Search results for "Calculus"
showing 10 items of 617 documents
Multiscale Biomechanical Characterization of Ligaments and Tendons of the Human Knee
2020
Nonlinear vibrations of elastic beams with external general visco-elastic devices
2011
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus
2022
AbstractWe present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given a simplicial mesh, we first refine the mesh into smaller simplices which can be used to define higher order Whitney forms. Cochains on this refined mesh can then be interpolated using higher order Whitney forms. Hence, when the refined mesh is used with methods based on discrete exterior calculus, the solution can be expressed as a higher order Whitney form. We present algorithms for the three required steps: refining the mesh, solving the coefficients of the interpolant, and evaluating the interpolant at a given point. With our algorithms, the order of…
On a numerical solution of the Maxwell equations by discrete exterior calculus
2014
Applications of Microlocal Analysis in Inverse Problems
2020
This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, given in Helsinki and Shanghai in June 2019.
Generalized wave propagation problems and discrete exterior calculus
2018
We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulat…
On a stochastic SIR model
2007
We consider a stochastic SIR system and we prove the existence, uniqueness and positivity of solution. Moreover the existence of an invariant measure under a suitable condition on the coefficients is studied.
Understanding the microbial biogeography of ancient human dentitions to guide study design and interpretation
2021
AbstractThe oral cavity is a heterogeneous environment, varying in factors such as pH, oxygen levels, and salivary flow. These factors affect the microbial community composition and distribution of species in dental plaque, but it is not known how well these patterns are reflected in archaeological dental calculus. In most archaeological studies, a single sample of dental calculus is studied per individual and is assumed to represent the entire oral cavity. However, it is not known if this sampling strategy introduces biases into studies of the ancient oral microbiome. Here, we present the results of a shotgun metagenomic study of a dense sampling of dental calculus from four Chalcolithic i…
The Two-Jacobian Scheme for Systems of Conservation Laws
2006
Representation of Stationary Multivariate Gaussian Processes Fractional Differential Approach
2011
In this paper, the fractional spectral moments method (H-FSM) is used to generate stationary Gaussian multivariate processes with assigned power spectral density matrix. To this aim, firstly the N-variate process is expressed as sum of N fully coherent normal random vectors, and then, the representation in terms of HFSM is used.