Nonharmonic transverse vibration of the H-bonded molecules and the THz spectra in ice and water

A nonlinear equation of motion is found for the dimer comprising two charged H2O molecules. The THz dielectric response to nonharmonic vibration of a nonrigid dipole, forming the hydrogen bond (HB), is found in the direction transverse to this bond. An explicit expression is derived for the autocorrelator that governs the spectrum generated by transverse vibration (TV) of such a dipole. This expression is obtained by analytical solution of the truncated set of recurrence equations. The far infrared (FIR) spectra of ice at the temperature - 7 degrees C are calculated. The wideband, in the wavenumber (frequency) v range 0... 100.0 cm(-1), spectra are obtained for liquid water at room temperature and for supercooled water at -5.6 degrees C. All spectra are represented in terms of the complex permittivity epsilon(v) and the absorption coefficient alpha(v). The obtained analytical formula for epsilon comprises the term epsilon(perpendicular to) pertinent to the studied TV mechanism with three additional terms Delta epsilon(q), Delta epsilon(mu), and epsilon(or) arising, respectively, from: elastic harmonic vibration of charged molecules along the H-bond; elastic reorientation of HB permanent dipoles; and rather free libration of permanent dipoles in 'defects' of water/ice structure. The suggested TV-dielectric relaxation mechanism allows us: (a) to remove the THz 'deficit' of loss epsilon" inherent in previous theoretical studies; (b) to explain the THz loss and absorption spectra in supercooled (SC) water; and (c) to describe, in agreement with the experiment, the low- and high-frequency tails of the two bands of ice H2O located in the range 10...300 cm(-1). Specific THz dielectric properties of SC water are ascribed to association of water molecules, revealed in our study by transverse vibration of HB charged molecules. (C) 2006 Published by Elsevier B.V.

Coupled consolidation of a solid, infinite cylinder using a Terzaghi formulation

Axisymmetric consolidation is a classical boundary value problem for geotechnical engineers. Under some circumstances an analysis in which the changes in pore pressure, effective stress and displacement can be uncoupled from each other is sufficient, leading to a Terzaghi formulation of the axisymmetric consolidation equation in terms of the pore pressure. However, representation of the Mandel-Cryer effect usually requires more complex, coupled, Biot formulations. A new coupled formulation for the plane strain, axisymmetric consolidation problem is presented for small, linear elastic deformations. A single, easily evaluated parameter couples changes in pore pressure to changes in effective stress, and the resulting differential equation for pore pressure dissipation is very similar to Terzaghi’s classic formulation. The governing equations are then solved using finite differences and the consolidation of a solid infinite cylinder analysed, calculating the variation with time and with radius of the excess pore pressure and the radial displacement. Comparison with a previously published semi-analytical solution indicates that the formulation successfully embodies the Mandel-Cryer effect.

Analysis of Degradation Data of Poly(L-lactide-co-L,D-lactic actide) and Poly(L-lactide) Obtained at Elevated and Physiological Temperatures Using Mathematical Models

The degradation of resorbable polymeric devices often takes months to years. Accelerated testing at elevated temperatures is an attractive but controversial technique. The purposes of this paper include: (a) to provide a summary of the mathematical models required to analyse accelerated degradation data and to indicate the pitfalls of using these models; (b) to improve the model previously developed by Han and Pan; (c) to provide a simple version of the model of Han and Pan with an analytical solution that is convenient to use; (d) to demonstrate the application of the improved model in two different poly(lactic acid) systems. It is shown that the simple analytical relations between molecular weight and degradation time widely used in the literature can lead to inadequate conclusions. In more general situations the rate equations are only part of a complete degradation model. Together with previous works in the literature, our study calls for care in using the accelerated testing technique.

Enhancement Factor for Gas Absorption in a Finite Liquid Layer. Part 2: First- and Second-Order Reactions in a Liquid in Plug Flow

Gas absorption accompanied by an irreversible chemical reaction of first-order or second-order in a liquid layer of finite thickness in plug flow has been investigated. The analytical solution to the enhancement factor has been derived for the case of a first-order reaction, and the exact solution to the enhancement factor has been obtained via numerical simulation for the case of a second-order reaction. The enhancement factor in both cases is presented as a function of the Fourier number and tends to deviate from the prediction of the existing enhancement factor expressions based on the penetration theory at Fourier numbers above 0.1 due to the absence of a well-mixed bulk region in the liquid layer. Approximate enhancement factor expressions that describe the analytical and exact solutions with an accuracy of 5?% and 9?%, respectively, have been proposed.

