Predicting rogue waves in random oceanic sea states

Using the inverse spectral theory of the nonlinear Schrodinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the JONSWAP spectrum with the proximity to homoclinic solutions of the NLS equation. We find in numerical simulations of the NLS equation that rogue waves develop for JONSWAP initial data that is ``near'' NLS homoclinic data, while rogue waves do not occur for JONSWAP data that is ``far'' from NLS homoclinic data. We show the nonlinear spectral decomposition provides a simple criterium for predicting the occurrence and strength of rogue waves (PACS: 92.10.Hm, 47.20.Ky, 47.35+i).Comment: 7 pages, 6 figures submitted to Physics of Fluids, October 25, 2004 Revised version submitted to Physics of Fluids, December 12, 200

Backward error analysis for multisymplectic discretizations of Hamiltonian PDEs

Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve associated local conservation laws and constraints very well in long time numerical simulations. Backward error analysis for PDEs, or the method of modified equations, is a useful technique for studying the qualitative behavior of a discretization and provides insight into the preservation properties of the scheme. In this paper we initiate a backward error analysis for PDE discretizations, in particular of multisymplectic box schemes for the nonlinear Schrodinger equation. We show that the associated modified differential equations are also multisymplectic and derive the modified conservation laws which are satisfied to higher order by the numerical solution. Higher order preservation of the modified local conservation laws is verified numerically.Comment: 12 pages, 6 figures, accepted Math. and Comp. Simul., May 200

Multi-Symplectic Integrators for Nonlinear Wave Equations

Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown to be robust, efficient and accurate in long-term calculations. In this thesis, we show how symplectic integrators have a natural generalization to Hamiltonian PDEs by introducing the concept of multi-symplectic partial differential equations (PDEs). In particular, we show that multi-symplectic PDEs have an underlying spatio-temporal multi-symplectic structure characterized by a multi-symplectic conservation law MSCL). Then multi-symplectic integrators (MSIs) are numerical schemes that preserve exactly the MSCL. Remarkably, we demonstrate that, although not designed to do so, MSIs preserve very well other associated local conservation laws and global invariants, such as the energy and the momentum, for very long periods of time. We develop two types of MSIs, based on finite differences and Fourier spectral approximations, and illustrate their superior performance over traditional integrators by deriving new numerical schemes to the well known 1D nonlinear Schrödinger and sine-Gordon equations and the 2D Gross-Pitaevskii equation. In sensitive regimes, the spectral MSIs are not only more accurate but are better at capturing the spatial features of the solutions. In particular, for the sine-Gordon equation we show that its phase space, as measured by the nonlinear spectrum associated with it, is better preserved by spectral MSIs than by spectral non-symplectic Runge-Kutta integrators. Finally, to further understand the improved performance of MSIs, we develop a backward error analysis of the multi-symplectic centered-cell discretization for the nonlinear Schrödinger equation. We verify that the numerical solution satisfies to higher order a nearby modified multi-symplectic PDE and its modified multi-symplectic energy conservation law. This implies, that although the numerical solution is an approximation, it retains the key feature of the original PDE, namely its multi-symplectic structure

Core-electron contributions to the molecular magnetic response

Orbital contributions to the magnetic response depend on the method used to compute them. Here, we show that dissecting nuclear magnetic shielding tensors using natural localized molecular orbitals (NLMOs) leads to anomalous core contributions. The arbitrariness of the assignment might significantly affect the interpretation of the magnetic response of nonplanar molecules such as C-60 or [14]helicene and the assessment of their aromatic character. We solve this problem by computing the core- and sigma-components of the induced magnetic field (and NICS) and the magnetically induced current density by removing the valence electrons (RVE). We estimate the core contributions to the magnetic response by performing calculations on the corresponding highly charged molecules, such as C6H630+ for benzene, using gauge-including atomic orbitals and canonical molecular orbitals (CMOs). The orbital contributions to nuclear magnetic shielding tensors are usually estimated by employing a natural chemical shielding (NCS) analysis in NLMO or CMO bases. The RVE approach shows that the core contribution to the magnetic response is small and localized at the nuclei, contrary to what NCS calculations suggest. This may lead to a completely incorrect interpretation of the magnetic sigma-orbital response of nonplanar structures, which may play a major role in the overall magnetic shielding of the system. The RVE approach is thus a simple and inexpensive way to determine the magnetic response of the core- and sigma-electrons.Peer reviewe

Cláusulas Restrictivas (covenants) en los contratos de bonos: evidencia empírica en Chile

