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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:07:34 +0000Biomechanical reevaluation of orthodontic asymmetric headgear
https://resolver.caltech.edu/CaltechAUTHORS:20120813-110404306
Authors: {'items': [{'id': 'Chi-Lu', 'name': {'family': 'Chi', 'given': 'Lu'}}, {'id': 'Cheng-Mulin', 'name': {'family': 'Cheng', 'given': 'Mulin'}}, {'id': 'Hershey-H-G', 'name': {'family': 'Hershey', 'given': 'H. Garland'}}, {'id': 'Nguyen-Tung', 'name': {'family': 'Nguyen', 'given': 'Tung'}}, {'id': 'Ko-Ching-Chang', 'name': {'family': 'Ko', 'given': 'Ching-Chang'}}]}
Year: 2012
DOI: 10.2319/052911-357.1
Objective: To investigate the distribution of distal and lateral forces produced by orthodontic
asymmetric headgear (AHG) using mathematical models to assess periodontal ligament (PDL)
influence and to attempt to resolve apparent inconsistencies in the literature.
Materials and Methods: Mechanical models for AHG were constructed to calculate AHG force
magnitudes and direction using the theory of elasticity. The PDL was simulated by elastic springs
attached to the inner-bow terminals of the AHG. The total storage energy (Et) of the AHG and the
supporting springs was integrated to evaluate the distal and lateral forces produced by minimizing
Et (Castigliano's theorem). All analytical solutions were derived symbolically.
Results: The spring-supported headgear model (SSHG) predicted the magnitude and distribution
of distal forces consistent with our data and the published data of others. The SSHG model
revealed that the lateral forces delivered to the inner-bow terminals were not equal, and the spring
constant (stiffness of the PDL) affected the magnitude and direction of the resultant lateral forces.
Changing the stiffness of the PDL produced a greater biomechanical effect than did altering the
face-bow design. The PDL spring model appeared to help resolve inconsistencies in the literature
between laboratory in vitro experiments and clinical in vivo studies.
Conclusion: Force magnitude and direction of AHG were predicted precisely using the present
model and may be applied to improve the design of AHG to minimize unwanted lateral tooth
movement. (Angle Orthod. 2012;82:682–690.)https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7wrte-rds53Variational integrators for electric circuits
https://resolver.caltech.edu/CaltechAUTHORS:20130628-141442082
Authors: {'items': [{'id': 'Ober-Blöbaum-S', 'name': {'family': 'Ober-Blöbaum', 'given': 'Sina'}}, {'id': 'Tao-Molei', 'name': {'family': 'Tao', 'given': 'Molei'}}, {'id': 'Cheng-Mulin', 'name': {'family': 'Cheng', 'given': 'Mulin'}}, {'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'Houman'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}]}
Year: 2013
DOI: 10.1016/j.jcp.2013.02.006
In this contribution, we develop a variational integrator for the simulation of (stochastic and multiscale) electric circuits. When considering the dynamics of an electric circuit, one is faced with three special situations: 1. The system involves external (control) forcing through external (controlled) voltage sources and resistors. 2. The system is constrained via the Kirchhoff current (KCL) and voltage laws (KVL). 3. The Lagrangian is degenerate. Based on a geometric setting, an appropriate variational formulation is presented to model the circuit from which the equations of motion are derived. A time-discrete variational formulation provides an iteration scheme for the simulation of the electric circuit. Dependent on the discretization, the intrinsic degeneracy of the system can be canceled for the discrete variational scheme. In this way, a variational integrator is constructed that gains several advantages compared to standard integration tools for circuits; in particular, a comparison to BDF methods (which are usually the method of choice for the simulation of electric circuits) shows that even for simple LCR circuits, a better energy behavior and frequency spectrum preservation can be observed using the developed variational integrator.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5ckx6-5a228A dynamically bi-orthogonal method for time-dependent
stochastic partial differential equations II: Adaptivity and
generalizations
https://resolver.caltech.edu/CaltechAUTHORS:20130701-154101667
