new types of Stokes switching: a higher-order Stokes line which is a Stokes line in the approximation of the late terms of the asymptotic series, and which switches on or off Stokes lines themselves; and a second-generation Stokes line, in which a subdominant exponential switched on at a primary Stokes line is itself responsible for switching on another smaller exponential. The ‘new’ Stokes lines discussed by Berk et al. (Berk et al. 1982 J. Math. Phys.23, 988–1002) are second-generation Stokes lines, while the ‘vanishing’ Stokes lines discussed by Aoki et al. (Aoki et al. 1998 In Microlocal analysis and complex Fourier analysis (ed. K. F. T. Kawai), pp. 165–176) are switched off by a higher-order Stokes line

MULTI-BAND ELECTRICAL CONDUCTION

Scattering amplitudes arising from lattice vibrations are calculated for electrons in a transition metal, with special reference to nickel. The potential in the crystal is treated as a deformable potential, with corrections to adjust the zero of potential and to include effects of the redistribution of charge during lattice vibration.</p

The Arbitrary Trajectory Quantization Method

The arbitrary trajectory quantization method (ATQM) is a time dependent approach to quasiclassical quantization based on the approximate dual relationship that exists between the quantum energy spectra and classical periodic orbits. It has recently been shown however, that, for polygonal billiards, the periodicity criterion must be relaxed to include closed almost-periodic (CAP) orbit families in this relationship. In light of this result, we reinvestigate the ATQM and show that at finite energies, a smoothened quasiclassical kernel corresponds to the modified formula that includes CAP families while the delta function kernel corresponding to the periodic orbit formula is recovered at high energies. Several clarifications are also provided.Comment: revtex, ps figure

Mode structure and ray dynamics of a parabolic dome microcavity

We consider the wave and ray dynamics of the electromagnetic field in a parabolic dome microcavity. The structure of the fundamental s-wave involves a main lobe in which the electromagnetic field is confined around the focal point in an effective volume of the order of a cubic wavelength, while the modes with finite angular momentum have a structure that avoids the focal area and have correspondingly larger effective volume. The ray dynamics indicates that the fundamental s-wave is robust with respect to small geometrical deformations of the cavity, while the higher order modes are associated with ray chaos and short-lived. We discuss the incidence of these results on the modification of the spontaneous emission dynamics of an emitter placed in such a parabolic dome microcavity.Comment: 50 pages, 17 figure

On the boundary of the attainable set of the Dirichlet spectrum

Denoting by $\mathcal{E}\subseteq \R^2$ the set of the pairs $(\lambda_1(\Omega),\lambda_2(\Omega))$ for all the open sets $\Omega\subseteq\R^N$ with unit measure, and by $\Theta\subseteq\R^N$ the union of two disjoint balls of half measure, we give an elementary proof of the fact that \partial\E has horizontal tangent at its lowest point $(\lambda_1(\Theta),\lambda_2(\Theta))$.Comment: 7 pages, 3 figure

Pause Point Spectra in DNA Constant-Force Unzipping

Under constant applied force, the separation of double-stranded DNA into two single strands is known to proceed through a series of pauses and jumps. Given experimental traces of constant-force unzipping, we present a method whereby the locations of pause points can be extracted in the form of a pause point spectrum. A simple theoretical model of DNA constant-force unzipping is demonstrated to produce good agreement with the experimental pause point spectrum of lambda phage DNA. The locations of peaks in the experimental and theoretical pause point spectra are found to be nearly coincident below 6000 bp. The model only requires the sequence, temperature and a set of empirical base pair binding and stacking energy parameters, and the good agreement with experiment suggests that pause points are primarily determined by the DNA sequence. The model is also used to predict pause point spectra for the BacterioPhage PhiX174 genome. The algorithm for extracting the pause point spectrum might also be useful for studying related systems which exhibit pausing behavior such as molecular motors.Comment: 15 pages, 12 figure