Process of debonding in RC beams shear-strengthened with FRP U-strips or side strips

Reinforced concrete (RC) beams may be strengthened for shear using externally bonded fiber reinforced polymer (FRP) composites in the form of side bonding, U-jacketing or complete wrapping. The shear failure of almost all RC beams shear-strengthened with side bonded FRP and the majority of those strengthened with FRP U-jackets, is due to debonding of the FRP. The bond behavior between the externally-bonded FRP reinforcement (referred to as FRP strips for simplicity) and the concrete substrate therefore plays a crucial role in the failure process of these beams. Despite extensive research in the past decade, there is still a lack of understanding of how debonding of FRP strips in such a beam propagates and how the debonding process affects its shear behavior. This paper presents an analytical study on the progressive debonding of FRP strips in such strengthened beams. The complete debonding process is modeled and the contribution of the FRP strips to the shear capacity of the beam is quantified. The validity of the analytical solution is verified by comparing its predictions with numerical results from a finite element analysis. This analytical treatment represents a significant step forward in understanding how interaction between FRP strips, steel stirrups and concrete affects the shear resistance of RC beams shear-strengthened with FRP strips.

Mass-wasting episodes in the geological evolution of the Azores islands : timing, recurrence, mechanisms and consequence

Tese de doutoramento (co-tutela), Geologia (Geodinâmica Interna), Faculdade de Ciências da Universidade de Lisboa, Faculté des Sciences D’Orsay-Université Paris-Sud, 2014

Applications of Statistical Modeling in Iterative CT Image Reconstruction

Thesis (Master's)--University of Washington, 2015

Patient-specific anisotropic model of human trunk based on MR data

There are many ways to generate geometrical models for numerical simulation, and most of them start with a segmentation step to extract the boundaries of the regions of interest. This paper presents an algorithm to generate a patient-specific three-dimensional geometric model, based on a tetrahedral mesh, without an initial extraction of contours from the volumetric data. Using the information directly available in the data, such as gray levels, we built a metric to drive a mesh adaptation process. The metric is used to specify the size and orientation of the tetrahedral elements everywhere in the mesh. Our method, which produces anisotropic meshes, gives good results with synthetic and real MRI data. The resulting model quality has been evaluated qualitatively and quantitatively by comparing it with an analytical solution and with a segmentation made by an expert. Results show that our method gives, in 90% of the cases, as good or better meshes as a similar isotropic method, based on the accuracy of the volume reconstruction for a given mesh size. Moreover, a comparison of the Hausdorff distances between adapted meshes of both methods and ground-truth volumes shows that our method decreases reconstruction errors faster. Copyright © 2015 John Wiley & Sons, Ltd.

Spin-orbit effects in GaAs quantum wells: Interplay between Rashba, Dresselhaus, and Zeeman interactions

The interplay between Rashba, Dresselhaus, and Zeeman interactions in a quantum well submitted to an external magnetic field is studied by means of an accurate analytical solution of the Hamiltonian, including electron-electron interactions in a sum-rule approach. This solution allows us to discuss the influence of the spin-orbit coupling on some relevant quantities that have been measured in inelastic light scattering and electron-spin resonance experiments on quantum wells. In particular, we have evaluated the spin-orbit contribution to the spin splitting of the Landau levels and to the splitting of charge- and spin-density excitations. We also discuss how the spin-orbit effects change if the applied magnetic field is tilted with respect to the direction perpendicular to the quantum well.

Spin-orbit effects in GaAs quantum wells: Interplay between Rashba, Dresselhaus, and Zeeman interactions

The interplay between Rashba, Dresselhaus, and Zeeman interactions in a quantum well submitted to an external magnetic field is studied by means of an accurate analytical solution of the Hamiltonian, including electron-electron interactions in a sum-rule approach. This solution allows us to discuss the influence of the spin-orbit coupling on some relevant quantities that have been measured in inelastic light scattering and electron-spin resonance experiments on quantum wells. In particular, we have evaluated the spin-orbit contribution to the spin splitting of the Landau levels and to the splitting of charge- and spin-density excitations. We also discuss how the spin-orbit effects change if the applied magnetic field is tilted with respect to the direction perpendicular to the quantum well.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Life-cycle simulations of shallow frontal waves and the impact of deformation strain