Authors: {'items': [{'id': 'Cheng-Mulin', 'name': {'family': 'Cheng', 'given': 'Mulin'}}, {'id': 'Hou-T-Y', 'name': {'family': 'Hou', 'given': 'Thomas Y.'}}, {'id': 'Zhang-Zhiwen', 'name': {'family': 'Zhang', 'given': 'Zhiwen'}, 'orcid': '0000-0002-3123-8885'}]}
Year: 2013
DOI: 10.1016/j.jcp.2013.02.020
This is part II of our paper in which we propose and develop a dynamically bi-orthogonal method (DyBO) to study a class of time-dependent stochastic partial differential equations (SPDEs) whose solutions enjoy a low-dimensional structure. In part I of our paper [9], we derived the DyBO formulation and proposed numerical algorithms based on this formulation. Some important theoretical results regarding consistency and bi-orthogonality preservation were also established in the first part along with a range of numerical examples to illustrate the effectiveness of the DyBO method. In this paper, we focus on the computational complexity analysis and develop an effective adaptivity strategy to add or remove modes dynamically. Our complexity analysis shows that the ratio of computational complexities between the DyBO method and a generalized polynomial chaos method (gPC) is roughly of order O((m/N_p)^3) for a quadratic nonlinear SPDE, where m is the number of mode pairs used in the DyBO method and N_p is the number of elements in the polynomial basis in gPC. The effective dimensions of the stochastic solutions have been found to be small in many applications, so we can expect m is much smaller than N_p and computational savings of our DyBO method against gPC are dramatic. The adaptive strategy plays an essential role for the DyBO method to be effective in solving some challenging problems. Another important contribution of this paper is the generalization of the DyBO formulation for a system of time-dependent SPDEs. Several numerical examples are provided to demonstrate the effectiveness of our method, including the Navier–Stokes equations and the Boussinesq approximation with Brownian forcing.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/map26-f4d51A dynamically bi-orthogonal method for time-dependent
stochastic partial differential equations I: Derivation and
algorithms
https://resolver.caltech.edu/CaltechAUTHORS:20130702-134527463
Authors: {'items': [{'id': 'Cheng-Mulin', 'name': {'family': 'Cheng', 'given': 'Mulin'}}, {'id': 'Hou-T-Y', 'name': {'family': 'Hou', 'given': 'Thomas Y.'}}, {'id': 'Zhang-Zhiwen', 'name': {'family': 'Zhang', 'given': 'Zhiwen'}, 'orcid': '0000-0002-3123-8885'}]}
Year: 2013
DOI: 10.1016/j.jcp.2013.02.033
We propose a dynamically bi-orthogonal method (DyBO) to solve time dependent stochastic partial differential equations (SPDEs). The objective of our method is to exploit some intrinsic sparse structure in the stochastic solution by constructing the sparsest representation of the stochastic solution via a bi-orthogonal basis. It is well-known that the Karhunen–Loeve expansion (KLE) minimizes the total mean squared error and gives the sparsest representation of stochastic solutions. However, the computation of the KL expansion could be quite expensive since we need to form a covariance matrix and solve a large-scale eigenvalue problem. The main contribution of this paper is that we derive an equivalent system that governs the evolution of the spatial and stochastic basis in the KL expansion. Unlike other reduced model methods, our method constructs the reduced basis on-the-fly without the need to form the covariance matrix or to compute its eigendecomposition. In the first part of our paper, we introduce the derivation of the dynamically bi-orthogonal formulation for SPDEs, discuss several theoretical issues, such as the dynamic bi-orthogonality preservation and some preliminary error analysis of the DyBO method. We also give some numerical implementation details of the DyBO methods, including the representation of stochastic basis and techniques to deal with eigenvalue crossing. In the second part of our paper [11], we will present an adaptive strategy to dynamically remove or add modes, perform a detailed complexity analysis, and discuss various generalizations of this approach. An extensive range of numerical experiments will be provided in both parts to demonstrate the effectiveness of the DyBO method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/extph-hre57