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Explicit Formulation (explicit + formulation)
Selected AbstractsThe Ecology of Attachment in the FamilyFAMILY PROCESS, Issue 2 2003Jonathan Hill FRCPsych In this article we outline a conceptualization of attachment processes within the family. We argue that the key elements of attachment processes are affect regulation, interpersonal understanding, information processing, and the provision of comfort within intimate relationships. Although these have been described and assessed primarily in terms of individual functioning and development, they are equally applicable in family systems, provided three farther steps are taken. First, the description of attachment processes at the individual level is applied to the family using the concept of shared frames or representations of emotions, cognitions, and behaviors. Second, there is an explicit formulation of the way in which individual and family processes are linked. Third, there is a conceptualization of the nature and quality of the dynamic between attachment and other processes in family life. In this "ecology" of family processes, those that entail heightened affect and a need to create certainty through action, particularly in response to threats to safety, attachment needs, and discipline challenges, are contrasted with exploratory processes characterized by low affect, tolerance of uncertainty, and opportunities to review existing assumptions and knowledge. [source] Efficient explicit time stepping for the eXtended Finite Element Method (X-FEM)INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2006T. Menouillard Abstract This paper focuses on the introduction of a lumped mass matrix for enriched elements, which enables one to use a pure explicit formulation in X-FEM applications. A proof of stability for the 1D and 2D cases is given. We show that if one uses this technique, the critical time step does not tend to zero as the support of the discontinuity reaches the boundaries of the elements. We also show that the X-FEM element's critical time step is of the same order as that of the corresponding element without extended degrees of freedom. Copyright © 2006 John Wiley & Sons, Ltd. [source] Unified formulation of radiation conditions for the wave equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002Steen Krenk Abstract A family of radiation boundary conditions for the wave equation is derived by truncating a rational function approximation of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to different choices of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms of selected directions with ideal transmission is presented. A mechanical interpretation of the fictitious surface densities enables identification of suitable conditions at corners and boundaries of the radiating surface. Numerical examples illustrate excellent results with one or two fictitious layers with suitable corner and boundary conditions. Copyright © 2001 John Wiley & Sons, Ltd. [source] An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged bodyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007Christopher P. Kent Abstract An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave,body interaction problem into body and free-surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free-surface problem satisfies modified nonlinear free-surface boundary conditions. It is then shown that the nonlinear free-surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free-surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo-spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright © 2007 John Wiley & Sons, Ltd. [source] Assimilation of radar reflectivity into the LM COSMO model with a high horizontal resolutionMETEOROLOGICAL APPLICATIONS, Issue 4 2006Z. Sokol Abstract An assimilation of radar reflectivity into a numerical weather prediction (NWP) model with a horizontal resolution of 2.8 km is presented and applied to three severe convective events. The suggested assimilation method takes into account differences between the model and radar-derived precipitation in modifying vertical profiles of water vapour mixing ratio in each model time step by the nudging approach. Version 3.9 of the LM COSMO (Local Model COSMO) ,NWP model used in this study includes the explicit formulation of the cloud and rain processes involved. Two variants of the assimilation technique are designed and outputs of their implementation are compared. The first variant makes use of the ground data only, while the second utilises vertical profiles of precipitation water. Both variants provide an improvement of precipitation forecast in comparison with outputs of the control run without assimilation procedures applied. When the assimilated radar data indicate initial precipitation near an expected storm, the NWP model is capable of forecasting basic features of the storm development two to three hours ahead. Three case studies are presented. In one, the assimilation method that takes into account the vertical structure of the precipitation water yields better results than the others which utilise ground data only. However, for the remaining two case studies both types of the assimilation method produce comparable results. Copyright © 2006 John Wiley & Sons, Ltd. [source] | ||||||||||