17,626 research outputs found
Port-Hamiltonian systems: an introductory survey
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian systems is based on the canonical symplectic structure of the phase space or on a Poisson structure that is obtained by (symmetry) reduction of the phase space, in the case of a port-Hamiltonian system the geometric structure derives from the interconnection of its sub-systems. This motivates to consider Dirac structures instead of Poisson structures, since this notion enables one to define Hamiltonian systems with algebraic constraints. As a result, any power-conserving interconnection of port-Hamiltonian systems again defines a port-Hamiltonian system. The port-Hamiltonian description offers a systematic framework for analysis, control and simulation of complex physical systems, for lumped-parameter as well as for distributed-parameter models
Packing Characteristics of Different Shaped Proppants for use with Hydrofracing - A Numerical Investigation using 3D FEMDEM
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The role of different sliding resistances in limit analysis of hemispherical masonry domes
A limit analysis method for masonry domes composed of interlocking blocks with non-isotropic sliding resistance is under development. This paper reports the first two steps of that work. It first introduces a revision to an existing limit analysis approach using the membrane theory with finite hoop stresses to find the minimum thickness of a hemispherical dome under its own weight and composed of conventional blocks with finite isotropic friction. The coordinates of an initial axisymmetric membrane surface are the optimization variables. During the optimization, the membrane satisfies the equilibrium conditions and meets the sliding constraints where intersects the block interfaces. The results of the revised procedure are compared to those obtained by other approaches finding the thinnest dome. A heuristic method using convex contact model is then introduced to find the sliding resistance of the corrugated interlocking interfaces. Sliding of such interfaces is constrained by the Coulomb’s friction law and by the shear resistance of the locks keeping the blocks together along two orthogonal directions. The role of these two different sliding resistances is discussed and the heuristic method is applied to the revised limit analysis method
Emergent singular solutions of non-local density-magnetization equations in one dimension
We investigate the emergence of singular solutions in a non-local model for a
magnetic system. We study a modified Gilbert-type equation for the
magnetization vector and find that the evolution depends strongly on the length
scales of the non-local effects. We pass to a coupled density-magnetization
model and perform a linear stability analysis, noting the effect of the length
scales of non-locality on the system's stability properties. We carry out
numerical simulations of the coupled system and find that singular solutions
emerge from smooth initial data. The singular solutions represent a collection
of interacting particles (clumpons). By restricting ourselves to the
two-clumpon case, we are reduced to a two-dimensional dynamical system that is
readily analyzed, and thus we classify the different clumpon interactions
possible.Comment: 19 pages, 13 figures. Submitted to Phys. Rev.
Weakly Enforced Boundary Conditions for the NURBS-Based Finite Cell Method
In this paper, we present a variationally consistent formulation for the weak enforcement
of essential boundary conditions as an extension to the finite cell method, a fictitious
domain method of higher order. The absence of boundary fitted elements in fictitious domain or
immersed boundary methods significantly restricts a strong enforcement of essential boundary
conditions to models where the boundary of the solution domain coincides with the embedding
analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to
overcome this limitation but often suffer from various drawbacks with severe consequences for
a stable and accurate solution of the governing system of equations. In this contribution, we
follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace
problem taking weak boundary conditions into account. An extension to problems from linear
elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an
adequate convergence behavior. NURBS are chosen as a high-order approximation basis to
benefit from their smoothness and flexibility in the process of uniform model refinement
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