Solving seismic wave propagation in elastic media using the matrix exponential approach

Three numerical algorithms are proposed to solve the time-dependent elastodynamic equations in elastic solids. All algorithms are based on approximating the solution of the equations, which can be written as a matrix exponential. By approximating the matrix exponential with a product formula, an unconditionally stable algorithm is derived that conserves the total elastic energy density. By expanding the matrix exponential in Chebyshev polynomials for a specific time instance, a so-called ``one-step'' algorithm is constructed that is very accurate with respect to the time integration. By formulating the conventional velocity-stress finite-difference time-domain algorithm (VS-FDTD) in matrix exponential form, the staggered-in-time nature can be removed by a small modification, and higher order in time algorithms can be easily derived. For two different seismic events the accuracy of the algorithms is studied and compared with the result obtained by using the conventional VS-FDTD algorithm.Comment: 13 pages revtex, 6 figures, 2 table

Multimodal Interaction in a Haptic Environment

In this paper we investigate the introduction of haptics in a multimodal tutoring environment. In this environment a haptic device is used to control a virtual piece of sterile cotton and a virtual injection needle. Speech input and output is provided to interact with a virtual tutor, available as a talking head, and a virtual patient. We introduce the haptic tasks and how different agents in the multi-agent system are made responsible for them. Notes are provided about the way we introduce an affective model in the tutor agent

Morphological Image Analysis of Quantum Motion in Billiards

Morphological image analysis is applied to the time evolution of the probability distribution of a quantum particle moving in two and three-dimensional billiards. It is shown that the time-averaged Euler characteristic of the probability density provides a well defined quantity to distinguish between classically integrable and non-integrable billiards. In three dimensions the time-averaged mean breadth of the probability density may also be used for this purpose.Comment: Major revision. Changes include a more detailed discussion of the theory and results for 3 dimensions. Now: 10 pages, 9 figures (some are colored), 3 table

The Partial Averaging method

The partial averaging technique is defined and used in conjunction with the random series implementation of the Feynman-Kac formula. It enjoys certain properties such as good rates of convergence and convergence for potentials with coulombic singularities. In this work, I introduce the reader to the technique and I analyze the basic mathematical properties of the method. I show that the method is convergent for all Kato-class potentials that have finite Gaussian transform.Comment: 9 pages, no figures; one reference correcte

Beyond the poor man's implementation of unconditionally stable algorithms to solve the time-dependent Maxwell Equations

For the recently introduced algorithms to solve the time-dependent Maxwell equations (see Phys.Rev.E Vol.64 p.066705 (2001)), we construct a variable grid implementation and an improved spatial discretization implementation that preserve the property of the algorithms to be unconditionally stable by construction. We find that the performance and accuracy of the corresponding algorithms are significant and illustrate their practical relevance by simulating various physical model systems.Comment: 18 pages, 16 figure

Вимоги до оформлення статті

Myelination and voltage-gated ion channel clustering at the nodes of Ranvier are essential for the rapid saltatory conduction of action potentials. Whether myelination influences the structural organization of the axon initial segment (AIS) and action potential initiation is poorly understood. Using the cuprizone mouse model, we combined electrophysiological recordings with immunofluorescence of the voltage-gated Nav1.6 and Kv7.3 subunits and anchoring proteins to analyze the functional and structural properties of single demyelinated neocortical L5 axons. Whole-cell recordings demonstrated that neurons with demyelinated axons were intrinsically more excitable, characterized by increased spontaneous suprathreshold depolarizations as well as antidromically propagating action potentials ectopically generated in distal parts of the axon. Immunofluorescence examination of demyelinated axons showed that βIV-spectrin, Nav1.6, and the Kv7.3 channels in nodes of Ranvier either dissolved or extended into the paranodal domains. In contrast, while the AIS in demyelinated axons started more closely to the soma, ankyrin G, βIV-spectrin, and the ion channel expression were maintained. Structure-function analysis and computational modeling, constrained by the AIS location and realistic dendritic and axonal morphologies, confirmed that a more proximal onset of the AIS slightly reduced the efficacy of action potential generation, suggesting a compensatory role. These results suggest that oligodendroglial myelination is not only important for maximizing conduction velocity, but also for limiting hyperexcitability of pyramidal neurons

Loss of Saltation and Presynaptic Action Potential Failure in Demyelinated Axons

In cortical pyramidal neurons the presynaptic terminals controlling transmitter release are located along unmyelinated axon collaterals, far from the original action potential (AP) initiation site, the axon initial segment (AIS). Once initiated, APs will need to reliably propagate over long distances and regions of geometrical inhomogeneity like branch points (BPs) to rapidly depolarize the presynaptic terminals and confer temporally precise synaptic transmission. While axon pathologies such as demyelinating diseases are well established to impede the fidelity of AP propagation along internodes, to which extent myelin loss affects propagation along BPs and axon collaterals is not well understood. Here, using the cuprizone demyelination model, we performed optical voltage-sensitive dye (VSD) imaging from control and demyelinated layer 5 pyramidal neuron axons. In the main axon, we find that myelin loss switches the modality of AP propagation from rapid saltation towards a slow continuous wave. The duration of single AP waveforms at BPs or nodes was, however, only slightly briefer. In contrast, by using two-photon microscopy-guided loose-seal patch recordings from axon collaterals we revealed a presynaptic AP broadening in combination with a reduced velocity and frequency-dependent failure. Finally, internodal myelin loss was also associated with de novo sprouting of axon collaterals starting from the primary (demyelinated) axon. Thus, the loss of oligodendrocytes and myelin sheaths bears functional consequences beyond the main axon, impeding the temporal fidelity of presynaptic APs and affecting the functional and structural organization of synaptic connectivity within the neocortex