On variational and symplectic time integrators for Hamiltonian systems

Various systems in nature have a Hamiltonian structure and therefore accurate time integrators for those systems are of great practical use. In this paper, a fi nite element method will be explored to derive symplectic time stepping schemes for (non-)autonomous systems in a systematic way. The technique used is a variational discontinuous Galerkin nite element method in time. This approach provides a uni ed framework to derive known and new symplectic time integrators. An extended analysis for the new time integrators will be provided. The analysis shows that a novel third order time integrator presented in this paper has excellent dispersion properties. These new time stepping schemes are necessary to get accurate and stable simulations of (forced) water waves and other non-autonomous variational systems, which we illustrate in our numerical results

Variational water-wave model with accurate dispersion and vertical vorticity

A new water-wave model has been derived which is based on variational techniques and combines a depth-averaged vertical (component of) vorticity with depth-dependent potential flow. The model facilitates the further restriction of the vertical profile of the velocity potential to n-th order polynomials or a finite-element profile with a small number of elements (say), leading to a framework for efficient modeling of the interaction of steepening and breaking waves near the shore with a large-scale horizontal flow. The equations are derived from a constrained variational formulation which leads to conservation laws for energy, mass, momentum and vertical vorticity. It is shown that the potential-flow water-wave equations and the shallow-water equations are recovered in the relevant limits. Approximate shock relations are provided, which can be used in numerical schemes to model breaking waves

Hybrid Rossby-shelf modes in a laboratory ocean

Idealized laboratory experiments reveal the existence of forced–dissipative hybrid Rossby-shelf modes. The laboratory ocean consists of a deeper ocean (accommodating basin-scale Rossby modes) and a coastal step shelf (accommodating trapped shelf modes). Planetary Rossby modes are mimicked in the laboratory via a uniform topographic slope in the north–south direction. Hybrid modes are found as linear modes in numerical calculations, and similar streamfunction patterns exist in streak photography of the rotating tank experiments. These numerical calculations are based on depth-averaged potential vorticity dynamics with Ekman forcing and damping. Preliminary nonlinear calculations explore the deficiencies observed between reality and the linear solutions. The aim of the work is twofold: to show that idealized hybrid Rossby-shelf modes exist in laboratory experiments and to contribute in a general sense to the discussion on the coupling and energy exchange associated with hybrid modes between shallow coastal seas and deep-ocean basins

In vitro and in vivo evaluation of cephalosporins for the treatment of Lyme disease

Venkata Raveendra Pothineni,1,* Mansi B Parekh,1,* Mustafeez Mujtaba Babar,1 Aditya Ambati,2 Peter Maguire,1 Mohammed Inayathullah,1 Kwang-Min Kim,1 Lobat Tayebi,3 Hari-Hara SK Potula,1 Jayakumar Rajadas1,4 1Biomaterials and Advanced Drug Delivery, Stanford Cardiovascular Pharmacology Division, Cardiovascular Institute, School of Medicine, Stanford University, Palo Alto, CA, USA; 2Center for Sleep Sciences and Medicine, Department of Psychiatry and Behavioral Sciences, School of Medicine, Stanford University, Palo Alto, CA, USA; 3Department of Developmental Sciences, Marquette University School of Dentistry, Milwaukee, WI, USA; 4Department of Bioengineering and Therapeutic Sciences, Schools of Pharmacy and Medicine, University of California San Francisco, San Francisco, CA, USA *These authors contributed equally to this work Background: Lyme disease accounts for >90% of all vector-borne disease cases in the United States and affects ~300,000 persons annually in North America. Though traditional tetracycline antibiotic therapy is generally prescribed for Lyme disease, still 10%–20% of patients treated with current antibiotic therapy still show lingering symptoms.Methods: In order to identify new drugs, we have evaluated four cephalosporins as a therapeutic alternative to commonly used antibiotics for the treatment of Lyme disease by using microdilution techniques like minimum inhibitory concentration (MIC) and the minimum bactericidal concentration (MBC). We have determined the MIC and MBC of four drugs for three Borrelia burgdorferi s.s strains namely CA8, JLB31 and NP40. The binding studies were performed using in silico analysis.Results: The MIC order of the four drugs tested is cefoxitin (1.25 µM/mL) > cefamandole (2.5 µM/mL), > cefuroxime (5 µM/mL) > cefapirin (10 µM/mL). Among the drugs that are tested in this study using in vivo C3H/HeN mouse model, cefoxitin effectively kills B. burgdorferi. The in silico analysis revealed that all four cephalosporins studied binds effectively to B. burgdorferi proteins, SecA subunit penicillin-binding protein (PBP) and Outer surface protein E (OspE).Conclusion: Based on the data obtained, cefoxitin has shown high efficacy killing B. burgdorferi at concentration of 1.25 µM/mL. In addition to it, cefoxitin cleared B. burgdorferi infection in C3H/HeN mice model at 20 mg/kg. Keywords: Lyme disease, Borrelia burgdorferi, antimicrobials, penicillin-binding protein