The life-cycle of shallow frontal waves and the impact of deformation strain on their development is investigated using the idealised version of the Met Office non-hydrostatic Unified Model which includes the same physics and dynamics as the operational forecast model. Frontal wave development occurs in two stages; first, a deformation strain is applied to a front and a positive potential vorticity (PV) strip forms, generated by latent heat release in the frontal updraft; second, as the deformation strain is reduced the PV strip breaks up into individual anomalies. The circulations associated with the PV anomalies cause shallow frontal waves to form. The structure of the simulated frontal waves is consistent with the conceptual model of a frontal cyclone. Deeper frontal waves are simulated if the stability of the atmosphere is reduced. Deformation strain rates of different strengths are applied to the PV strip to determine whether a deformation strain threshold exists above which frontal wave development is suppressed. An objective method of frontal wave activity is defined and frontal wave development was found to be suppressed by deformation strain rates $\ge 0.4\times10^{-5}\mbox{s}^{-1}$. This value compares well with observed deformation strain rate thresholds and the analytical solution for the minimum deformation strain rate needed to suppress barotropic frontal wave development. The deformation strain rate threshold is dependent on the strength of the PV strip with strong PV strips able to overcome stronger deformation strain rates (leading to frontal wave development) than weaker PV strips.

A kinematically distorted flux rope model for magnetic clouds

Constant-α force-free magnetic flux rope models have proven to be a valuable first step toward understanding the global context of in situ observations of magnetic clouds. However, cylindrical symmetry is necessarily assumed when using such models, and it is apparent from both observations and modeling that magnetic clouds have highly noncircular cross sections. A number of approaches have been adopted to relax the circular cross section approximation: frequently, the cross-sectional shape is allowed to take an arbitrarily chosen shape (usually elliptical), increasing the number of free parameters that are fit between data and model. While a better “fit” may be achieved in terms of reducing the mean square error between the model and observed magnetic field time series, it is not always clear that this translates to a more accurate reconstruction of the global structure of the magnetic cloud. We develop a new, noncircular cross section flux rope model that is constrained by observations of CMEs/ICMEs and knowledge of the physical processes acting on the magnetic cloud: The magnetic cloud is assumed to initially take the form of a force-free flux rope in the low corona but to be subsequently deformed by a combination of axis-centered self-expansion and heliocentric radial expansion. The resulting analytical solution is validated by fitting to artificial time series produced by numerical MHD simulations of magnetic clouds and shown to accurately reproduce the global structure.

On the steadiness of separating meandering currents

The existence of inertial steady currents that separate from a coast and meander afterward is investigated. By integrating the zonal momentum equation over a suitable area, it is shown that retroflecting currents cannot be steady in a reduced gravity or in a barotropic model of the ocean. Even friction cannot negate this conclusion. Previous literature on this subject, notably the discrepancy between several articles by Nof and Pichevin on the unsteadiness of retroflecting currents and steady solutions presented in other papers, is critically discussed. For more general separating current systems, a local analysis of the zonal momentum balance shows that given a coastal current with a specific zonal momentum structure, an inertial, steady, separating current is unlikely, and the only analytical solution provided in the literature is shown to be inconsistent. In a basin-wide view of these separating current systems, a scaling analysis reveals that steady separation is impossible when the interior flow is nondissipative (e.g., linear Sverdrup-like). These findings point to the possibility that a large part of the variability in the world’s oceans is due to the separation process rather than to instability of a free jet.

Tephra fallout hazard assessment for a Plinian eruption scenario at Volcán de Colima (Mexico)

Volcanic ash fallout associated with renewal of explosive activity at Colima, represents a serious threat to the surrounding urbanized area. Here we assess the tephra fallout hazard associated with a Plinian eruption scenario. The eruptive history of Volcán de Colima shows that Plinian eruptions occur approximately every 100 years and the last eruption, the 1913, represents the largest historic eruption of this volcano. We used the last eruption as a reference to discuss volcanic hazard and risk scenarios connected with ash fallout. Tephra fallout deposits are modeled using HAZMAP, a model based on a semi-analytical solution of the advection– diffusion–sedimentation equation for volcanic particles. Based on a statistical study of wind profiles at Colima region, we first reconstructed ash loading maps and then computed ground load probability maps for different seasons. The obtained results show that a Plinian eruptive scenario at Volcán de Colima, could seriously damage more than 10 small towns and ranches, and potentially affect big cities located at tens of kilometers from the eruptive center. The probability maps obtained are aimed to give support to the risk mitigation strategies