Vladimir A. Galaktionov

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We study the asymptotic behaviour of classes of global and blow-up solutions of a semilinear parabolic equation of Cahn-Hilliard type u t = −∆(∆u + |u| p−1 u) in R N × R + , p > 1, with bounded integrable initial data. We show that in some {p, N }-parameter ranges it admits a countable set of blow-up similarity patterns. The most interesting set of blow-up(More)
We study the Cauchy problem in R × R + for one-dimensional 2mth-order, m > 1, semilinear parabolic PDEs of the form (Dx = ∂/∂x) ut = (−1) m+1 D 2m x u + |u| p−1 u, where p > 1, and ut = (−1) m+1 D 2m x u + e u with bounded initial data u 0 (x). Specifically, we are interested in those solutions that blow up at the origin in a finite time T. We show that, in(More)
Tone mapping operators are used to compress a large range of pixel luminances into a smaller range, which can be displayed on a monitor screen. In this paper, an effective and easy-to-use tone mapping operator based on the latest ideas developed in this field is presented. The parameter estimation process relies on the sampling method. Special attention is(More)
Increased demand for global illumination, image based-lighting and simplified workflow have pushed raytracing into mainstream. Many rendering and simulation algorithms that were considered strictly offline are becoming more interactive on massively parallel GPUs. Unfortunately, the amount of available memory on modern GPUs is relatively small. Scenes for(More)
Algorithms used to generate physically accurate images are usually based on the Monte Carlo methods for the forward and backward ray tracing. These methods are used to numerically solve the light energy transport equation (the rendering equation). Stochastic methods are used because the integration is performed in a high-dimensional space, and the(More)
We present a system for real-time realistic rendering of 3D scenes. Most of available on the market 3d visualization systems lack physical correctness of rendering, especially concerning complex materials and light sources. Our system is aimed to provide the physically correct visualization to the extent possible by modern graphics hardware. It supports(More)
We present an efficient algorithm for building an adaptive bounding volume hierarchy (BVH) in linear time on commodity graphics hardware using CUDA. BVHs are widely used as an acceleration data structure to quickly ray trace animated polygonal scenes. We accelerate the construction process with auxiliary grids that help us build high quality BVHs with SAH(More)
The use of high dynamic range images as a source of the natural daylight illumination and a background for virtual scenes containing objects with complex optic properties (fabrics, automobile multilayer paints, etc.) is considered. Physically justified algorithms for calculating the luminance of a point, recognition of the sun, generation of shadows, and(More)
This paper introduces an efficient and simple algorithm for constructing Multiple Reference (MR) octrees on a GPU in application to Photon Mapping and Irradiance Caching techniques. Although MR-octrees are hierarchical structures, we successfully ignore their hierarchical nature and present an approach with plain construction, compact data layout and(More)