GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS

Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

Exact series solutions of reactive transport models with general initial conditions

Exact solutions of partial differential equation models describing the transport and decay of single and coupled multispecies problems can provide insight into the fate and transport of solutes in saturated aquifers. Most previous analytical solutions are based on integral transform techniques, meaning that the initial condition is restricted in the sense that the choice of initial condition has an important impact on whether or not the inverse transform can be calculated exactly. In this work we describe and implement a technique that produces exact solutions for single and multispecies reactive transport problems with more general, smooth initial conditions. We achieve this by using a different method to invert a Laplace transform which produces a power series solution. To demonstrate the utility of this technique, we apply it to two example problems with initial conditions that cannot be solved exactly using traditional transform techniques.

A quantitative analysis of the phytoplankton of the Gulf of Panama III. General ecological conditions and the phytoplankton dynamics at 8°45'N, 79°23'W from November 1954 to May 1957

Bi-weekly phytoplankton samples were collected at 0, 10, and 20 m and enumerated by the Utermöhl sedimentation technique; 14C productivity measurements at 10 m, oblique zooplankton tows, and routine hydrographic observations were also made. Northerly winds induce upwelling during December-April, followed by a rainy season; a slight resurgence in upwelling may occur during July and/or August. Annual variations in upwelling intensity and rainfall occur. During upwelling, the upper 50 m, about 30 per cent of the total volume of the Gulf of Panama, is replaced with water 5 to 10 C colder than the more stratified, turbid and nutrient impoverished watermass present during the rainy season. The mean annual runoff accompanying an average annual precipitation of 2731 mm is estimated to equal a layer of fresh water 3.2 m thick. About 10 per cent of the phytoplankton phosphate and inorganic nitrogen requirements during the rainy season are accreted. (PDF contains 260 pages.)

Order conditions of stochastic Runge-Kutta methods by B-series

In this paper, general order conditions and a global convergence proof are given for stochastic Runge Kutta methods applied to stochastic ordinary differential equations ( SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied to deterministic ordinary differential equations (ODEs) to the stochastic case and allows a completely general formalism for constructing high order stochastic methods, either explicit or implicit. Some numerical results will be given to illustrate this theory.

General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time

This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.

[Gerodontology consultation in geriatric facilities: general health status (I)]

Dental undertreatment is often seen in the older population. This is particularly true for the elderly living in nursing homes and geriatric hospitals. The progression of chronic diseases results in loss of their independence. They rely on daily support and care due to physical or mental impairment. The visit of a dentist in private praxis becomes difficult or impossible and is a logistic problem. These elderly patients are often not aware of oral and dental problems or these are not addressed. The geriatric hospital Bern, Ziegler, has integrated dental care in the concept of physical rehabilitation of geriatric patients. A total of 139 patients received dental treatment in the years 2005/2006. Their mean age was 83 years, but the segment with > 85 years of age amounted to 46%. The general health examinations reveald multiple and complex disorders. The ASA classification (American Society of Anesthesiologists, Physical Status Classification System) was applied and resulted in 15% = P2 (mild systemic disease, no functional limitation), 47% = P3 (severe systemic disease, definite functional limitations) and 38% = P4 (severe systemic disease, constant threat to life). Eighty-seven of the patients exhibited 3 or more chronic diseases with a prevalence of cardiovascular diseases, musculoskelettal disorders and dementia. Overall the differences between men and women were small, but broncho-pulmonary dieseases were significantly more frequent in women, while men were more often diagnosed with dementia and depression. Verbal communication was limited or not possible with 60% of the patients due to cognitive impairment or aphasia after a stroke. Although the objective treatment need is high, providing dentistry for frail and geriatric patients is characterized by risks due to poor general health conditions, difficulties in communication, limitations in feasibility and lack of adequate aftercare. In order to prevent the problem of undertreatment, elderly independently living people should undergo dental treatment regularly and in time. Training of nurses and doctors of geriatric hospitals in oral hygiene should improve the awareness. A multidisciplinary assessment of geriatric patients should include the oral and dental aspect if they enter the hospital.

Preventing the selection of “deaf embryos” under the Human Fertilisation and Embryology Act 2008 : problematizing disability?

Section 14(4) of the Human Fertilisation and Embryology Act 2008 imposes – within the general licensing conditions listed in the Human Fertilisation and Embryology Act 1990 – a prohibition to prevent the selection and implantation of embryos for the purpose of creating a child who will be born with a “serious disability.” This article offers a perspective that demonstrates the problematic nature of the consultation, review, and legislative reform process surrounding s 14(4). The term “serious disability” is not defined within the legislation, but we highlight the fact that s 14(4) was passed with the case of selecting deaf children in mind. We consider some of the literature on the topic of disability and deafness, which, we think, casts some doubt on the view that deafness is a “serious disability.” The main position we advance is that the lack of serious engagement with alternative viewpoints during the legislative process was unsatisfactory. We argue that the contested nature of deafness necessitates a more robust consultation process and a clearer explanation and defence of the normative position that underpins s 14(4).

