An integrated approach for evaluating coastal vulnerability in a changing climate

Coastal hazards such as flooding and erosion threaten many coastal communities and ecosystems. With documented increases in both storm frequency and intensity and projected acceleration of sea level rise, incorporating the impacts of climate change and variability into coastal vulnerability assessments is becoming a necessary, yet challenging task. We are developing an integrated approach to probabilistically incorporate the impacts of climate change into coastal vulnerability assessments via a multi-scale, multi-hazard methodology. By examining the combined hazards of episodic flooding/inundation and storm induced coastal change with chronic trends under a range of future climate change scenarios, a quantitative framework can be established to promote more sciencebased decision making in the coastal zone. Our focus here is on an initial application of our method in southern Oregon, United States. (PDF contains 5 pages)

Effect of an annular pupil filter on differential confocal microscopy

Combining differential confocal microscopy and an annular pupil filter, we obtained the normalized axial intensity distribution curve of an optical system. We used the sharp slopes of the axial response curve of the optical system to measure the surface profile of a reflection grating. Experimental results prove that this method can extend the axial dynamic range and improve the transverse resolution of three-dimensional profilometry by sacrificing axial resolution. (C) 2000 Optical Society of America.

Socio-economic vulnerability of African Americans in the Gulf coast counties

The states bordering the Gulf of Mexico i.e. Texas, Louisiana, Mississippi, Alabama, and Florida have been historically devastated by hurricanes and tropical storms. A large number of African Americans live in these southern Gulf States which have high percentages of minorities in terms of total population. According to the U.S. Census, the total black population in the United States is about 40.7 million and about one-fourth of them live in these five Gulf States (U.S. Census, 2008). As evidenced from Hurricane Katrina and other major hurricanes, lowincome and under-served communities are usually the hardest hit during these disasters. The aim of this study is to identify and visualize socio-economic vulnerability of the African American population at the county level living in the hurricane risk areas of these five Gulf States. (PDF contains 5 pages)

A new ground motion intensity measure, peak filtered acceleration (PFA), to estimate collapse vulnerability of buildings in earthquakes

In this thesis, we develop an efficient collapse prediction model, the PFA (Peak Filtered Acceleration) model, for buildings subjected to different types of ground motions.

For the structural system, the PFA model covers modern steel and reinforced concrete moment-resisting frame buildings (potentially reinforced concrete shear wall buildings). For ground motions, the PFA model covers ramp-pulse-like ground motions, long-period ground motions, and short-period ground motions.

To predict whether a building will collapse in response to a given ground motion, we first extract long-period components from the ground motion using a Butterworth low-pass filter with suggested order and cutoff frequency. The order depends on the type of ground motion, and the cutoff frequency depends on the building’s natural frequency and ductility. We then compare the filtered acceleration time history with the capacity of the building. The capacity of the building is a constant for 2-dimentional buildings and a limit domain for 3-dimentional buildings. If the filtered acceleration exceeds the building’s capacity, the building is predicted to collapse. Otherwise, it is expected to survive the ground motion.

The parameters used in PFA model, which include fundamental period, global ductility and lateral capacity, can be obtained either from numerical analysis or interpolation based on the reference building system proposed in this thesis.

The PFA collapse prediction model greatly reduces computational complexity while archiving good accuracy. It is verified by FEM simulations of 13 frame building models and 150 ground motion records.

Based on the developed collapse prediction model, we propose to use PFA (Peak Filtered Acceleration) as a new ground motion intensity measure for collapse prediction. We compare PFA with traditional intensity measures PGA, PGV, PGD, and Sa in collapse prediction and find that PFA has the best performance among all the intensity measures.

We also provide a close form in term of a vector intensity measure (PGV, PGD) of the PFA collapse prediction model for practical collapse risk assessment.

Multiscale model reduction methods for deterministic and stochastic partial differential equations

Partial differential equations (PDEs) with multiscale coefficients are very difficult to solve due to the wide range of scales in the solutions. In the thesis, we propose some efficient numerical methods for both deterministic and stochastic PDEs based on the model reduction technique.

For the deterministic PDEs, the main purpose of our method is to derive an effective equation for the multiscale problem. An essential ingredient is to decompose the harmonic coordinate into a smooth part and a highly oscillatory part of which the magnitude is small. Such a decomposition plays a key role in our construction of the effective equation. We show that the solution to the effective equation is smooth, and could be resolved on a regular coarse mesh grid. Furthermore, we provide error analysis and show that the solution to the effective equation plus a correction term is close to the original multiscale solution.

For the stochastic PDEs, we propose the model reduction based data-driven stochastic method and multilevel Monte Carlo method. In the multiquery, setting and on the assumption that the ratio of the smallest scale and largest scale is not too small, we propose the multiscale data-driven stochastic method. We construct a data-driven stochastic basis and solve the coupled deterministic PDEs to obtain the solutions. For the tougher problems, we propose the multiscale multilevel Monte Carlo method. We apply the multilevel scheme to the effective equations and assemble the stiffness matrices efficiently on each coarse mesh grid. In both methods, the $\KL$ expansion plays an important role in extracting the main parts of some stochastic quantities.