Within financial literature aimed at analyzing agency issues, a particularly interesting aspect of it corresponds to the conflict that arises between stockholders and bondholders. There is a fair amount of literature that dissects the different manifestations or outcomes that such a conflict might generate, as well as the possible ways of solving these, one of which is the use of covenants in debt contracts. This paper presents a discussion in the main features of the stockholder-bondholder conflict, a description of the regulatory framework of bond issuance in Chile and a clinical assessment of the characteristics of the covenants used in Chile, from 1987 to 2000, specially emphasizing of certain specific clauses in the Chilean debt market. This paper shows that the covenants most widely used in the Chilean Market, are those related to the claim dilution problem (83% of the contracts restrict the either financial policy or the capital structure).Dentro de la literatura dedicada al análisis de los problemas de agencia, un aspecto de particular interés corresponde al conflicto que surge entre accionistas y tenedores de bonos (bonista). Existe una extensa literatura que analiza las distintas manifestaciones o efectos que puede generar este conflicto, y sus posibles formas de solución, una de las cuales es el uso de cláusulas restrictivas en los contratos de emisión de deuda (covenants). El trabajo presenta una discusión sobre las principales características del conflicto accionista-bonista, una descripción del marco legal que norma las emisiones de bonos en Chile y un análisis clínico de las características de las cláusulas contractuales de las emisiones de deuda en Chile en el período 1987-200, en la cual se enfatizan especialmente los determinantes del uso frecuente de ciertas cláusulas específicas en el mercado de deuda chileno. El análisis muestra que las cláusulas más usadas en el mercado chileno son aquellas destinadas a impedir la dilución de derechos (principalmente a través de restricciones a la política de financiamiento en un 83% de los casos)

Conservation Of Phase Space Properties Using Exponential Integrators On The Cubic Schrödinger Equation

The cubic nonlinear Schrödinger (NLS) equation with periodic boundary conditions is solvable using Inverse Spectral Theory. The nonlinear spectrum of the associated Lax pair reveals topological properties of the NLS phase space that are difficult to assess by other means. In this paper we use the invariance of the nonlinear spectrum to examine the long time behavior of exponential and multisymplectic integrators as compared with the most commonly used split step approach. The initial condition used is a perturbation of the unstable plane wave solution, which is difficult to numerically resolve. Our findings indicate that the exponential integrators from the viewpoint of efficiency and speed have an edge over split step, while a lower order multisymplectic is not as accurate and too slow to compete. © 2006 Elsevier Inc. All rights reserved

¿Cómo se experimentan el estrés y su afrontamiento antes y después de dos años de cuidar en casa a un paciente con esquizofrenia?

Durante los primeros dos años de atender en casa a un paciente psiquiátrico, los cuidadores primarios informales presentan un deterioro progresivo en su salud física y mental, pero poco se ha estudiado lo que sucede al respecto después de este tiempo. En este estudio se analizan las diferencias en los tipos de afrontamiento y los índices de sobrecarga percibida y síndrome de burnout entre dos grupos de cuidadores: uno con menos y otro con más de dos años de experiencia asistiendo en casa a un paciente diagnosticado con esquizofrenia. Se trató de un estudio cuantitativo, comparativo y transversal realizado con una muestra de 121 cuidadores primarios informales. El estudio fue aprobado por un Comité de Ética, los participantes firmaron un consentimiento informado y respondieron los cuestionarios en la sala de espera de un hospital psiquiátrico de la Ciudad de México. Los datos se analizaron con estadística inferencial utilizando el programa SPSS v26. En los resultados se encontró que los cuidadores con menos de dos años de experiencia tuvieron mayor sobrecarga percibida y síndrome de burnout, y utilizaban con mayor frecuencia el afrontamiento activo para enfrentarse al estrés derivado del cuidado. Se concluye que los primeros dos años a cargo del cuidado informal de un paciente con esquizofrenia constituyen un periodo crítico para la salud mental del cuidador. Quienes han superado este lapso de tiempo presentan menos repercusiones psicológicas asociadas al estrés

Excel In Mathematics: Applications Of Calculus

Nationally only 40% of the incoming freshmen STEM majors are successful in earning a STEM degree [1]. The University of Central Florida (UCF) EXCEL program is an NSF funded STEP (Science, Technology, Engineering and Mathematics Talent Expansion Program) whose goal is to increase the number of UCF STEM graduates. One of the activities that EXCEL has identified as essential in retaining students in science and engineering disciplines is the development and teaching of special courses at the freshman level, called Applications of Calculus I and Applications of Calculus II, or Apps I and Apps II, respectively. In Apps I and II, science and engineering professors are asked to lecture twice, as guest lectures, and to demonstrate to students where calculus topics appear in upper level science and engineering classes as well as where faculty use calculus in their research programs. This paper outlines the process used in producing the educational materials for Apps I and II courses (textbook, presentations slides, in-class homework assignments, demos) and it also discusses the assessment results pertaining to this specific EXCEL activity. © American Society for Engineering Education, 2010