Inpatient Transition to Virtual Care During COVID-19 Pandemic

Introduction: During the coronavirus disease 2019 (COVID-19) outbreak, novel approaches to diabetes care have been employed. Care in both the inpatient and outpatient setting has transformed considerably. Driven by the need to reduce the use of personal protective equipment and exposure for patients and providers alike, we transitioned inpatient diabetes management services to largely "virtual" or remotely provided care at our hospital. Methods: Implementation of a diabetes co-management service under the direction of the University of North Carolina division of endocrinology was initiated in July 2019. In response to the COVID-19 pandemic, the diabetes service was largely transitioned to a virtual care model in March 2020. Automatic consults for COVID-19 patients were implemented. Glycemic outcomes from before and after transition to virtual care were evaluated. Results: Data over a 15-week period suggest that using virtual care for diabetes management in the hospital is feasible and can provide similar outcomes to traditional face-to-face care. Conclusion: Automatic consults for COVID-19 patients ensure that patients with serious illness receive specialized diabetes care. Transitioning to virtual care models does not limit the glycemic outcomes of inpatient diabetes care and should be employed to reduce patient and provider exposure in the setting of COVID-19. These findings may have implications for reducing nosocomial infection in less challenging times and might address shortage of health care providers, especially in the remote areas

Targeting hepatic glucokinase to treat diabetes with TTP399, a hepatoselective glucokinase activator

The therapeutic success of interventions targeting glucokinase (GK) activation for the treatment of type 2 diabetes has been limited by hypoglycemia, steatohepatitis, and loss of efficacy over time. The clinical characteristics of patients with GK-activating mutations or GK regulatory protein (GKRP) loss-of-function mutations suggest that a hepatoselective GK activator (GKA) that does not activate GK in cells or affect the GK-GKRP interaction may reduce hyperglycemia in patients with type 2 diabetes while limiting hypoglycemia and liver-associated adverse effects. Here, we review the rationale for TTP399, an oral hepatoselective GKA, and its progression from preclinical to clinical development, with an emphasis on the results of a randomized, double-blind, placebo- and active-controlled phase 2 study of TTP399 in patients with type 2 diabetes. In this 6-month study, TTP399 (800 mg/day) was associated with a clinically significant and sustained reduction in glycated hemoglobin, with a placebo-subtracted least squares mean HbA 1c change from baseline of −0.9% (P < 0.01). Compared to placebo, TTP399 (800 mg/day) also increased high-density lipoprotein cholesterol (3.2 mg/dl; P < 0.05), decreased fasting plasma glucagon (−20 pg/ml; P < 0.05), and decreased weight in patients weighing ≥100 kg (−3.4 kg; P < 0.05). TTP399 did not cause hypoglycemia, had no detrimental effect on plasma lipids or liver enzymes, and did not increase blood pressure, highlighting the importance of tissue selectivity and preservation of physiological regulation when targeting key metabolic regulators such as GK

Pogodnosti i izazovi determinističkog referentnog modela radijskog kanala

The paper introduces a new paradigm for reference channel models. Current reference channel models are designed as platforms that generate radio channels for testing using random values for their parameters. These parameters follow some pre-established distribution based on process called parameterization, i.e. statistical processing of previous real measurements or accurate ray tracing simulations. The paper argues that random generated channels give either no new insight or even delusive information and should be replaced with the initial set of radio channels that was used for parameterization. Therefore a deterministic reference channel model, as an emulator of previously recorded real radio channels, is proposed and its potential elaborated.U radu se uvodi nova paradigma za referentni model radijskog kanala. Postojeći referentni modeli radijskog kanala dizajnirani su kao platforma koja generira radio kanale za testiranje pomoću slučajnih vrijednosti za svoje parametre. Ovi parametri prate neke unaprijed utvrđene raspodjele koje potječu iz procesa parametrizacije, odnosno statističke obrade prethodnih mjerenja ili točnih simulacija metodom slijeđenja zrake. U radu se tvrdi da slučajno generirani kanali ili ne daju nove uvide ili čak daju obmanjujuće informacije i valja ih zamijeniti s početnim skupom radijskih kanala koji je korišten za parametrizaciju. Stoga je predložen deterministički referentni model radijskog kanala, kao emulator prethodno snimljenih stvarnih radio kanala, te je njegov potencijal razrađen