For both the deterministic and stochastic PDEs, numerical results are presented to demonstrate the accuracy and robustness of the methods. We also show the computational time cost reduction in the numerical examples.

Equivalent differential equations for nonlinear dynamical systems

A technique for obtaining approximate periodic solutions to nonlinear ordinary differential equations is investigated. The approach is based on defining an equivalent differential equation whose exact periodic solution is known. Emphasis is placed on the mathematical justification of the approach. The relationship between the differential equation error and the solution error is investigated, and, under certain conditions, bounds are obtained on the latter. The technique employed is to consider the equation governing the exact solution error as a two point boundary value problem. Among other things, the analysis indicates that if an exact periodic solution to the original system exists, it is always possible to bound the error by selecting an appropriate equivalent system.

Three equivalence criteria for minimizing the differential equation error are compared, namely, minimum mean square error, minimum mean absolute value error, and minimum maximum absolute value error. The problem is analyzed by way of example, and it is concluded that, on the average, the minimum mean square error is the most appropriate criterion to use.

A comparison is made between the use of linear and cubic auxiliary systems for obtaining approximate solutions. In the examples considered, the cubic system provides noticeable improvement over the linear system in describing periodic response.

A comparison of the present approach to some of the more classical techniques is included. It is shown that certain of the standard approaches where a solution form is assumed can yield erroneous qualitative results.

Stability of parametrically excited differential equations

Sufficient stability criteria for classes of parametrically excited differential equations are developed and applied to example problems of a dynamical nature.

Stability requirements are presented in terms of 1) the modulus of the amplitude of the parametric terms, 2) the modulus of the integral of the parametric terms and 3) the modulus of the derivative of the parametric terms.

The methods employed to show stability are Liapunov’s Direct Method and the Gronwall Lemma. The type of stability is generally referred to as asymptotic stability in the sense of Liapunov.

The results indicate that if the equation of the system with the parametric terms set equal to zero exhibits stability and possesses bounded operators, then the system will be stable under sufficiently small modulus of the parametric terms or sufficiently small modulus of the integral of the parametric terms (high frequency). On the other hand, if the equation of the system exhibits individual stability for all values that the parameter assumes in the time interval, then the actual system will be stable under sufficiently small modulus of the derivative of the parametric terms (slowly varying).

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .1. STATIC TRANSMISSION CASE

Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-medium interactive system. On the basis of the postulation, the behaviors of light transmitting through the medium with refractive index n are investigated, the investigation covering the realms of both geometrical optics and wave optics. The wave equation of light in static transmission is studied modally, the postulation being employed to derive the exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the relationships concerning the conservation of optical fluid and the dynamic properties are given, and some simple applications of the theories mentioned are presented.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .2. TIME-DEPENDENT TRANSMISSION THEORY

By generalization of the methods presented in Part I of the study [J. Opt. Soc. Am. A 12, 600 (1994)] to the four-dimensional (4D) Riemannian manifold case, the time-dependent behavior of light transmitting in a medium is investigated theoretically by the geodesic equation and curvature in a 4D manifold. In addition, the field equation is restudied, and the 4D conserved current of the optical fluid and its conservation equation are derived and applied to deduce the time-dependent general refractive index. On this basis the forces acting on the fluid are dynamically analyzed and the self-consistency analysis is given.

Centro de Acogida Inmediata –CAI- para víctimas de violencia de género: marco teórico

El presente documento hace parte del Proyecto Técnico “Centro de Acogida Inmediata –CAI- para víctimas de violencia de género”, elaborado para la Asociación BETA, Asociación para el Desarrollo de Proyectos de Intervención Social, presentado a la convocatoria del Departamento de Asuntos Sociales y de las Personas Mayores (Nº Expediente 2014//CONASP0148; CÓDIGO CPV: 85311000 Servicios de Asistencia Social con alojamiento).

Data Gathering Bias: Trait Vulnerability to Psychotic Symptoms?

Background Jumping to conclusions (JTC) is associated with psychotic disorder and psychotic symptoms. If JTC represents a trait, the rate should be (i) increased in people with elevated levels of psychosis proneness such as individuals diagnosed with borderline personality disorder (BPD), and (ii) show a degree of stability over time. Methods The JTC rate was examined in 3 groups: patients with first episode psychosis (FEP), BPD patients and controls, using the Beads Task. PANSS, SIS-R and CAPE scales were used to assess positive psychotic symptoms. Four WAIS III subtests were used to assess IQ. Results A total of 61 FEP, 26 BPD and 150 controls were evaluated. 29 FEP were revaluated after one year. 44% of FEP (OR = 8.4, 95% CI: 3.9-17.9) displayed a JTC reasoning bias versus 19% of BPD (OR = 2.5, 95% CI: 0.8-7.8) and 9% of controls. JTC was not associated with level of psychotic symptoms or specifically delusionality across the different groups. Differences between FEP and controls were independent of sex, educational level, cannabis use and IQ. After one year, 47.8% of FEP with JTC at baseline again displayed JTC. Conclusions JTC in part reflects trait vulnerability to develop disorders with expression of psychotic symptoms.

Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.