An anticipative reactive control strategy to deal with unforeseen obstacles during a multi-sensor-based navigation task

We address the problem of the rangefinder-based avoidance of unforeseen static obstacles during a visual navigation task. We extend previous strategies which are efficient in most cases but remain still hampered by some drawbacks (e.g., risks of collisions or of local minima in some particular cases, etc.). The key idea is to complete the control strategy by adding a controller providing the robot some anticipative skills to guarantee non collision and by defining more general transition conditions to deal with local minima. Simulation results show the proposed strategy efficiency.

The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena

Two mixed boundary value problems associated with two-dimensional Laplace equation, arising in the study of scattering of surface waves in deep water (or interface waves in two superposed fluids) in the linearised set up, by discontinuities in the surface (or interface) boundary conditions, are handled for solution by the aid of the Weiner-Hopf technique applied to a slightly more general differential equation to be solved under general boundary conditions and passing on to the limit in a manner so as to finally give rise to the solutions of the original problems. The first problem involves one discontinuity while the second problem involves two discontinuities. The reflection coefficient is obtained in closed form for the first problem and approximately for the second. The behaviour of the reflection coefficient for both the problems involving deep water against the incident wave number is depicted in a number of figures. It is observed that while the reflection coefficient for the first problem steadily increases with the wave number, that for the second problem exhibits oscillatory behaviour and vanishes at some discrete values of the wave number. Thus, there exist incident wave numbers for which total transmission takes place for the second problem. (C) 1999 Elsevier Science B.V. All rights reserved.

Two-dimensional moist stratified turbulence and the emergence of vertically sheared horizontal flows

Moist stratified turbulence is studied in a two-dimensional Boussinesq system influenced by condensation and evaporation. The problem is set in a periodic domain and employs simple evaporation and condensation schemes, wherein both the processes push parcels towards saturation. Numerical simulations demonstrate the emergence of a moist turbulent state consisting of ordered structures with a clear power-law type spectral scaling from initially spatially uncorrelated conditions. An asymptotic analysis in the limit of rapid condensation and strong stratification shows that, for initial conditions with enough water substance to saturate the domain, the equations support a straightforward state of moist balance characterized by a hydrostatic, saturated, vertically sheared horizontal flow (VSHF). For such initial conditions, by means of long time numerical simulations, the emergence of moist balance is verified. Specifically, starting from uncorrelated data, subsequent to the development of a moist turbulent state, the system experiences a rather abrupt transition to a regime which is close to saturation and dominated by a strong VSHF. On the other hand, initial conditions which do not have enough water substance to saturate the domain, do not attain moist balance. Rather, the system is observed to remain in a turbulent state and oscillates about moist balance. Even though balance is not achieved with these general initial conditions, the time scale of oscillation about moist balance is much larger than the imposed time scale of condensation and evaporation, thus indicating a distinct dominant slow component in the moist stratified two-dimensional turbulent system. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3694805]

Error exponent analysis of energy-based Bayesian decentralized spectrum sensing under fading

This paper considers decentralized spectrum sensing, i.e., detection of occupancy of the primary users' spectrum by a set of Cognitive Radio (CR) nodes, under a Bayesian set-up. The nodes use energy detection to make their individual decisions, which are combined at a Fusion Center (FC) using the K-out-of-N fusion rule. The channel from the primary transmitter to the CR nodes is assumed to undergo fading, while that from the nodes to the FC is assumed to be error-free. In this scenario, a novel concept termed as the Error Exponent with a Confidence Level (EECL) is introduced to evaluate and compare the performance of different detection schemes. Expressions for the EECL under general fading conditions are derived. As a special case, it is shown that the conventional error exponent both at individual sensors, and at the FC is zero. Further, closed-form lower bounds on the EECL are derived under Rayleigh fading and lognormal shadowing. As an example application, it answers the question of whether to use pilot-signal based narrowband sensing, where the signal undergoes Rayleigh fading, or to sense over the entire bandwidth of a wideband signal, where the signal undergoes lognormal shadowing. Theoretical results are validated using Monte Carlo simulations. (C) 2015 Elsevier B.V. All rights reserved.

An optimal theory for an expansion of flow quantities to capture the flow structures

An optimal theory on how database analysis to capture the flow structures has been developed in this paper, which include the POD method as its special case. By means of the remainder minimization method in the Sobolev space, for more general optimal conditions the new theory has the potential to overcome an inherent limitation of the POD method, i.e., it cannot be used to the situations in which the optimal condition is other than the inner product global one. As an example, using the new theory, the database of a two-dimensional flow over a backward-facing step is analyzed in detail, with velocity and vorticity bases.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.