169,877 research outputs found
Special uniform approximations of continuous vector-valued functions. Part II: special approximations in CX(T)⊗CY(S)
No full textAbstractIn this paper, which is a continuation of Timofte (J. Approx. Theory 119 (2002) 291–299, we give special uniform approximations of functions from CX⊗Y(T×S) and C∞(T×S,X⊗Y) by elements of the tensor products CX(T)⊗CY(S), respectively C0(T,X)⊗C0(S,Y), for topological spaces T,S and Γ-locally convex spaces X,Y (all four being Hausdorff)
Homogenization results for a coupled system of reaction–diffusion equations
No full textThe macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction–diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying several metabolic processes taking place in living cells, in which biochemical species can diffuse in the cytosol and react both in the cytosol and also on the organellar membranes. The coupling of the concentrations of the biochemical species is realized via various properly scaled nonlinear reaction terms. These nonlinearities, which model, at the microscopic scale, various volume or surface reaction processes, give rise in the macroscopic model to different effects, such as the appearance of additional source or sink terms or of a non-standard diffusion matrix
Well-posedness for a modified bidomain model describing bioelectric activity in damaged heart tissues
No full textWe prove the existence and the uniqueness of a solution for a modified bidomain model, describing the electrical behaviour of the cardiac tissue in pathological situations. The main idea is to reduce the problem to an abstract parabolic setting, which requires to introduce several auxiliary differential systems and a non-standard bilinear form.
The main difficulties are due to the degeneracy of the bidomain system and to its non-standard coupling with the diffusion equation
Homogenization of a modified bidomain model involving imperfect transmission
No full textWe study, by means of the periodic unfolding technique, the homogenization of a modified bidomain model, which describes the propagation of the action potential in the cardiac electrophysiology. Such a model, allowing the presence of pathological zones in the heart, involves various geometries and non-standard transmission conditions on the interface between the healthy and the damaged part of the cardiac muscle
Interface potential in composites with general imperfect transmission conditions
No full textThe model analyzed in this paper has its origins in the description of composites made by a hosting medium containing a periodic array of inclusions coated by a thin layer consisting of sublayers of two different
materials.
This two-phase coating material is such that the external part has a
low diffusivity in the orthogonal direction, while the internal one has high diffusivity along the tangential direction.
In a previous paper [14], by means of a concentration procedure, the internal layer was replaced by an imperfect interface.
The present paper is concerned with the concentration of the external coating layer and the homogenization, via the periodic unfolding method, of the resulting model, which is far from being a standard one.
Despite the fact that the limit problem looks like a classical Dirichlet problem for an elliptic equation, in the construction of the homogenized matrix and of the source term, a very delicate analysis is required
Asymptotic analysis for non-local problems in composites with different imperfect contact conditions
No full textWe consider a composite material made up of a hosting medium containing an \eps-periodic array of perfect thermal conductors. Comparing with the previous contributions in the literature, in the present paper, the inclusions are completely disconnected and form two families with dissimilar physical behaviour. More specifically, the imperfect contact between the hosting medium and the inclusions
obeys two different laws, according to the two different types of inclusions.
The contact conditions involve the small parameter \eps and two positive constants \contuno,\contdue. We investigate the homogenization limit \eps\to 0 and the limits for \contuno,\contdue going to or , taken in any order, with the aim to find out the cases in which the two limits commute
A degenerate pseudo-parabolic equation with memory
No full textWe prove the existence and uniqueness for a degenerate pseudo-parabolic problem with memory. This kind of problem arises in the study of the homogenization of some differential systems involving the Laplace-Beltrami operator and describes the effective behaviour of the electrical conduction in some composite materials
Well-posedness of two pseudo-parabolic problems for electrical conduction in heterogeneous media
No full textWe prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the concentration limit of the other one, when the thickness of the dielectric inclusions goes to zero. The concentrated problem involves a transmission condition through
interfaces, which is mediated by a suitable Laplace-Beltrami type equation
Combining traffic sign detection with 3D tracking towards better driver assistance
No full textWe briefly review the advances in driver assistance systems and present a real-time version that integrates single view detection with region-based 3D tracking of traffic signs. The system has a typical pipeline: detection and recognition of traffic signs in independent frames, followed by tracking for temporal integration. The detection process finds an optimal set of candidates and is accelerated using AdaBoost cascades. A hierarchy of SVMs handles the recognition of traffic sign types. The 2D detections are then employed in simultaneous 2D segmentation and 3D pose tracking, using the known 3D model of the recognized traffic sign. Thus, we achieve not only 2D tracking of the recognized traffic signs, but we also obtain 3D pose information, which we use to establish the relevance of the traffic sign to the driver. The performance of the system is demonstrated by tracking multiple road signs in real-world scenarios.Radu Timofte, Victor Adrian Prisacariu, Luc Van Gool, and Ian Rei
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