scholarly journals Generalized wave propagation problems and discrete exterior calculus

2018 ◽  
Vol 52 (3) ◽  
pp. 1195-1218
Author(s):  
Jukka Räbinä ◽  
Lauri Kettunen ◽  
Sanna Mönkölä ◽  
Tuomo Rossi
Keyword(s):  
Wave Propagation ◽  
Harmonic Wave ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Time Stepping ◽  
Discrete Exterior Calculus ◽  
Exterior Calculus ◽  
Finite Dimensional ◽  
Order Of Magnitude ◽  
Wave Problems

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 cumulative pollution error can be practically eliminated in the case of harmonic wave problems. The restrictions following from the CFL condition can be bypassed with a local time-stepping scheme. The computational savings are at least one order of magnitude.

Constitutive relations in classical optics in terms of geometric algebra

2015 ◽  
Vol 55 (2) ◽  
Author(s):  
Adolfas Dargys
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Wave ◽  
Vector Space ◽  
Closed System ◽  
Geometric Algebra ◽  
Electromagnetic Wave Propagation ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Basis Vectors

To have a closed system, the Maxwell electromagnetic equations should be supplemented by constitutive relations which describe medium properties and connect primary fields (E, B) with secondary ones (D, H). J.W. Gibbs and O. Heaviside introduced the basis vectors {i, j, k} to represent the fields and constitutive relations in the three-dimensional vectorial space. In this paper the constitutive relations are presented in a form of Cl3,0 algebra which describes the vector space by three basis vectors {σ1, σ2, σ3} that satisfy Pauli commutation relations. It is shown that the classification of electromagnetic wave propagation phenomena with the help of constitutive relations in this case comes from the structure of Cl3,0 itself. Concrete expressions for classical constitutive relations are presented including electromagnetic wave propagation in a moving dielectric.

Plane harmonic wave propagation in three-dimensional composite media

1999 ◽  
Vol 33 (4) ◽  
pp. 263-282 ◽  
Author(s):  
Todd W. McDevitt ◽  
Gregory M. Hulbert ◽  
Noboru Kikuchi
Keyword(s):  
Wave Propagation ◽  
Harmonic Wave ◽  
Three Dimensional ◽  
Composite Media ◽  
Plane Harmonic Wave

Nonlinear Hyperbolic Waves in Hyperelastic Solids

1993 ◽  
Vol 46 (12) ◽  
pp. 527-539
Author(s):  
J. B. Haddow
Keyword(s):  
Wave Propagation ◽  
Thermal Effects ◽  
Constitutive Relations ◽  
Spatial Dimension ◽  
Similarity Solutions ◽  
Nonlinear Wave Propagation ◽  
Longitudinal Wave Propagation ◽  
Hyperbolic Waves ◽  
Wave Problems ◽  
Rubberlike Materials

This paper considers hyperbolic, one spatial dimension nonlinear wave propagation in a hyperelastic solid, and a discussion of the basic theory is presented. Constitutive relations for compressible rubberlike materials, whose internal energies can be expressed as the sum of a function of specific volume only and a function of temperature only, are discussed. These relations are assumed for the analysis of a class of plane wave problems and similarity solutions are obtained. Thermal effects, including the effect of the jump in entropy across a shock for a problem of uncoupled longitudinal wave propagation, are taken into account, however heat conduction is neglected. Solutions for a piezotropic model, which is a model for which mechanical and thermal effects are uncoupled, are obtained for comparison purposes. An axisymmetric problem is also discussed.

Detection, Averaging, and 3D Reconstruction of Biological Specimens on Hypercubes (Transputer-based) Computers

1990 ◽  
Vol 48 (1) ◽  
pp. 454-455
Author(s):  
Jose-Maria Carazo ◽  
I. Benavides ◽  
S. Marco ◽  
J.L. Carrascosa ◽  
E.L. Zapata
Keyword(s):  
3D Reconstruction ◽  
3D Structure ◽  
Three Dimensional ◽  
Software Tools ◽  
Mapping Method ◽  
Computer Architectures ◽  
Parallel Computer ◽  
Reconstruction Process ◽  
Computing Power ◽  
Order Of Magnitude

Obtaining the three-dimensional (3D) structure of negatively stained biological specimens at a resolution of, typically, 2 - 4 nm is becoming a relatively common practice in an increasing number of laboratories. A combination of new conceptual approaches, new software tools, and faster computers have made this situation possible. However, all these 3D reconstruction processes are quite computer intensive, and the middle term future is full of suggestions entailing an even greater need of computing power. Up to now all published 3D reconstructions in this field have been performed on conventional (sequential) computers, but it is a fact that new parallel computer architectures represent the potential of order-of-magnitude increases in computing power and should, therefore, be considered for their possible application in the most computing intensive tasks.We have studied both shared-memory-based computer architectures, like the BBN Butterfly, and local-memory-based architectures, mainly hypercubes implemented on transputers, where we have used the algorithmic mapping method proposed by Zapata el at. In this work we have developed the basic software tools needed to obtain a 3D reconstruction from non-crystalline specimens (“single particles”) using the so-called Random Conical Tilt Series Method. We start from a pair of images presenting the same field, first tilted (by ≃55°) and then untilted. It is then assumed that we can supply the system with the image of the particle we are looking for (ideally, a 2D average from a previous study) and with a matrix describing the geometrical relationships between the tilted and untilted fields (this step is now accomplished by interactively marking a few pairs of corresponding features in the two fields). From here on the 3D reconstruction process may be run automatically.

Scanning-tunneling spectroscopy on conjugated polymer films

2003 ◽  
Vol 771 ◽  
Author(s):  
M. Kemerink ◽  
S.F. Alvarado ◽  
P.M. Koenraad ◽  
R.A.J. Janssen ◽  
H.W.M. Salemink ◽  
...  
Keyword(s):  
Polymer Films ◽  
Conjugated Polymer ◽  
Three Dimensional ◽  
Field Enhancement ◽  
Direct Consequence ◽  
Scanning Tunneling Spectroscopy ◽  
Tunneling Spectroscopy ◽  
Band Alignment ◽  
Scanning Tunneling ◽  
Order Of Magnitude

AbstractScanning-tunneling spectroscopy experiments have been performed on conjugated polymer films and have been compared to a three-dimensional numerical model for charge injection and transport. It is found that field enhancement near the tip apex leads to significant changes in the injected current, which can amount to more than an order of magnitude, and can even change the polarity of the dominant charge carrier. As a direct consequence, the single-particle band gap and band alignment of the organic material can be directly obtained from tip height-voltage (z-V) curves, provided that the tip has a sufficiently sharp apex.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

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