1,721,056 research outputs found
Controllability for the Burgers model
No full textIn this paper we study vibrations of viscoelastic materials, whose behaviour can be represented by mechanical models given as combinations of springs and dashpots, and establish reachability results.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/)
A Semilinear Integro-Differential Equation: Global Existence and Hidden Regularity
No full textHere we show a hidden regularity result for nonlinear wave equations with an integral term of convolution type and Dirichlet boundary conditions. Under general assumptions on the nonlinear term and on the integral kernel we are able to state results about global existence of strong and mild solutions without any further smallness on the initial data. Then we define the trace of the normal derivative of the solution showing a regularity result. In such a way we extend to integrodifferential equations with nonlinear term well-known results available in the literature for linear wave equations with memory
Numerical approximations for energy preserving microfacet models
No full textMicrofacet models suffer from a significant limitation: they are not energy preserving, resulting in an unexpected darkening of rough specular surfaces. Energy compensation methods face this limitation by adding to the BSDF a secondary component accounting for multiple scattering contributions. While these methods are fast, robust and can be added to a renderer with relatively minor modifications, they involve the computation of the directional albedo. This quantity is expressed as an integral that does not have a closed-form solution, but it needs to be precomputed and stored in tables. These look-up tables are notoriously cumbersome to use, in particular on GPUs. This work obviates the need of look-up tables by fitting an analytic approximation of the directional albedo, which is a more practical solution. We enforce energy preservation by rescaling the specular albedo, thus maintaining the same lobe shape. We propose a 2D rational polynomial of degree three to fit conductors and a 3D rational polynomial of degree three to fit dielectrics and materials composed of a specular layer on top of a diffuse one, such as plastics. As an alternative, multi-layer perceptrons can be used, ensuring a more accurate approximation for dielectrics at the expense of a larger number of parameters to store. We validated our results via the furnace test, highlighting that materials rendered using our analytic approximations almost exactly match the behavior of the ones rendered with the use of look-up tables, resulting in an energy-preserving model even at maximum roughness. The software we use to fit coefficients is open-source and can be used to fit other BSDF models as well
Trace regularity for biharmonic evolution equations with Caputo derivatives
No full textOur goal is to establish a hidden regularity result for solutions of time fractional Petrovsky systems. The order α of the Caputo fractional derivative belongs to the interval (1, 2). We achieve such result for a suitable class of weak solutions
Fractional diffusion-wave equations: hidden regularity for weak solutions
No full textWe prove a "hidden"regularity result for weak solutions of time fractional diffusion-wave equations where the Caputo fractional derivative is of order α ε (1, 2). To establish such result we analyse the regularity properties of the weak solutions in suitable interpolation spaces
Weak solutions for time-fractional evolution equations in hilbert spaces
No full textOur purpose is to introduce a notion of weak solution for a class of abstract fractional differential equations. We point out that the time fractional derivative occurring in the equations is in the sense of the Caputo derivative. We prove existence results for weak and strong solutions. To justify the abstract theory we develop, we apply two examples of concrete equations: time-fractional wave equations and time-fractional Petrovsky systems. Both these concrete examples are of great interest in the theory of fractional partial differential equations
Foundation of the time-fractional beam equation
No full textWe derive the model for fractional beam equations by making use of a modified constitutive assumption, that is the relationship between stress and strain depending on the creep compliance given by a fractional power-type function
pOp: Parameter Optimization of Differentiable Vector Patterns
No full textProcedural materials are extensively used in computer graphics, since they provide editable, resolution-independent representation of textures. However, tuning the parameters of procedural generators to achieve a desired result remains time-consuming for users. Recently, inverse procedural material algorithms have been developed, exploiting differentiable rendering methods to find the parameters of a procedural model that match a target image. These approaches focus on raster textures. We propose pOp, a practical method for estimating the parameters of vector patterns, that are formed by collections of vector shapes arranged by an arbitrary procedural program. In our approach, patterns are defined as arbitrary programs, that control the translation, rotation and scale or vector graphics elements. We support elements typical of vector graphics, namely points, lines, circle, rounded rectangles, and quadratic Bèzier drawings, in multiple colors. We optimize the program parameters by automatically differentiating the signed distance field of the drawing, which we found to be significantly more reliable than using differentiable rendering of the final image. We demonstrate our method on a variety of cases, representing the variations found in structured vector patterns
Uniqueness of solution with zero boundary condition for time-fractional wave equations
No full textWe consider a solution u to an initial boundary value problem in a bounded domain ohm over a time interval (0, T) for a time-fractional wave equation where the order of time derivative is between 1 and 2. We prove that if u|omega x(0,T ) = 0 for arbitrarily chosen subdomain omega subset of ohm, then u = 0 in ohm x (0, T).(c) 2023 Elsevier Ltd. All rights reserved
NodeGit: Diffing and Merging Node Graphs
No full textThe use of version control is pervasive in collaborative software projects. Version control systems are based on two primary operations: diffing two versions to compute the change between them and merging two versions edited concurrently. Recent works provide solutions to diff and merge graphics assets such as images, meshes and scenes. In this work, we present a practical algorithm to diff and merge procedural programs written as node graphs. To obtain more precise diffs, we version the graphs directly rather than their textual representations. Diffing graphs is equivalent to computing the graph edit distance, which is known to be computationally infeasible. Following prior work, we propose an approximate algorithm tailored to our problem domain. We validate the proposed algorithm by applying it both to manual edits and to a large set of randomized modifications of procedural shapes and materials. We compared our method with existing state-of-the-art algorithms, showing that our approach is the only one that reliably detects user edits
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