A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Valuing a Natura 2000 network site to inform land use options using a discrete choice experiment: An illustration from the Basque Country

One of the main problems that public institutions face in the management of protected areas, such as the European Natura 2000 network, is determining how to design and implement sustainable management plans that account for the wide range of marketed and non-marketed benefits they provide to society. This paper presents an application of a stated preference valuation approach aimed at evaluating the social preferences of the population of the Basque Country, Spain, for the key attributes of a regional Natura 2000 network site. According to our results, individuals’ willingness-to-pay (WTP) is higher for attributes associated with non-use values (native tree species and biodiversity conservation) than for attributes associated with use values (agricultural development and commercial forestry). The paper concludes that management policies related to Natura 2000 network sites should account for both for the importance of non-use values and the heterogeneity of the population's preferences in order to minimize potential land use conflicts.

Dynamics of discrete bubble in nucleate pool boiling on thin wires in microgravity

A space experiment on bubble behavior and heat transfer in subcooled pool boiling phenomenon has been performed utilizing the temperature-controlled pool boiling (TCPB) device both in normal gravity in the laboratory and in microgravity aboard the 22(nd) Chinese recoverable satellite. The fluid is degassed R113 at 0.1 MPa and subcooled by 26 degrees C nominally. A thin platinum wire of 60 mu m in diameter and 30 mm in length is simultaneously used as heater and thermometer. Only the dynamics of the vapor bubbles, particularly the lateral motion and the departure of discrete vapor bubbles in nucleate pool boiling are reported and analyzed in the present paper. It's found that these distinct behaviors can be explained by the Marangoni convection in the liquid surrounding vapor bubbles. The origin of the Marangoni effect is also discussed.

ENEKuS – a key model for managing the transformation of the normalisation of the Basque language in the workplace

The aim of this study is to develop a reference model for intervention in the language processes applied to the transformation of language normalisation within organisations of a socio-economic nature. It is based on the case study of an experience carried out over10 years within a trades’ union confederation, and has pursued a strategy of a basically qualitative research carried out in three stages: 1) undertaking field work through application of action-research methodology, 2) reconstructing experiences following processes of systematisation and conceptualisation of the systematised data, applying methodologies for the Systematisation of Experiences and Grounded Theory, and 3) formulating a model for intervention, applying the Systems Approach methodology. Finally, we identified nine key ideas that make up the conceptual framework for the ENEKuS reference model, which is structured in nine ‘action points', each having an operating sub-model applicable in practice.

Laser Guiding in the Randomicity of Discrete Surface Strengthening by Arc Discharge

Several discharge areas by laser-guided discharge (LGD) were compared with those by common arc discharge. The randomicity of discharge areas by common arc discharge was controlled by laser guiding on two scales: large scale (the spacing of the discharge areas) and small scale (the inside of the discharge area). The position of the discharge area overlapped completely with a laser focus; therefore, the distribution and surface shape of the discharge areas were controlled. The stochastic movement of anode spot in the discharge area was controlled by laser guiding. As such, the repetitive melting and solidifying of microstructures in the discharge area was constrained. The tempered microstruc- tures in the discharge area were voided, the utilization efficiency of input energy was improved, and the strengthened depth of the discharge areas was increased. The regularity of cross-sectional shape of the discharge area was also improved. The hardness of microstructures in both discharge areas is greater than that of the base material. The highest level of hardness of microstructures in both discharge areas measures above 1000 HV. In summary, the hardness ofmicrostructures in the discharge area by LGD is larger and more discrete than that by common arc discharge.

Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

Various families of exact solutions to the Einstein and Einstein-Maxwell field equations of General Relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations.

The physical situations in which such equations arise include: a) the external gravitational field of an axisymmetric, uncharged steadily rotating body, b) cylindrical gravitational waves with two degrees of freedom, c) colliding plane gravitational waves, d) the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and e) colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein-Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa.

The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

Resource management of dynamic coastal environments using synoptic measures from remote sensing

In addition to providing vital ecological services, coastal areas of North Carolina provide prized areas for habitation, recreation, and commercial fisheries. However, from a management perspective, the coasts of North Carolina are highly variable and complex. In-water constituents such as nutrients, suspended sediments, and chlorophyll a concentration can vary significantly over a broad spectrum of time and space scales. Rapid growth and land-use change continue to exert pressure on coastal lands. Coastal environments are also very vulnerable to short-term (e.g., hurricanes) and long-term (e.g., sea-level rise) natural changes that can result in significant loss of life, economic loss, or changes in coastal ecosystem functioning. Hence, the dynamic nature, effects of human-induced change over time, and vulnerability of coastal areas make it difficult to effectively monitor and manage these important state and national resources using traditional data collection technologies such as discrete monitoring stations and field surveys. In general, these approaches provide only a sparse network of data over limited time and space scales and generally are expensive and labor-intensive. Products derived from spectral images obtained by remote sensing instruments provide a unique vantage point from which to examine the dynamic nature of coastal environments. A primary advantage of remote sensing is that the altitude of observation provides a large-scale synoptic view relative to traditional field measurements. Equally important, the use of remote sensing for a broad range of research and environmental applications is now common due to major advances in data availability, data transfer, and computer technologies. To facilitate the widespread use of remote sensing products in North Carolina, the UNC Coastal Studies Institute (UNC-CSI) is developing the capability to acquire, process, and analyze remotely sensed data from several remote sensing instruments. In particular, UNC-CSI is developing regional remote sensing algorithms to examine the mobilization, transport, transformation, and fate of materials between coupled terrestrial and coastal ocean systems. To illustrate this work, we present the basic principles of remote sensing of coastal waters in the context of deriving information that supports efficient and effective management of coastal resources. (PDF contains 4 pages)

Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.